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This study introduces a hybrid decision-making framework to evaluate and prioritize energy retrofit strategies in airport infrastructure, addressing the dual goals of sustainability and operational feasibility. The proposed model integrates the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) for generating Pareto-optimal solutions, K-Means clustering for classifying strategies, and the Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP) for prioritizing alternatives under uncertainty. The framework was applied to a representative mid-sized international airport scenario, constrained by a maximum budget of $1 million, implementation timelines of up to 18 months, and an operational disruption threshold of 3 on a 5-point scale. Nine distinct retrofit strategies were identified, with costs ranging from $850,000 to $1,000,000 and energy savings between 20% (250,000 kWh) and 30% (360,000 kWh) annually. Carbon reductions ranged from 15% (approximately 102 metric tons per year) to 30% (around 144 metric tons per year), while implementation times varied from 6.16 to 11.92 months. Disruption levels ranged from minimal (1.23) to moderate (5.00). Among these, Solution 9 achieved the highest overall priority score (0.708), offering 30% energy and carbon savings at a cost of $1,000,000, with an 11.03-month timeline and moderate disruption level (4.09). Cluster analysis grouped solutions into three profiles: low-cost (average cost $859,375, energy savings 20.63%), balanced (average cost $906,250, energy savings 23.75%), and high-impact (average cost $973,750, energy savings up to 30%). Sensitivity analysis further confirmed the robustness of the prioritization, with only minor score fluctuations under adjusted scenarios. These findings provide concrete, actionable guidance for airport decision-makers to support strategic energy retrofit investments aligned with ICAO’s CORSIA framework and UN Sustainable Development Goals, enabling tangible progress toward net-zero operations.
Introduction
As global air traffic rebounds in the post-pandemic era, the aviation sector faces intensifying pressure to decarbonize its operations and infrastructure in alignment with climate targets. The International Civil Aviation Organization (ICAO) formally adopted a long-term global aspirational goal of achieving net-zero carbon emissions from international aviation by 2050, supported by initiatives such as the Carbon Offsetting and Reduction Scheme for International Aviation (CORSIA), which now involves 129 participating states1. In parallel, the International Air Transport Association (IATA) has updated its Net Zero Roadmaps, calling for coordinated action across aircraft innovation, sustainable aviation fuels (SAFs), operational efficiencies, and, critically, airport infrastructure2.
Within this context, airports are undergoing a strategic shift toward energy modernization through retrofit projects that reduce emissions and optimize efficiency. High-impact initiatives such as Louisville Muhammad Ali International Airport’s geothermal HVAC system — reducing emissions by over 80%3—and London Gatwick’s staged upgrades to HVAC, lighting, and energy monitoring4— reflect the growing adoption of sustainable technologies in terminal systems. Forecasts suggest that the electrification of ground operations, heating systems, and vehicle fleets will cause power demand at major airports to increase fivefold by 2050, underscoring the urgency of strategic energy planning in airport environments5.
Simultaneously, emerging technologies such as hydrogen fuel and AI-enhanced energy systems are redefining the future of sustainable aviation infrastructure. Studies on hydrogen storage, refueling, and integration into airport systems highlight the safety, feasibility, and potential of this zero-emission energy source6. Meanwhile, artificial intelligence is increasingly applied to optimize energy management systems, enabling real-time decision-making, predictive maintenance, and fault detection across energy networks7. The convergence of AI with smart grid infrastructure and battery storage also provides scalable solutions for managing dynamic loads in airports and industrial hubs8.
However, despite significant technological advances in energy optimization and smart infrastructure integration, there remains a critical research gap in the domain of sustainable airport energy planning. Existing models often focus narrowly on either optimizing retrofit strategies, classifying solutions, or prioritizing alternatives — yet very few offer a unified framework that integrates all three components in a decision-relevant, expert-informed structure. Optimization techniques such as NSGA-II are powerful for generating Pareto-optimal solutions across multiple criteria9, but without post-optimization classification, these solutions can be difficult to interpret or contextualize for stakeholders facing real-world implementation constraints. Similarly, MCDM methods such as fuzzy AHP and TOPSIS are widely used in infrastructure planning10, yet they frequently rely on deterministic assessments and struggle to incorporate the hesitancy and partial confidence that characterize expert judgments in complex, high-stakes decision environments. More advanced fuzzy sets, such as Pythagorean fuzzy logic, allow greater expression of uncertainty by incorporating membership, non-membership, and hesitancy degrees, but their use in airport energy retrofit prioritization remains limited11.
Moreover, while clustering techniques like K-Means have been employed in other domains to organize solutions into meaningful categories12, their integration into energy retrofit planning for airports has received little attention. This lack of interpretability becomes a practical barrier when decision-makers must select among numerous technically viable solutions under budgetary, operational, or environmental constraints. Compounding this is the limited incorporation of emerging decarbonization technologies — such as hydrogen energy, hybrid battery systems, and AI-enabled load forecasting — into retrofit planning models tailored to aviation settings6. As airports aim to align their infrastructure strategies with global policy initiatives like ICAO’s CORSIA and the United Nations Sustainable Development Goals (SDGs), there is an urgent need for a holistic, adaptive, and expert-informed framework capable of guiding these complex decisions.
To respond to this gap, it is essential to move beyond fragmented methodologies and adopt an integrated, hybrid approach that brings together the strengths of optimization, classification, and expert-driven prioritization. Such a model should be capable of optimizing retrofit strategies across multiple objectives, classifying those solutions into coherent categories for different policy or operational priorities, and prioritizing them using a decision support tool that accounts for ambiguity and expert uncertainty. The hybrid methodology not only enhances the technical robustness of the planning process but also ensures that the outputs are decision-relevant, stakeholder-oriented, and aligned with long-term climate and sustainability goals.
The contributions of this research are fourfold:
This is the first study to systematically combine NSGA-II, K-Means, and PFAHP into a single framework for airport energy retrofit planning, enabling seamless transition from solution optimization to prioritized decision-making.
By incorporating Pythagorean fuzzy sets, the framework captures expert hesitancy more accurately than traditional AHP or basic fuzzy models, enhancing robustness in high-stakes decisions.
The model is tested using empirical data from recent retrofit initiatives (e.g., geothermal systems, solar integration, energy-efficient HVAC), reflecting actual trade-offs faced by airport planners.
The framework supports decision-makers in aligning infrastructure strategies with ICAO’s CORSIA requirements and the United Nations Sustainable Development Goals (particularly SDG 7 and SDG 13).
By addressing a clear methodological gap and leveraging recent technological advancements, this study offers both a theoretical advancement in multi-criteria energy planning and a practical, scalable tool for supporting sustainability transitions in the aviation sector.
Literature review
This section reviews the current literature on multi-criteria decision-making (MCDM) methods in sustainable energy planning, with a specific focus on their applications in aviation infrastructure and airport energy management. The aim is to examine the methodological evolution of MCDM models—especially those integrating optimization, clustering, and fuzzy prioritization—and to identify existing gaps that the present study addresses. To ensure comprehensive coverage of the field, a systematic literature search was conducted using the Scopus and Web of Science databases. The following keywords and their combinations were used: “multi-criteria decision-making”, “MCDM”, “fuzzy AHP”, “Pythagorean fuzzy”, “NSGA-II”, “K-means clustering”, “airport energy planning”, “sustainable infrastructure”, “aviation energy strategy”, and “smart airport decision model”. Boolean operators (AND/OR) were applied to filter articles, and results were narrowed to peer-reviewed journal publications from 2018 to 2025. Preference was given to studies published in high-impact journals in the fields of energy systems, decision sciences, and aviation management. This review also synthesizes the state of the art in hybrid decision models that combine optimization, clustering, and expert-driven prioritization under uncertainty. The following subsections provide a structured analysis of these domains, setting the foundation for the hybrid framework proposed in this study.
Multi-criteria decision-making in sustainable energy and infrastructure planning
Multi-Criteria Decision-Making (MCDM) methods have become indispensable for solving complex problems in sustainable energy and infrastructure planning, where decisions must incorporate conflicting criteria such as cost, environmental impact, technical feasibility, operational risks, and social acceptance. Classical MCDM methods, including Analytic Hierarchy Process (AHP), Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), and VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), have provided foundational decision support frameworks by transforming qualitative assessments into quantifiable rankings.
For instance, Dash et al.13 employed AHP to assign subjective weights to criteria such as economic cost, capacity factor, and environmental impact for evaluating wind energy alternatives in India. They then used TOPSIS to identify the solution closest to an ideal point, and VIKOR to rank alternatives based on a compromise solution that considers group utility and individual regret. This comparative application demonstrated that integrating multiple classical MCDM methods can enhance decision robustness and build consensus among stakeholders. Similarly, Kshanh and Tanaka14 applied AHP to structure hierarchical criteria and sub-criteria for energy efficiency investments in a petrochemical complex, followed by PROMETHEE to evaluate and rank alternatives through pairwise comparisons using preference functions. Their study highlighted PROMETHEE’s ability to discriminate effectively among closely ranked options and its compatibility with stakeholder engagement processes.
Geographic Information Systems (GIS) integrated with MCDM have allowed for spatially explicit evaluations. Richards et al.15 used GIS-based MCDM with a Weighted Linear Combination (WLC) approach to incorporate spatial layers such as environmental sensitivity, wind resource distribution, and land-use conflicts in onshore wind energy planning in Japan. Luhaniwal et al.16 combined GIS and AHP to assess offshore wind farm sites, calculating relative importance scores for factors like wind speed, sea depth, and proximity to grid infrastructure. Saraswat et al.17 extended this approach by integrating hybrid MCDM methods, including entropy weighting for objective criteria and fuzzy AHP for subjective criteria, into GIS for multi-renewable energy potential site analysis. Santos et al.18 further combined GIS, Building Information Modeling (BIM), and MCDM, creating a comprehensive spatial-technical framework for infrastructure project planning that supports complex multi-layer data integration.
Fuzzy and hybrid MCDM approaches have advanced the capacity to manage vagueness and uncertainty inherent in expert judgments. Li et al.19 integrated fuzzy sets with cumulative prospect theory within an MCDM framework to capture stakeholders’ risk attitudes toward renewable energy development paths in Malaysia. This hybrid model combined subjective weighting of criteria with a behavioral component to better reflect real-world decision-making under risk. Jameel et al.20 proposed an integrated hybrid MCDM framework incorporating both subjective (AHP-based) and objective (entropy-based) weighting methods for renewable energy strategy prioritization, effectively balancing conflicting sustainability criteria.
Advanced applications combining SWOT analysis, game theory, and MCDM highlight strategic energy planning dimensions. Hasankhani et al.21 applied SWOT analysis to identify internal and external factors affecting waste-to-energy options in Iran, then used a hybrid MCDM framework involving fuzzy AHP for weighting and game theory for strategic interaction modeling among stakeholders. Zhao and Guo22 utilized a hybrid MCDM approach combining DEMATEL (Decision Making Trial and Evaluation Laboratory) for identifying interdependencies among criteria, and VIKOR for selecting optimal urban integrated energy system plans, balancing technical, economic, and social considerations. Ruiz-Vélez et al.23 developed a custom NSGA-II model with specialized repair operators to optimize sustainable road infrastructure solutions, merging evolutionary multi-objective optimization with MCDM evaluations to ensure Pareto-efficient and practically feasible outcomes.
In industrial settings, MCDM methods have been used to evaluate renewable energy integration with detailed technical considerations. Parvaneh and Hammad24 employed a hybrid MCDM approach using fuzzy AHP for weighting technological, environmental, and economic criteria to select sustainable power-generating technologies. Yılmaz and Uyan25 utilized a combination of AHP and GIS-based overlay analysis to prioritize potential sites for green hydrogen production, emphasizing solar insolation, grid accessibility, and environmental restrictions. Sugumar and Anglani26 developed a decision-support framework that integrates MCDM with resilience analysis for microgrid technology siting, explicitly considering spatial geographic constraints and alignment with Sustainable Development Goals (SDGs).
AI and machine learning integrations into MCDM frameworks are at the forefront of recent methodological advances. Alijoyo7 proposed a deep learning-enhanced MCDM framework wherein convolutional neural networks (CNN) forecast energy consumption profiles in smart buildings, and fuzzy AHP subsequently prioritizes energy conservation strategies. Binyamin and Slama27 introduced IntelliGrid AI, combining blockchain for secure data sharing, deep learning for consumption pattern recognition, and fuzzy logic within MCDM for optimizing vehicle-to-home and home-to-vehicle energy exchanges. Talebi et al.28 developed a machine learning-driven hybrid MCDM system to strategically plan electric vehicle charging and renewable energy infrastructure, improving real-time adaptability and stakeholder-informed prioritization.
Further cross-domain applications demonstrate MCDM’s versatility. Babatunde et al.29 utilized fuzzy AHP and TOPSIS to evaluate simulation software for sustainable power systems education, emphasizing usability, modeling capabilities, and long-term learning impact. Thakur et al.30 applied Pythagorean fuzzy sets within MCDM to support complex urban development decisions under high uncertainty. Başeğmez et al.31 (2025) integrated GIS, machine learning, and MCDM to manage urban green spaces sustainably, prioritizing ecological value, accessibility, and maintenance cost. Saraswat et al.17 further showcased hybrid MCDM for renewable site analyses across multi-layer spatial and regulatory contexts. Comprehensive reviews by Sahoo et al.32 (2025) and Kumar and Pamucar33 systematically documented these developments, highlighting increased adoption of hybrid, fuzzy, and AI-enhanced MCDM methods to address growing complexity in sustainability-driven decisions. Dwivedi and Sharma34 demonstrated the use of MCDM to assess SDG performance across Indian states, illustrating its utility in large-scale policy evaluation and regional planning.
Recent studies have advanced cross-disciplinary decision frameworks for renewable energy deployment, illustrating important lessons for aviation infrastructure planning. Almutairi et al.35 conducted a comprehensive case study in Iran that integrated SWOT analysis to identify strategic directions, weaknesses, opportunities, and threats, combined with SWARA weighting and ARAS-Grey for ranking, further supported by fuzzy Shapley values. Their results showed that strategies emphasizing high-efficiency wind and solar technologies, complemented by hydrogen production and battery storage, achieved superior environmental and economic performance. Similarly, Almutairi et al.36 demonstrated the effectiveness of a hybrid wind–solar–diesel–battery microgrid model for supplying power to remote facilities, emphasizing resilience and adaptability—qualities crucial for airports operating in isolated or emergency contexts. In parallel, Dehshiri et al.37 proposed a blockchain-enhanced framework for renewable energy supply chains that integrates strategic alliances and smart contracts to strengthen transparency and traceability, aligning with future airport energy ecosystem needs. Furthermore, Dehshiri et al.38 introduced a Pythagorean fuzzy-based decision-making approach combining the Best–Worst Method (BWM) and Interval-Valued Pythagorean Fuzzy WASPAS (IVPF-WASPAS) to assess renewable energy projects under economic, social, and environmental sustainability criteria. Their findings highlighted solar energy as the optimal source in their comparative analysis, validated through sensitivity testing—emphasizing the importance of robust uncertainty modeling in critical infrastructure energy decisions. Collectively, these studies underscore the value of integrating hybrid decision models, advanced optimization, and transparent supply chain strategies to guide future airport energy planning and retrofit prioritization.
Despite the substantial progress across these studies, many models remain focused on single-stage ranking or do not fully integrate optimization algorithms with clustering and robust expert-based prioritization. The present study addresses this critical methodological gap by integrating a non-dominated sorting genetic algorithm (NSGA-II) for generating Pareto-optimal solutions, K-Means clustering for interpretable solution grouping, and a Pythagorean fuzzy analytic hierarchy process (PFAHP) for handling uncertainty in expert prioritization. This unified, technically advanced framework equips decision-makers with a transparent and holistic approach to guide complex, sustainability-focused infrastructure decisions, such as airport energy retrofits, ensuring alignment with operational constraints and global environmental targets. To provide a clear overview of the diverse methodological contributions referenced in this section, Table 1 summarizes the key studies that have advanced the application of multi-criteria decision-making (MCDM) methods in sustainable energy and infrastructure planning.
Table 1. Summary of key MCDM applications in sustainable energy and infrastructure Planning.
Authors & Year | Focus Area | Application Context |
|---|---|---|
Dash et al.13 | AHP, TOPSIS, VIKOR integration | Wind energy alternative evaluation in India |
Kshanh & Tanaka14 | AHP with PROMETHEE | Energy efficiency investments in petrochemical |
Richards et al.15 | GIS-based MCDM with WLC | Onshore wind energy planning in Japan |
Luhaniwal et al.16 | GIS and AHP integration | Offshore wind farm site assessment |
Saraswat et al.17 | Hybrid MCDM with entropy weighting & fuzzy AHP | Multi-renewable site analysis |
Santos et al.18 | GIS-BIM-MCDM integration | Infrastructure project spatial-technical planning |
Li et al.19 | Fuzzy MCDM with cumulative prospect theory | Renewable energy development in Malaysia |
Jameel et al.20 | Integrated hybrid MCDM framework | Renewable energy strategy prioritization |
Hasankhani et al.21 | SWOT, fuzzy AHP, game theory integration | Waste-to-energy strategy in Iran |
Zhao & Guo22 | DEMATEL and VIKOR combined | Urban energy system planning |
Ruiz-Vélez et al.23 | NSGA-II with MCDM evaluations | Sustainable road infrastructure solutions |
Parvaneh & Hammad24 | Hybrid fuzzy AHP | Sustainable power technology selection |
Yılmaz & Uyan25 | AHP and GIS-based overlay | Green hydrogen site selection in Türkiye |
Sugumar & Anglani26 | MCDM with resilience analysis | Microgrid siting for SDG alignment |
Alijoyo7 | Deep learning-enhanced MCDM | Smart building energy conservation |
Binyamin & Slama27 | AI, blockchain, fuzzy MCDM | Vehicle-to-home energy exchanges |
Talebi et al.28 | Machine learning-driven hybrid MCDM | EV and renewable infrastructure planning |
Babatunde et al.29 | Fuzzy AHP and TOPSIS | Power systems simulation software selection |
Thakur et al.30 | Pythagorean fuzzy MCDM | Urban planning under uncertainty |
Başeğmez et al.31 | GIS, ML, MCDM integration | Urban green space management |
Sahoo et al.32 | Review of hybrid and fuzzy MCDM | Broad overview of sustainability decisions |
Kumar & Pamucar33 | Review of hybrid MCDM advancements | General review across sectors |
Dwivedi & Sharma34 | MCDM for SDG performance evaluation | Policy and regional planning in India |
Almutairi et al.35 | SWOT analysis, hybrid MCDM, game theory integration | Renewable energy growth strategy determination in Iran |
Almutairi et al.36 | Hybrid wind–solar–diesel–battery systems | Off-grid and remote facility energy supply |
Dehshiri et al.37 | Blockchain integration and strategic alliances in supply chains | Sustainable renewable energy procurement and traceability |
Dehshiri et al.38 | Pythagorean fuzzy-based hybrid decision approach | Evaluation of renewable energy projects under sustainability goals |
Energy decision-making in aviation and airport infrastructure
Energy decision-making in the aviation sector has evolved significantly as airports strive to align operations with global decarbonization targets such as ICAO’s CORSIA framework and the IATA Net Zero Roadmap. Airports increasingly adopt Multi-Criteria Decision-Making (MCDM) techniques to evaluate energy retrofit strategies, optimize resource allocation, and prioritize sustainability initiatives. For example, Mizrak, Polat, and Tasar developed an integrated model combining entropy weighting and a 2-tuple linguistic T-spherical fuzzy MCDM to prioritize sustainability actions at Istanbul Airport. Their model addressed both subjective and objective weighting challenges and robustly prioritized criteria such as emission reduction potential, energy cost savings, and regulatory adaptability39.
Similarly, Raad and Rajendran created a hybrid framework for selecting optimal airport sites by integrating Slacks-Based Measure Data Envelopment Analysis (SBM-DEA), multiple regression, and GIS-MCDM. Their approach evaluated solar radiation, land availability, and noise impacts, while DEA provided efficiency scores, enabling data-driven and spatially informed decisions40. Beyond strategic planning, MCDM techniques also support detailed energy infrastructure integration. SaberiKamarposhti and colleagues emphasized how fuzzy-based MCDM methods—such as Pythagorean fuzzy AHP and fuzzy TOPSIS—enable nuanced evaluation of hydrogen storage, grid synchronization, and load forecasting in smart grid-enhanced airport systems40. Sasi Bhushan and co-authors applied a mixed-integer optimization model integrated with fuzzy logic to manage heterogeneous battery energy storage systems (BESS) under time-varying loads. Their approach considered discharge rates, solar input fluctuations, and backup needs while using fuzzy rule-based systems to rank storage options based on safety, capacity, and lifecycle cost41. These models are particularly relevant as airports electrify ground operations and integrate advanced HVAC systems, a transition that poses significant infrastructure challenges42.
Multi-objective optimization frameworks such as NSGA-II have become popular for solving trade-offs among multiple criteria in airport energy strategy development. Originally designed to combine Pareto optimality with elitism and crowding distance sorting, NSGA-II facilitates diverse and efficient solution sets, helping decision-makers understand operational and sustainability scenarios9. In related work, Dey, Dash, and Basu applied NSGA-II to optimize hybrid power systems integrating solar, wind, and thermal sources, illustrating its flexibility for complex energy systems43. In retrofitting contexts, NSGA-II supports simultaneous optimization of cost, emissions reduction, implementation time, and operational disruption, aligning technical and strategic objectives.
Clustering methods such as K-Means have been used to categorize retrofit strategies into interpretable groups, aiding stakeholder understanding and decision confidence. Liu, Wu, and Xu introduced probabilistic K-Means clustering for large-scale group decision-making, providing structured groupings like “low-cost/high-disruption” or “high-impact/green,” critical for complex airport projects12. Qingguo and colleagues enhanced this by using genetic algorithms in K-Means, offering refined grouping capabilities for dynamic and stakeholder-rich contexts44.
Real-world applications further demonstrate the feasibility of MCDM in airport energy planning. Baxter assessed retrofitting strategies at London Gatwick Airport using weighted scoring and benchmarking for HVAC, lighting, and building management systems, showing measurable sustainability and operational improvements4. Ereser and Beyhan evaluated terminal architectural alternatives through cost-benefit and lifecycle sustainability metrics, illustrating the architectural impact on overall energy profiles45. At Copenhagen Airport, Baxter and Wild applied structured frameworks to improve energy performance, focusing on airside operations and auxiliary services46. Goh and colleagues proposed an adaptive energy management strategy integrating solar, wind, and waste-to-energy systems to help airports achieve carbon neutrality, using dynamic weighting to adapt to seasonal and operational conditions47.
Emerging frameworks increasingly emphasize smart technologies and long-term resilience. Gao and He applied the Fuzzy Best–Worst Method to prioritize drivers of smart aviation, highlighting renewable energy intelligence, predictive analytics, and cybersecurity as central to future-ready airport systems48. Seker developed a hybrid fuzzy MCDM model to assess agility in low-cost carriers adopting sustainability-oriented innovations, underscoring energy flexibility as a strategic capability49. Malefaki and colleagues compared normalization techniques in MCDM applications, demonstrating how normalization choice significantly affects rankings — a critical consideration given the data heterogeneity in airport energy planning50. Zhou introduced a systems-level perspective, proposing integrated airport energy ecosystems within smart cities, leveraging hydrogen-based renewable–grid–storage architectures to ensure long-term flexibility and sustainability51.
Despite these advancements, challenges persist in applying MCDM to complex aviation energy planning problems. Traditional methods often struggle to capture expert uncertainty, especially in interdisciplinary evaluations. While approaches such as those by Shahzad and colleagues proposed Pythagorean fuzzy-based methods to represent hesitant expert opinions, they typically lack integrated optimization or solution interpretability, limiting practical use10. Moreover, large Pareto-optimal solution sets from algorithms like NSGA-II can overwhelm decision-makers, making it difficult to select contextually appropriate strategies52. Although clustering offers potential interpretability improvements, such techniques are not widely operationalized in airport workflows12. Method integration also remains fragmented: Mizrak, Polat, and Tasar’s model for airport sustainability lacked an optimization phase39, while Raad and Rajendran’s approach did not include prioritization under uncertainty36.
To address these challenges, recent studies advocate for modular hybrid frameworks that combine data-driven analysis, expert reasoning, and scenario-based iteration while maintaining transparency and interpretability. However, a fully integrated, uncertainty-resilient, and practically interpretable framework specifically tailored to airport energy retrofit decision-making remains underdeveloped, reinforcing the significance of the approach proposed in this study. Table 2 provides a consolidated summary of key studies discussed in Sect. 2.2. It highlights the main contributions of each study to the field of energy decision-making in aviation and airport infrastructure, emphasizing methodological advancements, application contexts, and integration of multi-criteria and optimization approaches.
Table 2. Summary of key studies on energy Decision-Making in aviation and airport Infrastructure.
Reference | Main Contribution |
|---|---|
Mizrak et al.39 | Developed an entropy-weighted 2-tuple linguistic T-spherical fuzzy MCDM model for prioritizing sustainability strategies at Istanbul Airport. |
Raad & Rajendran40 | Proposed a hybrid SBM-DEA, regression, and GIS-MCDM framework for airport site selection, integrating spatial and efficiency analysis. |
SaberiKamarposhti et al.8 | Highlighted fuzzy-based MCDM for hydrogen storage and smart grid integration in airports. |
Sasi Bhushan et al.41 | Applied mixed-integer optimization with fuzzy logic to manage heterogeneous battery storage systems in airport energy strategies. |
Lindberg & Leijon42 | Discussed challenges and energy demand implications of electrifying airport ground and auxiliary operations. |
Deb et al.9 | Introduced NSGA-II for multi-objective optimization, supporting complex airport energy trade-off analysis. |
Dey et al.43 | Applied NSGA-II to hybrid renewable power systems, illustrating its flexibility in energy planning contexts. |
Liu et al.12 | Proposed probabilistic K-Means clustering for large-scale group decision-making, enhancing interpretability in complex projects. |
Qingguo et al.44 | Combined genetic algorithms with K-Means clustering for refined solution grouping in dynamic contexts. |
Baxter4 | Assessed retrofitting measures at London Gatwick Airport, showing improvements in HVAC, lighting, and energy management systems. |
Ereser & Beyhan45 | Evaluated architectural alternatives in airport terminals based on lifecycle sustainability metrics. |
Baxter & Wild46 | Applied structured energy assessment frameworks at Copenhagen Airport, focusing on airside and support services. |
Goh et al.47 | Proposed adaptive energy management integrating solar, wind, and waste-to-energy systems for carbon neutrality in airports. |
Gao & He48 | Used the Fuzzy Best–Worst Method to prioritize smart aviation drivers, emphasizing renewable intelligence and predictive analytics. |
Seker49 | Developed a hybrid fuzzy MCDM model to assess agility and energy flexibility in low-cost carriers’ sustainability innovations. |
Malefaki et al.50 | Compared normalization techniques in MCDM, showing their impact on final rankings in airport energy planning. |
Zhou51 | Proposed integrated airport energy ecosystems within smart cities, leveraging hydrogen and renewable grid-storage solutions. |
Shahzad et al.10 | Emphasized Pythagorean fuzzy-based approaches to capture hesitancy in expert judgments for energy planning. |
Ma et al.10 | Discussed challenges in interpreting large Pareto-optimal solution sets from NSGA-II in airport energy planning. |
Research gap and justification for the hybrid framework
While Multi-Criteria Decision-Making (MCDM) models have become essential for evaluating sustainability strategies in energy and infrastructure planning, particularly when facing conflicting objectives, a significant gap persists in approaches that integrate optimization, interpretability, and uncertainty-aware expert prioritization into a single framework. Many studies have focused on individual components of this analytical triad. For example, multi-objective optimization models using NSGA-II are widely used to generate Pareto-optimal solutions for complex energy system problems, especially to analyze trade-offs among cost, emissions, and energy savings9. However, these solutions are usually presented as abstract sets without providing structured guidance or context for decision-makers, limiting their practical usability.
Clustering methods like K-Means are frequently applied for data classification in engineering and sustainability contexts, yet they are rarely employed as a bridging layer to organize Pareto solutions into clear, policy-relevant strategy groups that planners can easily interpret53. Meanwhile, fuzzy prioritization techniques, such as those utilizing Pythagorean fuzzy sets, are often applied in isolation as ranking tools without incorporating insights from optimization outputs or clustering processes, restricting their contribution to integrated planning54.
In the aviation sector, the need for comprehensive, integrated frameworks is particularly pronounced. Although airports have been rapidly advancing sustainability initiatives, most studies fail to deliver decision models that simultaneously incorporate expert input, evolving operational requirements, and technical trade-offs. For example, Mizrak, Polat, and Tasar developed a 2-tuple linguistic T-spherical fuzzy MCDM model with entropy weighting to prioritize sustainability strategies at Istanbul Airport, capturing expert hesitancy effectively but lacking an optimization mechanism to generate feasible retrofit scenarios39. Similarly, Raad and Rajendran combined GIS, DEA, and MCDM for airport site selection in Iran but did not address expert uncertainty or multi-objective trade-offs, leaving the model incomplete for holistic planning needs40. Gao and He employed the Fuzzy Best–Worst Method to rank factors supporting smart aviation development, yet their work centered on prioritizing factors rather than creating an end-to-end strategy design48.
In broader energy and infrastructure contexts, recent studies have highlighted the importance of hybrid approaches but continue to focus on individual stages. For example, Sahoo and colleagues emphasized the advantages of integrating MCDM for renewable energy prioritization yet pointed out the lack of comprehensive frameworks that unify optimization, expert analysis, and interpretability32. Karbassi Yazdi and co-authors examined the use of MCDM for selecting locations for green energy projects but did not integrate post-selection strategy clustering or expert uncertainty modeling55 Similarly, Jameel, Yasin, and Riaz proposed an integrated hybrid MCDM framework for sustainable energy project prioritization but still focused on independent ranking rather than actionable grouping and scenario optimization20.
Further illustrating this gap, Talebi and colleagues advanced machine learning-driven MCDM models for sustainable infrastructure deployment, yet their models lacked integrated expert prioritization layers and interpretability mechanisms necessary for operational decision-making in complex airport settings28. Santos and co-authors proposed combining GIS and BIM with MCDM for infrastructure planning, adding spatial and design dimensions but stopping short of integrating iterative optimization and uncertainty-resilient prioritization18. Likewise, Parvaneh and Hammad applied MCDM to evaluate power-generating technologies for sustainability, focusing primarily on comparative ranking rather than providing holistic implementation guidance24.
To address these methodological shortcomings, this study introduces a three-stage hybrid decision-making framework that integrates NSGA-II for multi-objective optimization, K-Means clustering for solution classification and interpretability, and Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP) for expert-based prioritization under uncertainty. In the first stage, NSGA-II explores trade-offs among key criteria such as cost, emissions reduction, energy savings, implementation time, and operational disruption. By combining fast non-dominated sorting, elitism, and crowding distance mechanisms, NSGA-II facilitates the generation of diverse Pareto-optimal strategies, offering planners comprehensive insight into competing objectives43. In the second stage, K-Means clustering groups Pareto-optimal solutions into interpretable strategy clusters, converting abstract solution vectors into decision-ready categories like “cost-efficient,” “balanced,” or “high-impact.” Each solution vector comprises multiple performance indicators derived from NSGA-II outputs, and clustering helps minimize intra-cluster variance, thereby supporting clearer communication and easing stakeholder engagement in decision processes12. Finally, the third stage introduces Pythagorean Fuzzy AHP to rank and prioritize these clustered strategies. Unlike traditional AHP, which relies on crisp judgments, Pythagorean fuzzy sets express expert opinions as a combination of membership, non-membership, and hesitancy degrees, allowing for a more realistic representation of expert uncertainty in decision environments characterized by incomplete or evolving data56. This approach ensures that decisions remain robust and context-sensitive, especially in multidisciplinary airport planning teams.
Although recent literature demonstrates significant progress in adopting discrete techniques like fuzzy prioritization, clustering, or NSGA-II optimization, these methods are still used in a fragmented manner and do not fully integrate to address the combined needs of optimization, expert uncertainty, and strategic interpretability in airport energy planning. In summary, while past studies have successfully advanced individual elements, they often fail to provide a comprehensive, practical approach that addresses real-world implementation challenges in complex retrofit projects. By combining NSGA-II, K-Means clustering, and Pythagorean Fuzzy AHP, the proposed framework directly responds to this gap, delivering a holistic, uncertainty-resilient, and stakeholder-informed tool for developing actionable, technically feasible, and policy-aligned airport retrofit strategies.
State of the art in hybrid decision models for sustainable airport infrastructure
Recent advances in decision science, energy systems engineering, and infrastructure planning have led to the development of increasingly sophisticated hybrid models that integrate optimization, machine learning, and fuzzy logic within multi-criteria decision-making (MCDM) frameworks. In the energy sector, combining evolutionary algorithms such as the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) with fuzzy prioritization and advanced weighting methods has become a prominent approach for managing complex, multi-objective decision environments. NSGA-II is widely recognized for its capacity to generate diverse sets of Pareto-optimal solutions across conflicting objectives, enabling planners to consider trade-offs among criteria like cost, emissions, and operational reliability. However, despite its mathematical strength in providing diverse solution frontiers, its outputs often lack the interpretive structures needed to guide practical stakeholder discussions or translate technical insights into actionable strategies for decision-makers. This disconnect has been emphasized in comprehensive reviews that call for the integration of interpretive and participatory layers into technical optimization frameworks to improve real-world applicability52.
In parallel, there has been significant progress in the development and application of fuzzy MCDM models aimed at better capturing and representing expert uncertainty and hesitancy in complex evaluations. The introduction of Pythagorean fuzzy sets has marked a major milestone in this field, allowing decision-makers to express evaluations using degrees of membership, non-membership, and hesitancy all at once. This modeling capability provides a more nuanced and realistic way of capturing human judgments compared to traditional fuzzy or intuitionistic fuzzy methods. While these models are valuable for improving robustness and reflecting subjective judgments in scenarios with high uncertainty, they often remain isolated from optimization or clustering techniques. As a result, although they strengthen the credibility of expert evaluations, they are rarely utilized in conjunction with solution-space generation mechanisms such as genetic algorithms or scenario clustering, thereby limiting their practical effectiveness in comprehensive planning exercises54.
Meanwhile, clustering algorithms have increasingly been recognized for their ability to improve the interpretability and usability of large, complex solution sets derived from optimization models. Classical methods like K-Means and its advanced variants, including probabilistic and genetic versions, have been successfully employed in group decision-making, market segmentation, and risk analysis. By transforming complex, multi-dimensional solution spaces into categorized and interpretable strategy groups, clustering helps reduce cognitive overload and supports clearer communication among diverse stakeholder groups. However, despite these advantages, clustering techniques are rarely integrated into infrastructure planning models as a crucial intermediate stage that links technical optimization with expert-informed prioritization. Comparative studies on normalization techniques and ranking logic across different MCDM approaches have revealed that inconsistencies in these steps can dramatically alter final decision outcomes, further underscoring the necessity for cohesive, integrated hybrid systems that ensure transparency and consistency throughout all stages of the decision-making process12.
Within the aviation sector, there has been a growing body of research exploring the application of advanced MCDM methods to evaluate sustainability initiatives and inform strategic transformation efforts at airports. For example, a study at Istanbul Airport employed entropy weighting and a 2-tuple linguistic T-spherical fuzzy MCDM approach to prioritize sustainability strategies, successfully accommodating expert hesitancy but ultimately lacking integrated optimization or clustering stages that could guide decision-makers in selecting coherent retrofit packages35. Similarly, research combining robust data envelopment analysis (DEA), geographic information systems (GIS), and MCDM for airport site selection focused on evaluating technical, environmental, and spatial criteria but did not account for uncertainty in expert prioritization or the dynamic trade-offs involved in large-scale energy retrofits36. Other studies, such as those applying the Fuzzy Best–Worst Method to identify critical enablers for smart aviation development or employing hybrid AHP–SWOT models to enhance airport facility management, have shown promise in specific prioritization and assessment tasks but do not offer a fully integrated framework that connects optimization, solution grouping, and final strategy ranking into a unified workflow.
On the infrastructure and operational side, there have been important contributions focusing on energy management strategies and technological modernization in airports. For instance, recent research has proposed carbon-neutral energy strategies for airports by integrating renewable sources like solar and wind, yet these studies often lack structured decision models for comparing alternative retrofit or modernization pathways, leaving planners with generic recommendations rather than concrete, prioritized action plans47. Technical assessments on airport electrification have detailed the equipment and grid upgrades required to support future demands, forecasting up to a fivefold increase in power requirements by 2050. However, these analyses typically do not include systematic decision-support frameworks to quantify trade-offs or align strategies with evolving policy and financial constraints, thereby limiting their value for strategic implementation38. Research exploring hydrogen integration and smart airport ecosystems has outlined forward-looking visions and systemic connections to urban energy grids but has largely stopped short of offering modular, adaptive decision tools capable of supporting tactical prioritization and resource allocation in real-world airport environments57.
Outside the aviation domain, hybrid MCDM frameworks have demonstrated significant advances in diverse sectors such as resilient supply chains, smart city logistics, and sustainable food production systems. For example, the integration of possibilistic programming with multi-stage hybrid models in supply chain resilience planning showcases how combining robust mathematical optimization with flexible uncertainty modeling can support dynamic, multi-level decision processes58. Similarly, applying fuzzy MCDM to drone-based urban logistics and other infrastructure contexts has shown the adaptability and effectiveness of these frameworks for urban planning and operational design under uncertainty. However, these applications generally treat optimization, clustering, and prioritization as separate stages rather than elements of an interconnected and iterative decision flow. Studies involving fuzzy AHP-TOPSIS frameworks or benchmarking of metaheuristic algorithms illustrate how expert assessments can be synthesized with technical optimization, yet they often lack integrated categorization stages to translate solutions into actionable strategy bundles, which is essential for large-scale infrastructure and energy retrofitting projects58.
Despite these advancements, a critical methodological gap persists in the literature. Many studies continue to approach optimization, classification, and prioritization as isolated tasks rather than as interconnected phases of a holistic decision-making system. While NSGA-II models are highly effective at generating diverse solution spaces that capture multi-objective trade-offs, they frequently lack interpretive layers that are necessary for practical stakeholder communication and iterative scenario analysis. Clustering approaches, while beneficial for organizing solution sets, are seldom embedded into operational infrastructure models to guide subsequent prioritization and implementation phases. Moreover, fuzzy MCDM techniques, though excellent at accommodating subjective expert inputs, often operate with fixed weighting schemes and do not leverage optimization outputs, thus failing to reflect the full strategic complexity required in modern energy and infrastructure planning.
The hybrid framework proposed in this study directly addresses these shortcomings by seamlessly integrating NSGA-II for trade-off-based solution generation, K-Means clustering for translating these solutions into clearly defined strategic groups, and Pythagorean Fuzzy Analytic Hierarchy Process for expert-informed prioritization under uncertainty. This modular and cohesive approach bridges existing methodological divides and empowers decision-makers to move from abstract technical analyses to concrete, prioritized strategies that are actionable and aligned with policy and operational goals. By offering a comprehensive, uncertainty-resilient, and stakeholder-oriented decision support structure, the framework sets a new standard for sustainable airport infrastructure planning and advances the state of the art in hybrid MCDM applications.
Theoretical and operational foundations of the proposed model
The proposed framework is conceptually grounded in a growing body of interdisciplinary decision science literature that emphasizes the need for robust, adaptive, and uncertainty-resilient models in complex infrastructure systems. At the theoretical level, the model draws from constructivist decision theory, fuzzy set theory, and evolutionary multi-objective optimization—all of which support rational decision-making in conditions of ambiguity, incomplete information, and multidimensional trade-offs. These theories are particularly relevant in the context of airport sustainability planning, where goals such as emissions reduction, financial viability, implementation feasibility, and regulatory compliance must be jointly considered across multiple stakeholder perspectives. The framework reflects the theoretical evolution of MCDM modeling from static and deterministic ranking tools toward dynamic, hybrid decision environments. It leverages conceptual advancements in epistemic uncertainty modeling, such as the adoption of Pythagorean fuzzy logic, which allows more expressive modeling of expert confidence and hesitancy compared to traditional fuzzy or intuitionistic sets. The prioritization logic embedded in the framework aligns with preference theory, while the classification layer draws upon unsupervised learning theory, particularly in its ability to transform solution spaces into human-readable patterns. Rather than offering a novel algorithmic component in isolation, the model represents a synthesis of theoretical ideas tailored to the realities of energy strategy development in high-stakes, regulated environments like airports. From an operational perspective, the model is designed to reflect decision-making as it occurs in practice, not merely as an abstract optimization problem. Decision-makers in airport planning often operate under fragmented information, evolving regulatory targets (such as ICAO’s LTAG or IATA’s net-zero roadmap), and the need to satisfy both internal and external stakeholders. This requires a model that supports not only analytical rigor but also strategic communication, consensus-building, and justification—functions often overlooked in traditional MCDM applications. Therefore, this study emphasizes model transparency, modularity, and adaptability, enabling its deployment in policy planning sessions, technical assessments, or cross-functional evaluation workshops. Importantly, this framework is positioned at the interface between theoretical innovation and applied infrastructure planning. It offers a structured pathway from computational generation of alternatives to stakeholder-informed strategic selection. In this way, the model provides both a conceptual bridge—linking formal methods to decision behavior—and an operational tool—supporting real-world sustainability transitions. This dual focus ensures the model’s value for both academic advancement and practitioner uptake, responding to the complex, multilevel challenges of sustainable aviation infrastructure development.
In this way, the model provides both a conceptual bridge—linking formal methods to decision behavior—and an operational tool—supporting real-world sustainability transitions. This dual focus ensures the model’s value for both academic advancement and practitioner uptake, responding to the complex, multilevel challenges of sustainable aviation infrastructure development.
Methodology
Framework overview
The proposed hybrid framework introduces a novel integration of three advanced decision-support techniques—Non-Dominated Sorting Genetic Algorithm II (NSGA-II), K-Means clustering, and Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP)—to optimize and prioritize retrofit strategies for achieving net-zero energy transitions in airport infrastructure. This integration is designed to overcome the limitations of previous models that typically apply these methods in isolation. While NSGA-II is widely used for multi-objective optimization, its outputs often lack interpretability52. Similarly, fuzzy MCDM methods can rank known alternatives but do not generate or structure strategy spaces. The proposed model bridges this methodological gap by connecting optimization, classification, and uncertainty-aware prioritization in a sequential and modular workflow tailored specifically for complex infrastructure planning.
In the first stage, NSGA-II is applied to generate a diverse set of Pareto-optimal solutions that reflect trade-offs across criteria such as cost, energy savings, carbon reduction, implementation time, and operational disruption. These solutions represent a high-dimensional decision space with no single optimum, reflecting the practical complexity of retrofitting decisions in the aviation sector. Next, K-Means clustering, originally introduced by MacQueen, is used to organize the Pareto-optimal strategies into distinct clusters based on performance similarities. This step addresses a critical gap in interpretability by allowing decision-makers to focus on thematically grouped strategies—such as cost-efficient, balanced, or high-impact options—thereby simplifying strategic communication and planning. In the final stage, Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP) is applied to rank the clustered strategies. PFAHP builds on the classical AHP by Saaty and extends through the Pythagorean fuzzy set theory introduced by Yager. It enables the incorporation of expert judgments while effectively modeling uncertainty and hesitancy, which is particularly valuable in sustainability-related infrastructure decisions where inputs are often based on expert estimations rather than deterministic data.
To enhance the robustness and practical reliability of the model, a sensitivity analysis was conducted on the final prioritization outcomes. This analysis assessed how variations in expert-provided criteria weights affect the ranking of retrofit strategies, with particular attention to high-priority solutions identified in the most impactful cluster. The findings revealed that while small changes in weights led to minor shifts within each cluster, the overall ranking hierarchy remained stable, demonstrating that the PFAHP stage is sufficiently resilient to moderate uncertainty in judgment inputs.
This sensitivity testing validates the decision-support integrity of the framework, confirming that it can provide consistent guidance for airport planners even under conditions of imperfect information or differing expert perspectives. The analytical workflow begins with comprehensive data collection, followed by NSGA-II optimization to generate efficient solutions. These solutions are then categorized using K-Means clustering to identify strategic clusters. The PFAHP is subsequently applied to prioritize alternatives based on expert evaluations. Finally, sensitivity analysis assesses the robustness of the outcomes, leading to the final decision output. This integrated framework ensures a balanced consideration of environmental, economic, and operational factors. Figure 1 presents the sequential steps undertaken in the analysis process.
Fig. 1 [Images not available. See PDF.]
Workflow of the proposed hybrid decision-making framework.
This hybrid approach is, to the best of the authors’ knowledge, the first to fully integrate NSGA-II, K-Means, and PFAHP in a structured decision-making framework for airport energy planning. It offers a methodological advancement over previous research by delivering an end-to-end solution: from solution space generation and interpretive clustering to expert-informed prioritization under uncertainty. This design enhances both computational robustness and operational usability, ensuring that the model can be adapted to varying airport contexts and used by both technical analysts and policy decision-makers.
Model assumptions and constraints
The development of the hybrid decision-support framework for airport energy retrofit planning is based on a set of clearly defined assumptions and practical constraints. These assumptions serve as the foundation for model formulation and ensure that the results remain realistic and operationally feasible for real-world implementation in airport environments. The model evaluates a discrete set of alternative retrofit strategies, each consisting of bundled technological and infrastructural energy-efficiency measures (e.g., solar panel integration, HVAC upgrades, geothermal systems). Each alternative is assessed across five objective criteria:
Capital Cost (minimization) – includes both installation and maintenance costs.
Energy Savings (maximization) – projected annual savings in energy consumption (%).
Carbon Emissions Reduction (maximization) – reduction in greenhouse gas emissions (%).
Implementation Time (minimization) – time required to complete the retrofit (months).
Operational Disruption (minimization) – a composite index (1–5) reflecting the impact on airport operations (e.g., service interruptions, downtime).
Each of these objectives reflects a key concern in sustainable infrastructure investment, where financial feasibility, energy performance, and service continuity must be balanced.
The model is developed under the following assumptions:
Each retrofit strategy is independent and mutually exclusive—only one strategy is selected for implementation per evaluation cycle.
Performance data for each strategy (e.g., cost, savings, emissions) is available or can be reliably estimated from historical data, sustainability reports, or benchmark projects.
Expert judgments used in PFAHP are static and context-specific, representing current priorities of decision-makers at the time of evaluation.
External factors such as energy prices, regulatory changes, or market volatility are held constant during optimization.
All retrofit strategies are technically feasible and compliant with safety and regulatory standards applicable to international airports.
The following real-world constraints were introduced into the model to maintain practical feasibility:
Budget Constraints: Total investment must not exceed a predefined capital expenditure threshold (e.g., $1 million), representing typical funding ceilings in airport retrofit planning.
Implementation Deadline: The selected strategy must be completed within an allowable project window (e.g., ≤ 18 months), ensuring alignment with airport operations and project planning cycles.
Service Continuity: Retrofit implementation must not surpass an operational disruption index of 3 (on a 5-point scale), ensuring that airport functionality is minimally impacted.
Environmental Targets: Strategies must meet a minimum emissions reduction threshold to remain eligible for ranking (e.g., ≥ 10% CO₂ reduction), aligning with ICAO CORSIA and national climate policies.
These assumptions and constraints define a bounded evaluation space for NSGA-II to operate in, enabling the algorithm to search for Pareto-optimal trade-offs among cost, sustainability performance, and operational feasibility. Solutions that violate hard constraints (e.g., exceed budget or disruption limits) are excluded from the solution pool during optimization and clustering. While these parameters may vary across airports or regions, the framework is intentionally modular—allowing users to adjust objective definitions, thresholds, or expert inputs as needed to fit local contexts. In future applications, these assumptions can be revisited or extended to include dynamic elements such as fluctuating energy prices, real-time system data, or stakeholder feedback, enhancing the model’s responsiveness to changing infrastructure and policy environments.
NSGA-II algorithm and parameter settings
The Non-Dominated Sorting Genetic Algorithm II (NSGA-II), introduced by Deb and colleagues, was selected as the multi-objective optimization engine due to its effectiveness in exploring Pareto fronts, maintaining diversity, and ensuring convergence through elitism and crowding distance9. Compared to methods such as Multi-Objective Particle Swarm Optimization (MOPSO), NSGA-II is less sensitive to parameter tuning and has been extensively validated in sustainable infrastructure and energy systems optimization59.
The optimization was configured with the following parameters:
Population size: 100
Number of generations: 50
Crossover probability: 0.9
Mutation probability: 0.1
Selection method: Binary tournament
Fitness sorting: Fast non-dominated sorting and crowding distance
The algorithm was used to minimize cost, implementation time, and disruption, while maximizing energy savings and carbon reduction across nine candidate retrofit solutions. The output was a set of non-dominated (Pareto-optimal) strategies. The detailed pseudocode for the NSGA-II implementation used in this study is provided in Appendix A to ensure transparency and reproducibility of the optimization process.
Data collection
Data collection for this study is divided into two key components: quantitative data and qualitative data. The quantitative data is gathered from publicly available sources and historical records of airport retrofit projects, while the qualitative data is derived from expert judgments on the relative importance of decision criteria. Both data types are essential for evaluating and prioritizing energy retrofit strategies using the Pythagorean fuzzy AHP and K-Means clustering methodologies.
Quantitative data
The quantitative data for this study was derived from publicly available sources, including sustainability reports, academic literature, and industry databases documenting retrofit projects at international airports. Key metrics—such as installation and maintenance costs, estimated energy savings, carbon reduction potentials, and implementation durations—were extracted to evaluate retrofit strategies using the proposed NSGA-II optimization, K-Means clustering, and Pythagorean Fuzzy AHP methodologies. These metrics formed the foundation for analyzing the complex trade-offs between economic feasibility, environmental benefits, and operational impacts in airport retrofitting scenarios. For example, Vancouver International Airport’s solar water heating system achieved annual savings of $110,000 and reduced energy use by 8,569 gigajoules, highlighting the economic and energy-saving potential of solar technologies. Similarly, Louisville Muhammad Ali International Airport’s geothermal HVAC system, launched in October 2023, achieved an 80% reduction in heating and cooling emissions and approximately $400,000 in annual cost savings, showcasing a short-term, high-impact retrofit solution.
Additional data were drawn from Copenhagen Airport’s renewable energy initiative, which supplies up to 81% of electricity needs in summer and cuts emissions by nearly 44 metric tons daily, albeit with high operational costs in winter months. At Dublin Airport, a 28-acre solar farm under construction in 2024 is expected to produce 7.46 GWh annually—enough to cover more than 10% of its electricity demand. Similarly, long-standing photovoltaic systems at Munich Airport and multi-site solar installations at Tallinn Airport further illustrate the scalability of renewable energy integration in airport infrastructure. These diverse case studies provided empirical grounding for evaluating cost-performance-environment trade-offs across different technological configurations. While airports like Vancouver and Munich represent cost-conscious, moderate-impact implementations, others like Copenhagen and Dublin emphasize deep decarbonization strategies, despite higher upfront investments. These examples collectively informed the simulation’s input parameters and strategic assumptions.
To contextualize the modeling framework, the study applied a representative scenario of a mid-sized international airport pursuing compliance with ICAO’s net-zero emissions objectives. While not anchored to a single airport, the data was benchmarked against documented retrofit initiatives from London Gatwick4, Louisville3, and Vancouver60, reflecting typical infrastructure characteristics, budget limits, and sustainability targets. Baseline energy use, carbon emission factors, and retrofit costs were synthesized from these real-world cases and standardized for modeling purposes. An operational disruption index (rated 1–5) was introduced based on expert input to facilitate strategy comparison under realistic constraints. The optimization model simulated nine distinct retrofit strategies under budgetary limitations (maximum $1 million), implementation timelines (≤ 18 months), and operational disruption thresholds (≤ 3). These constraints were established to reflect common conditions in airport energy planning and align the model with policy frameworks such as ICAO’s CORSIA and IATA’s Net Zero Roadmaps. Expert evaluations conducted via the Pythagorean Fuzzy AHP ensured that the prioritization of strategies was both practically grounded and responsive to uncertainty, completing a robust foundation for model execution and validation.
Qualitative data
Qualitative data is collected through expert judgments on the relative importance of various criteria in the decision-making process. Expert inputs are gathered using Pythagorean fuzzy pairwise comparisons, which allow for more nuanced decision-making by capturing uncertainties and hesitancies in expert judgments. Experts from various fields, including sustainability, airport management, and energy systems, evaluate the importance of criteria such as cost, energy efficiency, carbon reduction, and implementation time. A panel of 9 experts has been selected based on their experience and expertise. The experts provided pairwise comparisons between the criteria, using a Pythagorean fuzzy scale. Table 3 outlines the background and expertise of the selected experts.
Table 3. Information about Experts.
Expert ID | Field of Expertise | Position | Years of Experience | Specialization |
|---|---|---|---|---|
E1 | Sustainability and Energy Systems | Senior Sustainability Advisor | 15 years | Energy efficiency in airport systems and green building technologies |
E2 | Airport Management and Operations | Airport Operations Manager | 12 years | Airport infrastructure management and sustainable practices |
E3 | Environmental Policy and Governance | Environmental Consultant | 10 years | Policy formulation and sustainability strategies for airports |
E4 | Energy Systems Engineering | Senior Engineer | 18 years | Renewable energy systems and energy efficiency technologies |
E5 | Financial Analysis and Investment | Energy Investment Analyst | 14 years | Financial feasibility and cost analysis for energy projects |
E6 | Civil Engineering and Project Management | Project Manager | 20 years | Infrastructure projects and implementation of energy systems |
E7 | Urban Planning and Development | Urban Sustainability Expert | 16 years | Sustainable urban infrastructure and airport planning |
E8 | Renewable Energy and Environmental Research | Research Scientist | 11 years | Renewable energy technologies and environmental impact analysis |
E9 | Aviation and Climate Change | Climate Change Policy Expert | 13 years | Climate adaptation and mitigation strategies in aviation |
The expert panel was selected through purposive sampling based on specific inclusion criteria, including a minimum of ten years of professional experience, demonstrated specialization in airport sustainability or energy systems, and balanced representation across technical, managerial, and policy domains. Invitations were extended to professionals identified via academic networks, industry affiliations, and relevant conferences. The qualitative data was collected over a four-week period using structured online forms that incorporated Pythagorean fuzzy pairwise comparison matrices. Experts completed the forms independently to minimize group influence, and clarifications were provided through follow-up emails when necessary. The questions were designed to capture nuanced insights into the relative importance of decision-making criteria such as cost, energy efficiency, carbon reduction, and implementation time in the prioritization of airport energy retrofit strategies. Using a fuzzy pairwise comparison format, experts were asked to evaluate the importance of each criterion relative to others (e.g., “How important is cost compared to energy efficiency when evaluating retrofit strategies?”). Additional items probed their views on the feasibility, scalability, and operational impact of specific energy-saving technologies. Experts also provided judgments on the trade-offs between short-term implementation costs and long-term energy savings, as well as the strategic importance of carbon reduction in meeting broader sustainability objectives. This process ensured a rigorous, structured, and uncertainty-aware capture of expert perspectives to inform the prioritization framework.
NSGA-II optimization
The Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is a robust multi-objective optimization algorithm widely used for problems involving conflicting objectives, such as minimizing cost while maximizing energy savings in airport retrofit strategies. The NSGA-II optimization process can be broken down into the following components: formulation of objectives, constraints and decision variables, and population evolution with non-dominated sorting.
Formulation of objectives
In this study, the NSGA-II optimization framework is used to evaluate retrofit strategies under two conflicting objectives:
Objective 1: Minimize the total cost (installation + maintenance costs).
1
where:
: Expected annual maintenance cost of the system.
Annual energy savings (in kWh).
: Associated carbon emissions reduction (in ).
Decision Variables:
: Binary variables representing whether a specific retrofit technology (e.g., LED lighting, solar panels) is selected (1) or not (0).
: Continuous variables representing the scale or capacity of the selected technologies.
Constraints:
Budget Constraint:
Energy Savings Threshold:
Implementation Time Limit:
Chromosome Structure: Each chromosome is represented as a vector of decision variables:
is no worse than in all objectives.
is strictly better than in at least one objective.
is no worse than in all objectives:
: The -th objective function value for solution .
: Total number of objectives.
is strictly better than in at least one objective:
Solutions with are assigned rank 1 (non-dominated solutions).
For subsequent ranks, solutions dominated only by solutions of lower ranks are assigned the next rank.
Identify all solutions with (rank 1 solutions).
Remove rank 1 solutions from the population and repeat for the remaining solutions, incrementing the rank each time.
The population is divided into fronts , where:
: Non-dominated solutions (rank 1).
: Solutions dominated only by solutions (rank 2). And so on.
and : Objective values of the neighboring solutions.
and : Maximum and minimum values of the objective in the population.
Selection:
Parent solutions are selected using a tournament based on Pareto rank and crowding distance.
Solutions with lower ranks and higher crowding distances are preferred.
Crossover:
Mutation:
Maximum Number of Generations: The algorithm stops after a fixed number of generations :
is the Pareto front at generation .
is the change in the Pareto front between consecutive generations:
: Indicates that is not dominated by .
The condition for dominance is:
: Objective for solution .
must be no worse than for all objectives.
must be strictly better than for at least one objective.
The condition for dominance is: $868,750
Energy Savings: 21.25%
Annual baseline energy use: 1,200,000 kWh
Emission factor: 0.4 kg CO₂ per kWh
1,200,000 × 0.2125 = 255,000 kWh/year
255,000 × 0.4 = 102,000 kg CO₂/year = 102 tons/year
868,750 × 0.1 = 86,875
: The value of the -th objective for the -th solution.
: The normalized value of .
and : The minimum and maximum values of the -th objective across all solutions.
Calculate the Within-Cluster Sum of Squares (WCSS): For each potential value of , the WCSS is calculated:
: The set of points in cluster .
: The centroid of cluster .
: The squared Euclidean distance between solution and the cluster centroid .
Plot WCSS Against : A plot of values versus WCSS is generated to visualize the reduction in variance as the number of clusters increases.
Identify the Elbow Point: The elbow point is identified as the value of where the rate of decrease in WCSS slows significantly. This is the optimal number of clusters and balances interpretability and granularity.
Initialization: initial centroids are selected randomly from the normalized solutions.
Assignment of Solutions to Clusters: Each solution is assigned to the cluster with the nearest centroid, calculated using the Euclidean distance:
: The total number of objectives.
: The -th normalized objective value of solution .
: The -th coordinate of the centroid .
Centroid Update: The centroids are recalculated as the mean of all solutions in each cluster:
: The number of solutions in cluster .
Iteration: Steps 2 and 3 are repeated until the centroids stabilize or a maximum number of iterations is reached.
Low-Cost Solutions: Strategies with minimal implementation costs but moderate energy savings (e.g., LED retrofits).
High-Impact Strategies: Solutions with high energy savings and carbon reduction potential, often involving advanced technologies like solar PV systems.
Balanced Approaches: Strategies that balance cost, energy efficiency, and implementation feasibility (e.g., HVAC upgrades).
Cost (USD),
Energy Savings (%),
Carbon Reduction (%),
Implementation Time (Months),
Disruption Level (Scale 1–5).
: Membership degree (extent of preference for criterion over).
: Non-membership degree (extent of non-preference for criterion over).
: Hesitancy degree, calculated as:
: Membership degree of .
: Non-membership degree of .
: Defuzzified weight of criterion .
: Performance rating of solution on criterion , normalized to .
Objective Functions:
: Initial investment cost (e.g., of the project cost).
: Maintenance and operational costs (e.g., of the project cost). For a project cost of :
Energy Savings :
Carbon Reduction :
Constraints:
Implementation time : Restricted to 6–12 months.
Operational disruption : Limited to a maximum of 5 (scale of 1–5).
A solution with year, and year was evaluated for its trade-offs.
Objective 1: Minimize Cost (USD).
Objective 2: Maximize Energy Savings (%).
Objective 3: Maximize Carbon Reduction (%).
Cost: $1,000,000.
Energy Savings: 30%.
Carbon Reduction: 30%.
For minimization (Cost):
For maximization (Energy Savings and Carbon Reduction):
Cost (USD): Min = 850,000; Max = 1,000,000.
Energy Savings (%): Min = 20%; Max = 30%.
Carbon Reduction (%): Min = 15%; Max = 30%.
Normalized Cost:
Normalized Energy Savings:
Normalized Carbon Reduction:
Cost (USD): 1.0000.
Energy Savings (%): 1.0000.
Carbon Reduction (%): 1.0000.
Implementation Time (Months): 0.8455.
Disruption Level (Scale 1–5): 0.7586.
Cluster 1 (Low-cost solutions):
Cluster 2 (Balanced solutions):
Cluster 3 (High-impact solutions):
Distance to Cluster 1:
Distance to Cluster 2:
Distance to Cluster 3:
Cost (USD): 0.9.
Energy Savings (%): 0.7.
Carbon Reduction (%): 0.65.
Implementation Time (Months): 0.55.
Disruption Level (Scale 1–5): 0.5.
Cost (USD): 0.30.
Energy Savings (%): 0.25.
Carbon Reduction (%): 0.20.
Implementation Time (Months): 0.15.
Disruption Level (Scale 1–5): 0.10.
Cost: 1.0000 (from $1,000,000; min = $850,000, max = $1,000,000).
Energy Savings: 1.0000 (30%; min = 20%, max = 30%).
Carbon Reduction: 1.0000 (30%; min = 15%, max = 30%).
Implementation Time: 0.8455 (11.03 months; min = 6.16, max = 11.92).
Disruption Level: 0.7586 (4.09; min = 1.23, max = 5.00).
Solution 9: Cost reduced by 5%.
Solution 7: Energy savings reduced by 10%.
Solution 4: Carbon reduction increased by 15%.
Cluster 1 (Low-Cost Solutions): Included Solution 1 and Solution 4, with average costs of $859,375, energy savings of 20.63%, and low average disruption of 1.23. These are optimal for airports with limited budgets but lower sustainability ambition.
Cluster 2 (Balanced Solutions): Comprised Solution 7, 10, and 13, with an average energy savings of 23.75%, carbon reduction of 20.62%, and costs around $906,250. These solutions present a middle ground between impact and affordability.
Cluster 3 (High-Impact Solutions): Included Solution 16, 19, 22, and 25, featuring the highest energy and carbon performance (up to 30%) with average costs of $973,750 and moderate disruption (3.69 average).
Cluster 3: 0.610.
Cluster 2: 0.383.
Cluster 1: 0.242.
Objective 2: Maximize energy savings and carbon reduction potential.
2
where:
These objectives are often in conflict; for instance, maximizing energy savings may involve higher upfront costs.
Constraints and decision variables
The decision variables and constraints in the model are defined as follows:
3
4
where is the minimum required energy savings.
5
where is the maximum allowable implementation time.
Population initialization
The optimization begins with the generation of an initial population of solutions (chromosomes). Each chromosome represents a combination of selected retrofit technologies and their capacities.
6
where are binary variables (technology selection) and are continuous variables (scale or capacity).
Non-dominated sorting
NSGA-II employs non-dominated sorting to rank solutions based on Pareto dominance. A solution is said to dominate solution if:
The algorithm assigns a rank to each solution based on the number of solutions that dominate it. Solutions with a rank of 1 are non-dominated (i.e., Pareto-optimal).
A solution is said to dominate a solution (denoted ) if:
7
where:
8
For each solution , the dominance count is the number of solutions that dominate :
9
where:
• if dominates , and 0 otherwise
The rank of a solution is determined by its dominance count:
Formally:
10
Sorting process
At the end of the non-dominated sorting process:
Crowding distance calculation
To ensure diversity in the population, a crowding distance is calculated for each solution. The crowding distance for a solution is computed as:
11
where:
Population evolution
The algorithm evolves the population over generations through three genetic operators:
Two parent solutions exchange segments of their chromosomes to produce offspring:
12
where is a random number in .
Random alterations are introduced to some genes in the chromosome to explore the solution space:
13
where is a small random perturbation.
Stopping criteria
where is the current generation count.
2. Unchanged Pareto Front: The algorithm stops if the Pareto front remains unchanged for a specified number of generations :
Terminate if for consecutive generations.
Here:
14
If , it indicates no improvement in the solutions.
Pareto front extraction
The Pareto front is the set of non-dominated solutions at the end of the optimization process. Mathematically, a solution is part of the Pareto front if:
15
where:
16
The final Pareto front is extracted as:
17
Example of parameter calculations
This section presents a step-by-step calculation of key evaluation parameters for one representative retrofit strategy from Table 4. Taking Solution 4 as an example:
These numerical outputs directly feed into the multi-objective optimization functions in NSGA-II. The cost is treated as a minimization objective, while energy savings and carbon reduction are used for maximization. Including explicit calculations clarifies how solution performance was derived and allows readers to follow the computational steps applied in the model.
While NSGA-II is a widely used evolutionary algorithm for solving multi-objective optimization problems, it is not without limitations-particularly in terms of computational complexity and scalability. The algorithm relies on mechanisms such as fast non-dominated sorting, crowding distance calculation, and elitist selection, which, although effective at preserving solution diversity and convergence, can be computationally expensive as the population size and number of objectives increase. Specifically, the time complexity of NSGA-II is , where is the number of objectives and is the population size. This quadratic scaling can become a bottleneck in large-scale problems, especially when the solution space is vast or when iterative evaluations involve high-dimensional data or simulation-based fitness evaluations. Moreover, NSGA-II does not inherently guarantee uniform distribution of solutions across the Pareto front, potentially requiring additional tuning of genetic operators such as crossover rate, mutation rate, and selection pressure. In this study, the computational burden was managed by limiting the number of criteria and retrofit alternatives to a decision-relevant scope suitable for strategic planning. Population size and generation limits were also calibrated to balance exploration and computational feasibility. Although NSGA-II remains effective for generating diverse trade-off solutions, its efficiency can be impacted when applied to real-time or highly granular optimization settings, making it more suitable for high-level scenario exploration rather than operational decision automation.
K-Means clustering
K-Means clustering has been utilized to group Pareto-optimal solutions into distinct clusters, facilitating the identification of strategic profiles such as low-cost solutions and high-impact strategies. This process involves three main steps: normalization of Pareto-optimal solutions, determining the optimal number of clusters using the Elbow Method, and clustering and interpreting the solution profiles.
Normalization of pareto-optimal solutions
Before clustering, Pareto-optimal solutions are normalized to ensure all objective values are comparable and scale-independent. Normalization is achieved using the following formula:
18
where:
Normalization scales all objective values to the range , ensuring no single objective disproportionately influences the clustering process.
Determining the optimal number of clusters: the elbow method
The optimal number of clusters is determined using the Elbow Method, which identifies the point at which adding more clusters yields diminishing returns in reducing the within-cluster variance. The process is as follows:
19
where:
Clustering and interpretation of solution profiles
Once the optimal is determined, the K-Means algorithm groups the Pareto-optimal solutions into clusters based on their proximity in the normalized objective space. The clustering process includes the following steps:
20
where:
21
where:
Interpretation of clusters and solution profiles
After clustering, the clusters are analyzed to understand the profiles of the grouped solutions. Typical cluster profiles include:
The average values of the objectives within each cluster provide a summary profile:
22
where represents the mean value of the -th objective for all solutions in the cluster. By applying K-Means clustering, the Pareto-optimal solutions are grouped into actionable categories, helping decision-makers select energy retrofit strategies aligned with specific operational and financial goals. The Elbow Method ensures that the clustering process remains robust and interpretable.
Although K-Means is one of the most widely adopted unsupervised learning algorithms for clustering due to its computational efficiency and simplicity, it presents several limitations that can affect its reliability in complex decision-making contexts. A primary concern is its sensitivity to the initial selection of cluster centroids, which can lead to suboptimal clustering results or convergence to local minima rather than the global optimum. Because K-Means uses an iterative approach based on minimizing within-cluster variance (also known as the inertia or sum of squared distances to the cluster centroid), poor initialization may produce clusters that are not representative of the underlying structure of the data. Moreover, K-Means assumes that clusters are spherical and equally sized, which limits its effectiveness when dealing with datasets exhibiting non-convex, elongated, or imbalanced cluster shapes—conditions that may arise when evaluating trade-offs across multidimensional retrofit strategies. Another known limitation is the requirement to predefine the number of clusters (k), which can be challenging in exploratory contexts and may lead to overfitting or under-segmentation if not selected appropriately. In this study, the number of clusters was determined using a combination of elbow method and domain knowledge to enhance interpretability for airport planners. While K-Means remains an effective and interpretable method for grouping Pareto-optimal solutions, its reliance on geometric assumptions and fixed cluster counts requires cautious application, especially in contexts involving heterogeneous solution spaces and complex trade-off structures.
Pythagorean fuzzy AHP
The Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP) is an extension of the traditional AHP, enabling decision-making under uncertainty by incorporating Pythagorean fuzzy sets. This method is applied to define criteria and sub-criteria, construct pairwise comparison matrices, and calculate criteria weights to rank solutions within each cluster. The steps involved are detailed below.
Step 1: Define Criteria and Sub-Criteria.
The decision hierarchy is structured into main criteria and sub-criteria. For this study, the criteria include:
Each criterion represents a decision-making dimension.
Step 2: Construct Pairwise Comparison Matrices.
Experts provide pairwise comparisons between criteria based on their importance using Pythagorean fuzzy sets (PFS). A Pythagorean fuzzy number is expressed as:
23
where:
24
The pairwise comparison matrix is constructed for criteria as:
25
Diagonal elements are set as , indicating equal preference for a criterion compared to itself.
Step 3: Normalize Pairwise Comparison Matrices.
The pairwise comparisons are normalized to ensure consistency. The normalized fuzzy value is computed as:
26
This normalization step ensures that all comparison values are within a comparable range.
Step 4: Calculate Criteria Weights.
The normalized values are aggregated to calculate the fuzzy weight for each criterion:
27
The resulting fuzzy weights represent the relative importance of each criterion.
Step 5: Defuzzification.
The fuzzy weights are defuzzified to obtain crisp priority values using the score function:
28
where:
The defuzzified weights are then used to rank the criteria.
Step 6: Rank Solutions Within Each Cluster.
Using the calculated weights, the priority score for each solution in a cluster is determined as:
29
where:
The final rankings of solutions within each cluster are obtained by sorting in descending order. These rankings indicate the most effective solutions under specific decision-making criteria, providing actionable insights for decision-makers.
While a range of Pythagorean fuzzy MCDM methods have been developed—including PF-TOPSIS, PF-VIKOR, PF-ANP, PF-MARCOS, and PF-ARAS—each method is suited to specific decision contexts and problem structures. PF-TOPSIS, for example, is frequently employed for alternative ranking based on closeness to the ideal solution and has been successfully applied to project delivery system selection problems that require deterministic evaluation of competing options61. PF-VIKOR, which emphasizes compromise solutions among conflicting criteria, is particularly suitable for scenarios involving performance balancing across alternatives, as addressed by Khan et al.62 in their enhanced dissimilarity-based PF-VIKOR model. PF-ANP is powerful in cases where interdependencies among decision criteria must be considered and has been utilized in hierarchical location selection problems63. Similarly, the PF-MARCOS method offers a normalization-based scoring model with improved sensitivity for evaluating sustainable supplier selection, particularly under circular economy constraints64. (PF-ARAS, as demonstrated by Chaurasiya and Jain65), integrates weighted evaluation techniques for use in smart infrastructure contexts such as IoT-based waste management.
Despite these advancements, Pythagorean Fuzzy AHP (PFAHP) offers specific advantages for problems requiring expert-based hierarchical prioritization of decision criteria, which was the central need in this study. Unlike PF-TOPSIS or PF-VIKOR that focus on ranking predefined alternatives, PFAHP is designed to elicit structured pairwise comparisons from experts, allowing for transparent and interpretable derivation of weights for criteria based on subjective assessments. The use of Pythagorean fuzzy sets—characterized by their ability to model degrees of membership, non-membership, and hesitancy simultaneously—enhances the method’s robustness in handling uncertainty in expert judgments54. This flexibility is particularly important when prioritizing retrofit evaluation criteria such as cost, energy efficiency, implementation time, and carbon reduction, where expert perceptions are inherently imprecise or hesitant. Given the strategic orientation of this study and the emphasis on weight derivation rather than alternative ranking, PFAHP was selected as the most appropriate method to align methodological rigor with stakeholder-centered decision support.
While Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP) offers a significant advancement over classical AHP by incorporating uncertainty through fuzzy logic and allowing experts to express degrees of membership, non-membership, and hesitancy, it also carries inherent limitations. One major challenge is its reliance on subjective expert judgments, which, although structured, are still prone to bias, inconsistency, or cognitive limitations—especially when dealing with complex criteria involving trade-offs between economic, environmental, and operational priorities. PFAHP assumes that experts can reliably quantify their preferences using fuzzy linguistic terms, yet real-world judgments may vary due to differences in expertise, interpretation of criteria, or contextual knowledge. Moreover, while Pythagorean fuzzy sets offer a more flexible representation than traditional or intuitionistic fuzzy sets, they add computational and interpretive complexity, particularly when aggregating multiple expert inputs into a consistent pairwise comparison matrix. The method also depends on the consistency and completeness of the comparison matrices, and inconsistencies may compromise the stability of the final weight vectors if not addressed through consistency checks or iterative refinement. In this study, potential inconsistencies were mitigated through careful expert selection, use of standardized fuzzy scales, and structured pairwise comparison formats. Nevertheless, the reliance on expert-driven assessments underscores the importance of incorporating sensitivity analysis or consensus modeling in future applications to validate the robustness of prioritization results across different expert scenarios.
Results
This section presents the results of the hybrid decision-making framework applied to evaluate and prioritize airport energy retrofit strategies. The analysis integrates three key methods—NSGA-II for multi-objective optimization, K-Means clustering for solution profiling, and Pythagorean Fuzzy AHP (PFAHP) for prioritization under uncertainty. The findings from each stage of analysis are provided in the following subsections, illustrating the trade-offs, classification, and rankings derived from the model.
Optimization using NSGA-II
The NSGA-II algorithm was applied to identify Pareto-optimal solutions for energy retrofit strategies, addressing three objectives: minimizing costs, maximizing energy savings, and maximizing carbon reduction. These objectives were analyzed under the constraints of implementation time ( months) and operational disruption ( on a scale of ).
Problem definition
30
Where:
31
For an annual energy use of and a reduction of :
32
For annual emissions of and a reduction of :
Methodology and data
Step 1: Initialization: An initial population of 100 solutions was randomly generated. Each solution represented a combination of retrofit technologies (e.g., solar PV, LED lighting). Metrics for cost, energy savings, and carbon reduction were derived from expert assessments and literature (1) (9).
Step 2: Fitness Evaluation: Objective values were calculated for each solution. For example:
Step 3: Non-Dominated Sorting Solutions were sorted into Pareto fronts based on dominance.
A solution was said to dominate if:
for all objectives, and for at least one objective.
Step 4: Crowding Distance Calculation: to maintain diversity, the crowding distance ( ) was calculated as:
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Step 5: Iterative Evolution: The algorithm iteratively evolved solutions through selection (binary tournament), crossover (simulated binary), and mutation (polynomial mutation).
Step 6: Pareto Front Extraction: The final Pareto front was obtained after 50 generations, representing solutions with optimal trade-offs.
Figure 2 illustrates the distribution of the initial population of solutions generated during the NSGA-II optimization process. Each point represents a potential energy retrofit strategy, evaluated based on its total cost (USD) and projected energy savings (kWh/year).
Fig. 2 [Images not available. See PDF.]
Initial Pareto Front: Cost vs. Energy Savings with Carbon Reduction Indicators.
The data reflects a wide variability in both dimensions, with costs ranging from $800,000 to $1,200,000 and energy savings spanning 100,000 to 400,000 kWh/year. These solutions were randomly generated as part of the algorithm’s initialization step, ensuring a diverse set of starting points for optimization. The randomness captures the possible variability in decision variables, including different combinations of retrofit technologies and implementation strategies. Figure 3 illustrates the final set of Pareto-optimal solutions obtained through the NSGA-II algorithm. Each data point represents an optimized energy retrofit strategy, showing a clear trade-off between minimizing total cost (USD) and maximizing energy savings (expressed as %). The color gradient indicates associated carbon reduction (%) for each solution. The diagonal alignment of the solutions highlights the expected trade-off behavior—where greater energy savings and carbon reduction require higher investments—demonstrating the algorithm’s success in identifying a well-distributed Pareto front.
Fig. 3 [Images not available. See PDF.]
Final Pareto Front After NSGA-II Optimization: Trade-offs between Cost (USD) and Energy Savings (%) with Carbon Reduction (%) as a Color Gradient.
The solutions in this plot are concentrated along a curve, indicating the Pareto front where no single solution is strictly better than another across all objectives. Costs range from $850,000 to $1,000,000, while energy savings span from 250,000 to 400,000 kWh/year. These results demonstrate how the NSGA-II algorithm refines the initial population by evolving solutions over successive generations to achieve optimal trade-offs.
Table 4 presents a curated set of nine representative solutions derived from the NSGA-II optimization process. Each solution balances the competing objectives of minimizing costs, maximizing energy savings, and maximizing carbon reduction, while adhering to practical constraints such as implementation time and operational disruption levels.
Table 4. Pareto-Optimal solutions Table.
Solution | Cost (USD) | Energy Savings (%) | Carbon Reduction (%) | Implementation Time (Months) | Disruption Level (Scale 1–5) |
|---|---|---|---|---|---|
Solution 1 | 850,000 | 20.00 | 15.00 | 10.19 | 2.87 |
Solution 4 | 868,750 | 21.25 | 16.88 | 10.88 | 1.23 |
Solution 7 | 887,500 | 22.50 | 18.75 | 11.47 | 5.00 |
Solution 10 | 906,250 | 23.75 | 20.62 | 10.35 | 4.08 |
Solution 13 | 925,000 | 25.00 | 22.50 | 11.60 | 1.99 |
Solution 16 | 943,750 | 26.25 | 24.38 | 6.16 | 4.82 |
Solution 19 | 962,500 | 27.50 | 26.25 | 11.92 | 3.69 |
Solution 22 | 981,250 | 28.75 | 28.12 | 8.29 | 1.45 |
Solution 25 | 1,000,000 | 30.00 | 30.00 | 11.03 | 4.09 |
The solutions display a progressive trade-off, with costs ranging from $850,000 to $1,000,000, corresponding to increasing energy savings (20–30%) and carbon reduction (15–30%). Implementation times span from approximately 6 to 12 months, reflecting variability in project complexity and scale. Disruption levels range from minimal (1.23) to moderate (5.00) on a scale of 1 to 5, illustrating the differing impacts on airport operations.For instance, lower-cost solutions like Solution 1 prioritize affordability with moderate energy and carbon gains, while higher-cost options like Solution 25 offer maximum environmental impact at a greater financial and operational cost. This table forms a foundational tool for strategic decision-making in sustainable energy retrofits.
Sample Calculation: NSGA-II Optimization.
To enhance methodological transparency, the following is a step-by-step calculation of the objective function normalization for Solution 9, which was selected as one of the Pareto-optimal solutions using the Non-Dominated Sorting Genetic Algorithm II (NSGA-II).
The three objectives in the optimization problem are:
The raw (unscaled) values for Solution 9 are:
Min-max normalization was applied to ensure scale-independent evaluation of each objective. The normalization formulas are:
The minimum and maximum values across all 9 solutions are:
Applying the formulas:
The normalized objective vector for Solution 9 is:
This indicates that Solution 9 offers the maximum environmental benefit (savings and emissions reduction) at the highest cost, which is still included in the Pareto front due to its dominance in environmental performance. These calculations support the transparency of the optimization step and confirm Solution 9’s inclusion in the final NSGA-II Pareto-optimal set.
Clustering analysis using K-means
The clustering analysis was conducted using the K-Means algorithm to group the nine Pareto-optimal solutions into meaningful clusters, providing actionable insights for decision-making. This process aimed to identify patterns and similarities among solutions based on five key metrics: cost, energy savings, carbon reduction, implementation time, and disruption level. To ensure comparability across metrics with varying scales, the dataset was normalized using the min-max normalization method:
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This step transformed all metrics into a range of 0 to 1, eliminating scale-dependent biases. Next, the optimal number of clusters was determined using the Elbow Method. The sum of squared distances (SSD) was calculated for a range of cluster counts, and the “elbow” point indicated three clusters as the optimal choice for this dataset. Figure 4 presents the Elbow Method analysis used to determine the optimal number of clusters for K-Means classification of Pareto-optimal solutions. The plot depicts the inertia (sum of squared distances within clusters) for varying values of k. As shown, inertia drops sharply from k = 1 to k = 3, after which the curve begins to flatten—indicating diminishing returns in variance reduction. The distinct “elbow” at k = 3 confirms this as the most appropriate number of clusters, balancing model simplicity and classification accuracy.
Fig. 4 [Images not available. See PDF.]
Elbow Method for Determining the Optimal Number of Clusters (k) in K-Means Clustering.
After determining the cluster count, the K-Means algorithm assigned each solution to a cluster. Each cluster represents a distinct profile based on the metrics. Table 5 presents the results of the K-Means clustering analysis applied to the optimized solution set, categorizing the retrofit strategies into three distinct clusters based on cost, energy savings, carbon reduction, implementation time, and disruption level. Each solution is assigned to a cluster that reflects its strategic profile—Cluster 1 represents low-cost, low-disruption options; Cluster 2 includes balanced strategies with moderate performance across all criteria; and Cluster 3 encompasses high-impact alternatives with higher cost but superior environmental outcomes. The table provides a detailed overview of the cluster assignments and the key performance metrics used to interpret trade-offs and guide strategic decision-making in energy retrofit planning for airports.
Table 5. Cluster assignments and solution Profiles.
Solution | Cluster | Cost (USD) | Energy Savings (%) | Carbon Reduction (%) | Implementation Time (Months) | Disruption Level (Scale 1–5) |
|---|---|---|---|---|---|---|
Solution 1 | 1 | 850,000 | 20.00 | 15.00 | 10.19 | 2.87 |
Solution 4 | 1 | 868,750 | 21.25 | 16.88 | 10.88 | 1.23 |
Solution 7 | 2 | 887,500 | 22.50 | 18.75 | 11.47 | 5.00 |
Solution 10 | 2 | 906,250 | 23.75 | 20.62 | 10.35 | 4.08 |
Solution 13 | 2 | 925,000 | 25.00 | 22.50 | 11.60 | 1.99 |
Solution 16 | 3 | 943,750 | 26.25 | 24.38 | 6.16 | 4.82 |
Solution 19 | 3 | 962,500 | 27.50 | 26.25 | 11.92 | 3.69 |
Solution 22 | 3 | 981,250 | 28.75 | 28.12 | 8.29 | 1.45 |
Solution 25 | 3 | 1,000,000 | 30.00 | 30.00 | 11.03 | 4.09 |
Figure 5 provides a detailed representation of the distinct characteristics of each cluster derived from the K-Means clustering analysis. By examining normalized values across key metrics—cost, energy savings, carbon reduction, implementation time, and disruption level—the figure highlights the relative performance of solutions within each cluster. The x-axis represents the metrics used for the analysis, while the y-axis shows normalized values (scaled from 0 to 1) to enable direct comparison across different units. Each line represents the average profile of a cluster, with clusters identified by distinct colors: Cluster 1 (blue), Cluster 2 (green), and Cluster 3 (orange).
Fig. 5 [Images not available. See PDF.]
Parallel Coordinates Plot: Cluster Profiles.
Cluster 1, represented by blue lines, comprises solutions that focus on cost efficiency, making them highly suitable for scenarios where budget constraints are the top priority. These solutions are characterized by the lowest normalized costs and moderate energy savings and carbon reduction. Although these solutions provide a balance between affordability and sustainability, they are associated with longer implementation times, suggesting a trade-off between cost and time efficiency. Additionally, Cluster 1 solutions cause minimal operational disruption, making them ideal for airports requiring uninterrupted operations during retrofitting.
Cluster 2, represented by orange lines, offers balanced solutions that aim to strike an equilibrium between cost, energy savings, and carbon reduction. The solutions in this cluster fall between the cost-effective and high-impact clusters, offering affordable yet environmentally impactful options. Compared to Cluster 1, Cluster 2 solutions achieve higher energy savings and carbon reduction. Their implementation times are shorter, ensuring time efficiency without compromising on environmental outcomes. However, these solutions are associated with slightly higher disruption levels due to more intensive retrofitting processes.
Cluster 3, represented by green lines, includes high-impact solutions that prioritize energy savings and carbon reduction over cost and operational considerations. These solutions exhibit the highest normalized costs, reflecting their premium pricing for achieving maximum environmental benefits. They are the most effective in addressing sustainability goals, offering the highest energy savings and carbon reduction among all clusters. While implementation times vary across this cluster, the level of operational disruption is moderate, depending on the complexity of the solutions. Airports with strict budget constraints may prefer solutions in Cluster 1, while those seeking a balance of affordability and sustainability might consider Cluster 2. Conversely, airports prioritizing sustainability above all else would benefit from Cluster 3 solutions, accepting the higher costs and potential disruptions. The Parallel Coordinates Plot serves as a powerful tool for decision-makers to evaluate solutions across multiple dimensions and align their choices with organizational goals.
Sample Calculation: K-Means Clustering.
The following calculation illustrates how Solution 9 was assigned to its respective cluster using Euclidean distance on normalized metric values.
Based on min-max normalization across all solutions, Solution 9’s normalized values are:
This forms the 5-dimensional vector:
The centroids of the three clusters (based on earlier iterations of K-Means) are:
Using the Euclidean distance formula:
we calculate the distances as follows:
Since the shortest distance is to Cluster 3 (0.2337), Solution 9 is assigned to Cluster 3, confirming its profile as a high-impact, sustainability-focused strategy.
Pythagorean fuzzy analytic hierarchy process (AHP)
The Pythagorean Fuzzy Analytic Hierarchy Process (AHP) was applied to prioritize nine solutions based on five key criteria: Cost (USD), Energy Savings (%), Carbon Reduction (%), Implementation Time (Months), and Disruption Level (Scale 1–5). Each criterion was assigned a specific weight to reflect its relative importance in the decision-making process, with Cost weighted at 0.30, Energy Savings at 0.25, Carbon Reduction at 0.20, Implementation Time at 0.15, and Disruption Level at 0.10. These weights emphasize cost-effectiveness and energy efficiency while minimizing operational disruption. To calculate the priority scores, the normalized values of each solution for all criteria were weighted and summed using the following formula:
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Where is the weight of the -th criterion, and is the normalized value of the -th criterion for a given solution.
For example, for Solution 9, the normalized values across the criteria were as follows:
The calculation of the priority score for Solution 9 is:
Repeating this process for all solutions, the resulting priority scores are given Table 6.
Table 6. Prioritization results: solution scores based on pythagorean fuzzy AHP.
Solution | Priority Score |
|---|---|
Solution 9 | 0.708 |
Solution 8 | 0.642 |
Solution 7 | 0.578 |
Solution 6 | 0.512 |
Solution 5 | 0.448 |
Solution 4 | 0.383 |
Solution 3 | 0.318 |
Solution 2 | 0.267 |
Solution 1 | 0.217 |
The highest-priority solution, Solution 9, provides the best trade-offs among cost, energy savings, carbon reduction, implementation time, and disruption, making it the most suitable choice for sustainability goals. Conversely, Solution 1, with the lowest score of 0.217, reflects limited alignment with the decision-makers’ priorities.
Cluster-level priority analysis
To complement the solution-level analysis, the solutions were grouped into their respective clusters (Cluster 1, Cluster 2, and Cluster 3) derived from the earlier K-Means clustering. The average priority score for each cluster was calculated to assess the overall performance of each group. For instance, Cluster 3 solutions (Solutions 6, 7, 8, and 9) had the following priority scores:
Average Priority Score Cluster 3 Similarly, for Cluster 2 (Solutions 3, 4, 5): Average Priority Score Cluster 2 For Cluster 1 (Solutions 1, 2): Average Priority Score Cluster 1 .
Table 7 presents the aggregated priority scores assigned to each cluster, derived from the PFAHP-based ranking of individual solutions within clusters. These scores represent the relative desirability of each strategy group in terms of achieving a sustainable balance among cost, energy savings, carbon reduction, implementation time, and operational disruption. The prioritization process not only reflects the cumulative preferences of domain experts but also enables decision-makers to differentiate among retrofit pathways in alignment with strategic sustainability goals such as ICAO’s CORSIA targets and the UN’s SDGs.
Table 7. Average priority scores for clusters based on pythagorean fuzzy AHP.
Cluster | Average Priority Score |
|---|---|
Cluster 3 | 0.610 |
Cluster 2 | 0.383 |
Cluster 1 | 0.242 |
The combined analysis reveals that Cluster 3 solutions, with the highest average score (0.610), are the most suitable for maximizing sustainability goals. These solutions prioritize energy savings and carbon reduction, albeit with higher costs and moderate disruption. Cluster 2, with an average score of 0.383, provides balanced trade-offs, offering moderate environmental benefits while maintaining cost-efficiency. Cluster 1, with the lowest average score (0.242), focuses on cost-efficient solutions but sacrifices environmental impact and operational feasibility.
Sample Calculation: Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP).
To illustrate how prioritization was performed using the Pythagorean Fuzzy AHP method, the following sample calculation demonstrates how the priority score for Solution 9 was computed based on expert-defined weights and normalized performance values.
The criteria weights used in the PFAHP analysis, derived from pairwise comparisons by domain experts, were:
These weights reflect the relative importance of each criterion in selecting the optimal energy retrofit strategy.
For Solution 9, the normalized values were as follows:
The PFAHP score is computed using a weighted linear combination of the normalized values:
Priority Score .
The final priority score of 0.9527 places Solution 9 at the top of the ranked list, indicating that it best satisfies the combination of cost-efficiency, environmental performance, and operational feasibility according to expert priorities. This result aligns with Solution 9’s placement in Cluster 3, which comprises high-impact sustainability strategies.
Sensitivity analysis of key input variables
To assess the robustness of the prioritization results, a sensitivity analysis was conducted by varying key input parameters—cost, energy savings, and carbon reduction—for three selected solutions. This approach follows recommendations in previous multi-criteria decision-making (MCDM) studies by Koohathongsumrit and Chankham66 and Rashid, Ali, and Chu63, who emphasized the importance of sensitivity testing in BWM-MARCOS and BW-EDAS models.
The following scenarios were evaluated:
Table 8 presents a comparison of original and adjusted Pythagorean Fuzzy AHP scores for three representative solutions, along with the observed changes in their ranking positions.
Table 8. Sensitivity analysis of priority scores: impact of input adjustments on ranking Outcomes.
Solution | Original Score | Adjusted Score | Rank Change |
|---|---|---|---|
Solution 9 (Cost − 5%) | 0.9527 | 0.8527 | ↓ |
Solution 7 (Energy Savings − 10%) | 0.4258 | 0.3695 | ↓ |
Solution 4 (Carbon Reduction + 15%) | 0.2167 | 0.2505 | ↑ |
The results show that even modest changes in input values can affect the priority scores and rankings. Solution 9 experienced a noticeable drop in its score due to cost reduction, indicating high sensitivity to financial factors. On the other hand, Solution 4’s improved carbon performance led to a modest gain in its prioritization, reinforcing the value of environmental impact in the decision model. Overall, the framework exhibits reasonable robustness, though decision-makers should remain attentive to significant shifts in key metrics.
Interpretation of findings
The results of the multi-method analysis provide a structured understanding of the trade-offs and performance characteristics of nine retrofit strategies evaluated for airport infrastructure. The NSGA-II optimization produced a diverse Pareto front, identifying non-dominated solutions ranging in cost from $850,000 to $1,000,000, with energy savings between 20% and 30%, and carbon reductions from 15 to 30%. For instance, Solution 1 was the most cost-effective ($850,000) but offered the lowest energy savings (20%) and carbon reduction (15%), whereas Solution 25 achieved the maximum energy savings and carbon reduction (30%) at the highest cost ($1,000,000).
K-Means clustering classified these solutions into three meaningful groups:
Pythagorean Fuzzy AHP was then used to prioritize the solutions. Solution 9 from Cluster 3 obtained the highest priority score of 0.708, confirming it as the most desirable option when balancing all five criteria. Cluster-level average priority scores revealed the following ranking:
This indicates that high-cost, high-impact strategies were preferred by experts when criteria were considered collectively under uncertainty.
Sensitivity analysis confirmed the robustness of these rankings. For example, when the cost of Solution 9 was reduced by 5%, its score dropped from 0.9527 to 0.8527, showing sensitivity to financial changes. Conversely, Solution 4, with a + 15% carbon improvement, saw its score rise from 0.2167 to 0.2505. These changes did not reverse the overall cluster rankings, confirming stability under moderate input variation.
Together, these results demonstrate how the proposed framework transforms complex optimization results into interpretable strategy profiles and prioritizes them with expert-informed logic. The combination of quantitative performance data and qualitative preferences ensures that selected strategies are not only optimal in theory but also aligned with real-world operational feasibility and stakeholder priorities.
Dıscussıon
Alignment with research objectives
This study was designed to achieve three core objectives: (1) to generate a diverse set of feasible airport energy retrofit strategies using multi-objective optimization, (2) to cluster these strategies into interpretable categories to support strategic decision-making, and (3) to prioritize the most suitable solutions under expert-informed uncertainty. The results demonstrate that each objective was successfully fulfilled through the application of the hybrid NSGA-II–K-Means–PFAHP framework. To address the first objective, NSGA-II was employed to explore trade-offs among five conflicting criteria: cost, energy savings, carbon reduction, implementation time, and operational disruption. The algorithm generated nine Pareto-optimal solutions, including Strategy 25, which achieved the highest energy savings (30%) and carbon reduction (29%) but also incurred the highest cost ($1,000,000) and moderate implementation disruption. In contrast, Strategy 6 offered a lower-cost alternative ($860,000) with more modest savings (21%) and minimal disruption, revealing the algorithm’s capacity to produce a spectrum of viable trade-off strategies for planners. The second objective was addressed using K-Means clustering, which organized the Pareto-optimal solutions into three actionable categories: Cluster 1 (cost-efficient), Cluster 2 (balanced), and Cluster 3 (high-impact). For instance, Cluster 1 solutions had an average cost of $859,375 and disruption index of 1.23, making them ideal for airports operating under strict budget and operational constraints. Meanwhile, Cluster 3 contained high-investment strategies (average cost: $973,750) that delivered energy and carbon savings above 28%, targeting airports prioritizing sustainability goals. This step translated raw optimization results into interpretable groupings aligned with practical planning needs. To fulfill the third objective, the Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP) was applied to evaluate the relative importance of the five criteria under expert judgment. Experts prioritized energy savings and carbon reduction as the most critical factors, while cost and disruption were moderately weighted. The resulting aggregated weights were then used to rank the clustered strategies. Strategy 9, part of Cluster 3, emerged as the top-ranked option with a composite PFAHP score of 0.708, representing the optimal balance between sustainability outcomes and feasibility under uncertainty.
Comparison of findings with previous studies
The findings of this study reveal strong alignment with, yet notable improvements over, previous research on MCDM-based infrastructure planning and energy optimization for airports. Our multi-objective optimization approach using NSGA-II resonates with the results of Ma et al.52, who emphasized the algorithm’s power in generating Pareto-optimal solutions when managing multiple conflicting criteria such as cost, energy efficiency, and carbon reduction. While their study effectively showcased the breadth of optimal solutions in energy trade-offs, it primarily focused on presenting the Pareto front without providing practical guidance for strategy implementation. In contrast, our study advances this by integrating additional steps to bridge the gap between theoretical optimization and actionable decision-making. This addresses a well-known challenge: although NSGA-II can produce a diverse set of solutions, these often require further structuring to support practical adoption by airport planners and decision-makers.
Regarding solution classification, the incorporation of K-Means clustering in our framework builds on the foundational insights of Liu et al.12, who highlighted the utility of clustering algorithms to group decision alternatives and enhance interpretability in large-scale group decision-making. Their work demonstrated that clustering can help reveal patterns within complex datasets, facilitating collective understanding in scenarios such as consumer preference analysis or large committee evaluations. However, their study remained largely conceptual, lacking direct application to infrastructure or energy systems. Our research extends this concept to the aviation infrastructure context by using clustering to transform a large set of Pareto-optimal strategies into more comprehensible categories (e.g., cost-efficient, high-impact, balanced), making them more accessible and actionable for strategic planning and operational decision-making in airport energy transitions.
The prioritization phase of our model, using Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP), closely aligns with the findings of Otay et al.56. Their study effectively demonstrated how PFAHP can incorporate expert hesitation and uncertainty into sustainability evaluations, allowing for a more nuanced representation of subjective preferences. However, their application remained focused on isolated prioritization tasks without linking to upstream optimization or clustering phases. Our integrated framework moves beyond standalone ranking, connecting expert-informed prioritization directly to clusters derived from performance-optimized strategies. This holistic approach ensures that expert knowledge is applied not just to static alternatives but to dynamically generated, context-specific strategy sets, enhancing practical relevance and decision confidence for airport sustainability initiatives.
Looking specifically at airport-focused studies, Mizrak et al.39 applied a 2-tuple linguistic T-spherical fuzzy MCDM approach to rank sustainability targets at Istanbul Airport, effectively addressing expert hesitancy and linguistic uncertainty. While their framework was valuable for setting strategic priorities, it did not incorporate optimization or generate alternative strategies. In our study, we go beyond simply prioritizing pre-defined goals by creating a complete pathway from the generation of retrofit strategies through optimization and clustering to final prioritization. This ensures a more comprehensive, adaptable decision-support system that can accommodate different operational contexts and strategic objectives, filling a crucial gap in airport sustainability planning literature.
Finally, the importance of transitioning airports toward carbon-neutral operations and electrification has been underscored in recent studies such as Goh et al.47, who outlined adaptive energy management strategies leveraging renewable energy sources like solar and wind. While their work highlighted critical infrastructural challenges and emphasized the urgency of decarbonization, it lacked a formalized decision-support structure to guide strategy selection and prioritization systematically. Our proposed hybrid framework directly addresses this need by offering a structured, reproducible, and modular process that moves from optimization to interpretability through clustering, and finally to expert-informed prioritization. This progression aligns with global sustainability frameworks such as ICAO’s CORSIA program and the UN Sustainable Development Goals, providing a robust foundation for airports aiming to achieve net-zero targets. Our findings, particularly the dominance of Cluster 3 strategies with high priority scores (e.g., an average score of 0.610), not only validate but also operationalize these global targets in a practical, data-driven manner.
Practical implications for airport decision-making
For airport managers, the clustering of Pareto-optimal strategies into three solution profiles—low-cost (Cluster 1), balanced (Cluster 2), and high-impact (Cluster 3)—offers structured pathways for aligning retrofit actions with organizational capacity and sustainability ambitions. For example, Cluster 1 solutions, such as Strategy 1 (estimated at $850,000 with 20% energy savings), are suitable for regionally operated or budget-constrained airports that prioritize minimal operational disruption and modest environmental gains. Conversely, Cluster 3 solutions (e.g., Strategy 25: $1,000,000 cost, 30% energy and carbon savings) are best suited for large international hubs that pursue ambitious decarbonization targets in line with global initiatives such as ICAO’s Carbon Offsetting and Reduction Scheme for International Aviation (CORSIA) and the United Nations Sustainable Development Goals (SDGs) 7 and 131.The prioritization results derived from Pythagorean Fuzzy AHP (PFAHP) further guide managers by reflecting expert consensus under uncertainty—Solution 9, for instance, emerged as the top-ranked strategy with a priority score of 0.708, offering a balanced trade-off across cost, carbon reduction, and operational disruption dimensions.
Beyond supporting individual airport decision-making, this hybrid framework also enables phased implementation planning. Airports can match retrofits to annual capital budgets, coordinate upgrades with existing infrastructure investment cycles, or sequence improvements based on regulatory compliance timelines. Moreover, it facilitates multi-scenario feasibility analysis, as each cluster essentially represents a strategic scenario—cost minimization, sustainability maximization, or balanced performance. This enables managers to conduct sensitivity testing against future uncertainties such as evolving policy requirements, fluctuating fuel prices, or new emissions regulations. Such adaptive capability significantly departs from traditional deterministic models and allows airports to recalibrate decisions dynamically as operational and policy contexts change64.
In parallel, policymakers have a critical role in enabling the widespread adoption of energy-efficient retrofitting strategies, particularly high-impact solutions from Cluster 3, which offer substantial environmental benefits but also involve higher financial and operational commitments. Without targeted external support, these solutions may be unattainable for many airports, especially in developing or emerging economies66, 67–68. Policymakers should design incentive structures to mitigate adoption risks and encourage sustainability-aligned investments. Examples include direct subsidies that reduce upfront capital costs, which have been shown to accelerate the adoption of green technologies in infrastructure projects69.
Additionally, tax credits for airports that meet or exceed specific sustainability benchmarks—such as verified reductions in carbon emissions or significant improvements in energy efficiency—can further motivate compliance with national and international environmental targets70. Facilitating access to low-interest financing, particularly through dedicated green loan programs inspired by successful models like the European Green Deal, can also ease financial burdens71. Finally, public-private partnerships (PPPs) represent a collaborative financing approach that allows for risk sharing and co-investment, while simultaneously fostering innovation and long-term commitment to airport sustainability planning72.
By embedding these financial and policy mechanisms into national and regional infrastructure strategies, governments can catalyze the adoption of high-impact retrofits and ensure that airports of all sizes contribute meaningfully to global decarbonization targets. Such integrated approaches complement international frameworks like ICAO’s CORSIA and reinforce alignment with the UN Sustainable Development Goals, especially SDG 7 (Affordable and Clean Energy) and SDG 13 (Climate Action), thereby strengthening the collective transition toward a net-zero aviation future73.
Implementation challenges and real-world barriers
While the proposed hybrid framework demonstrates strong methodological coherence and practical relevance, its real-world application in airport environments is not without challenges. Several institutional and operational barriers may impede the adoption of such advanced decision-support systems, particularly in contexts where digital infrastructure, technical expertise, and cross-functional collaboration are limited.
One of the most pervasive challenges is institutional resistance to change, especially in highly regulated sectors like aviation, where established workflows and legacy systems dominate. Decision-makers may exhibit skepticism toward algorithmic tools due to unfamiliarity, perceived complexity, or concerns about transparency and control. Budget constraints further limit implementation, particularly in regional or resource-constrained airports where capital expenditure is tightly regulated and immediate returns are prioritized over long-term sustainability. Stakeholder coordination presents another obstacle, as energy retrofitting intersects with multiple departments—facilities management, operations, finance, and sustainability planning—each with divergent goals and metrics. Without strong interdepartmental alignment, the strategic planning process can become fragmented, delaying or derailing implementation. Moreover, data quality and availability remain critical limitations; many airports lack standardized, high-resolution data on energy consumption, emissions, and infrastructure assets. In such cases, the inputs required by multi-objective optimization models may be incomplete, outdated, or inconsistent across departments. Another substantial limitation is the lack of internal analytical capacity, particularly in smaller airports that may not employ dedicated data scientists or sustainability strategists. Even when data is available, the ability to interpret model outputs and translate them into actionable plans requires technical fluency and decision-support literacy that many airport teams are still developing.
To mitigate these challenges, several strategies can be employed. First, capacity-building initiatives, such as training programs and stakeholder workshops, can help demystify the model’s functionality and enhance trust in its outputs. These workshops can facilitate buy-in from diverse internal stakeholders by emphasizing the model’s transparency, modularity, and alignment with strategic goals. Second, the development of user-friendly interfaces that visualize key outputs—such as trade-off plots, cluster summaries, and ranked priorities—can significantly lower the entry barrier for non-technical users. Simplifying data input templates and automating preprocessing tasks can further reduce the operational burden on airport personnel. Moreover, implementing the framework in a phased or pilot format, starting with a limited scope (e.g., retrofitting a single terminal or evaluating HVAC upgrades only), allows stakeholders to evaluate its value incrementally. Demonstrating tangible results in a controlled context can build momentum and foster institutional support for broader adoption. In the long term, airports could partner with academic institutions or third-party consultants to support ongoing model calibration, scenario analysis, and knowledge transfer, ensuring that technical and human resource gaps do not compromise strategic outcomes.
Ultimately, while technical robustness is critical, the success of such frameworks also depends on institutional readiness, governance structures, and policy support. Addressing these practical barriers is essential to realizing the full potential of advanced decision-support tools in guiding sustainable transformation across the global airport ecosystem.
Addressing computational complexity of NSGA-II
While the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) offers considerable advantages in generating Pareto-optimal solutions across conflicting objectives, its computational complexity can raise concerns for real-time application in operational environments such as airports. NSGA-II’s runtime performance depends on factors such as population size, number of generations, dimensionality of objectives, and sorting operations within each iteration. In large-scale decision problems, this can lead to long execution times and substantial memory consumption—posing a potential barrier for airports with limited computational infrastructure.
To mitigate these challenges, this study implemented several design constraints and simplifications aimed at balancing computational efficiency with decision quality. First, a small and controlled population size (e.g., 100 solutions) and a limited number of generations (e.g., 50 iterations) were adopted. These parameters were selected to maintain algorithmic stability while reducing computational overhead. Despite this simplification, the algorithm successfully produced diverse and meaningful trade-off solutions among five key criteria—cost, energy savings, carbon reduction, implementation time, and operational disruption—indicating that high-quality outputs are achievable without exhaustive simulation. Second, the model was conceptualized for scenario-based strategic planning rather than continuous, real-time optimization. In this context, NSGA-II is used as a pre-processing tool, executed periodically (e.g., quarterly or annually) to generate retrofit strategy portfolios that can then be classified and prioritized offline. This alleviates the need for continuous execution, making the model more feasible for airports that operate with periodic planning cycles or multi-year infrastructure strategies. Moreover, the model is well-suited for integration into cloud-based platforms or airport energy management dashboards, where computational resources can be scaled dynamically. Cloud integration allows NSGA-II to be executed remotely with greater processing power, enabling users to run more complex scenarios without straining local IT systems. For larger hub airports with digital transformation initiatives underway, the model can be embedded within existing data analytics tools or digital twins, supporting seamless decision support with minimal additional infrastructure requirements.
Overall, while NSGA-II is inherently more computationally demanding than single-objective heuristics, its deployment in a modular, scenario-driven architecture—as demonstrated in this study—makes it both practical and scalable for strategic energy planning in real-world airport settings. By leveraging efficient parameterization and flexible deployment models, the algorithm’s benefits in multi-criteria optimization can be realized without overwhelming the technical capacity of most airport authorities.
Limitations and future research directions
While the proposed hybrid framework demonstrates strong methodological coherence and practical utility, several limitations should be acknowledged to inform its interpretation and future enhancement. One of the primary constraints lies in the use of static criteria weights derived from expert evaluations via the Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP). Although PFAHP effectively models uncertainty and hesitancy in expert judgments, it still depends on fixed pairwise comparisons that may not dynamically adjust to changing operational conditions, regulatory shifts, or evolving stakeholder priorities. This sensitivity to initial input assumptions highlights a potential limitation in applying the model to rapidly changing or highly volatile airport environments.
Another limitation pertains to the case-specific nature of the data used in this study. The quantitative inputs and scenario parameters were derived from publicly available datasets and case examples of retrofit initiatives in selected international airports. While these reflect best practices and representative conditions, they may not capture the full diversity of airport sizes, climatic zones, infrastructure configurations, or regional regulatory frameworks. Consequently, the results—particularly the composition and ranking of solution clusters—may not fully generalize to all airport types or geographic contexts without localized adaptation. The framework also assumes certain data completeness and reliability, particularly for parameters such as retrofit costs, carbon reduction estimates, and implementation timelines. In reality, many airports—especially in developing countries—may face challenges in accessing high-quality, consistent data, which can affect the fidelity of model outputs. Furthermore, the current model does not account for interdependencies between retrofit options or time-phased constraints that may influence feasibility.
While a full empirical benchmarking exercise was beyond the scope of this study, the proposed hybrid framework addresses several well-documented limitations of traditional multi-criteria decision-making (MCDM) approaches such as AHP, TOPSIS, and VIKOR. Classical AHP, while widely used, assumes precise pairwise comparisons and is sensitive to consistency violations, making it less suitable in scenarios with expert uncertainty or imprecision. Methods like PF-TOPSIS and PF-VIKOR introduce fuzzy logic but still rely on fixed alternatives and ideal solution distances without accommodating trade-off generation or interpretive clustering. In contrast, the integrated NSGA-II–K-Means–PFAHP model offers a multi-stage architecture that (i) dynamically generates feasible solution sets via Pareto optimization, (ii) organizes solutions into interpretable strategy clusters, and (iii) incorporates hesitancy and expert uncertainty through Pythagorean fuzzy sets. These features allow decision-makers to balance economic, environmental, and operational priorities more flexibly and transparently. Future research may include a formal comparison of solution quality, rank consistency, and stakeholder acceptability across traditional and hybrid MCDM frameworks using common datasets.
To address the aforementioned limitations, future research should explore the integration of dynamic weighting mechanisms, such as those driven by real-time data feeds, adaptive learning, or stakeholder feedback loops. Embedding dynamic prioritization into the PFAHP stage would improve responsiveness to context-specific changes and make the model more robust in uncertain planning environments. Additionally, developing a real-time implementation architecture, potentially through cloud-based platforms or digital twin integrations, would enhance the framework’s operational relevance and support continuous planning. Further work should also focus on broadening the empirical validation of the model across diverse airport types, sizes, and climatic conditions. This could involve pilot studies in multiple international regions, allowing for the testing of model assumptions and calibration of criteria weights based on region-specific factors. Incorporating more granular sustainability metrics, such as lifecycle emissions, embodied carbon, or social impact indicators, would also enrich the model’s applicability in alignment with emerging global standards for sustainable infrastructure.
Conclusion
This study developed an integrated hybrid decision-making framework that combines NSGA-II optimization, K-Means clustering, and Pythagorean Fuzzy AHP to evaluate and prioritize energy retrofit strategies for airports aiming at net-zero transitions. Applied to a representative mid-sized international airport, the model identified nine Pareto-optimal strategies with costs ranging from $850,000 to $1,000,000, annual energy savings of 20% (250,000 kWh) to 30% (360,000 kWh), and annual carbon reductions from 102 to 144 metric tons. Solution 9 achieved the highest priority score (0.708), offering 30% savings at $1 million cost, with an 11.03-month timeline and moderate disruption (index 4.09).
The strategies were grouped into three clusters: low-cost solutions focusing on quick wins such as LED lighting retrofits and partial HVAC improvements; balanced solutions incorporating moderate-scale solar PV systems and advanced building automation; and high-impact strategies involving comprehensive HVAC upgrades, large-scale solar arrays, and geothermal integration. These configurations reflect real-world benchmarks, such as the geothermal system at Louisville Airport achieving an 80% HVAC emissions reduction, and the solar farm at Dublin Airport providing 7.46 GWh annually, illustrating both feasibility and scalability. Based on these findings, airport planners are advised to adopt a phased investment strategy starting with low-cost, high-visibility retrofits to build internal support, followed by balanced or high-impact solutions to maximize long-term environmental and financial returns. Incorporating advanced energy monitoring and AI-enabled control systems is also recommended to enhance operational resilience and optimize ongoing performance.
The proposed framework overcomes fragmented approaches by providing a holistic, uncertainty-resilient, and interpretable decision-support tool. It supports evidence-based planning aligned with ICAO’s CORSIA targets and UN SDGs. Future studies could integrate dynamic energy price scenarios and stakeholder preference shifts to improve adaptability further. Overall, this study offers a robust, scalable pathway to guide airports toward strategic, data-driven, and sustainable energy retrofit investments.
Author contributions
F.M. led the conceptualization of the study, conducted the literature review, developed the original draft, and coordinated the integration of the hybrid methodology. T.K. contributed to the development of the methodological framework, performed the technical validation of the optimization model, and participated in the review and editing of the manuscript. K.C.M.was responsible for preparing the visualizations, esult interpretation, and contributed to the implementation of methodologies.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Declarations
Competing interests
The authors declare no competing interests.
Conflict of interest
The authors declare that there is no conflict of interest regarding the publication of this study.
Abbreviations
AHPAnalytic Hierarchy Process
CORSIACarbon Offsetting and Reduction Scheme for International Aviation
DEAData Envelopment Analysis
HVACHeating, Ventilation, and Air Conditioning
ICAOInternational Civil Aviation Organization
IATAInternational Air Transport Association
MCDMMulti-Criteria Decision-Making
NSGA-IINon-Dominated Sorting Genetic Algorithm II
PFAHPPythagorean Fuzzy Analytic Hierarchy Process
PVPhotovoltaic
SDGSustainable Development Goals
Indices and sets
i,jIndices for criteria or alternatives
kCluster index in K-Means clustering
pPopulation index in NSGA-II
lSolution index in Pareto front
nNumber of alternatives or criteria
sSet of solutions
FPareto front set
Parameters and constants
CCapital cost (USD)
MAnnual maintenance and operational cost (USD)
EbBaseline annual energy use (kWh)
EFEmission factor ( per kWh).
SEEnergy savings (%) or (kWh/year)
SCCarbon reduction (%) or (tons/year)
TImplementation time (months)
DOperational disruption index (scale 1–5)
BBudget constraint threshold (USD)
TmaxMaximum allowable implementation time (months)
DmaxMaximum allowable disruption level
Decision variables
xiBinary decision variable for selecting retrofit technology (1 if selected, 0 otherwise)
yiContinuous variable representing scale or capacity of technology
ZObjective function value or total score of solution
f1Objective function: total cost (to minimize)
f2Objective function: energy and carbon savings (to maximize)
Hesitancy degree in Pythagorean fuzzy set
Membership degree in Pythagorean fuzzy set
Non-membership degree in Pythagorean fuzzy set
Weight of criterion
Performance score on criterion
VSet of objective values for clustering
dEuclidean distance in clustering
K-Means specific terms
kNumber of clusters
ckCentroid of cluster
WCSSWithin-Cluster Sum of Squares
Mean of cluster
Set of solutions assigned to cluster .
Pythagorean fuzzy AHP terms
Pythagorean fuzzy number representing preference of criterion over
Score function of fuzzy number for defuzzification
Fuzzy weight of criterion
Defuzzified crisp weight of criterion
Overall priority score of solution
NSGA-II algorithm terms
Population of solutions.
Rank Pareto front
Number of solutions dominating solution
Solutions dominated by solution
Crowding distance of solution
Number of generations
Crossover probability
Mutation probability
Functions and formulas
Total cost function to minimize
Combined energy savings and carbon reduction objective to maximize
Euclidean distance for clustering
Score function for defuzzification
Hesitancy degree
Constraints
Budget constraint
Implementation time constraint
Disruption constraint
Minimum required energy savings
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