Hybridization of metaheuristic algorithms for resource scheduling in distributed robotic control system

Abstract

This paper presents a novel Distributed Blockchain-Assisted Secure Data Aggregation (Block-DSD) scheme designed to enhance data security, energy efficiency, and scalability in Mobile Ad-hoc Networks (MANETs) for disaster-resilient communication systems (DRCS). The proposed framework integrates an Artificial Neuro-Fuzzy Inference System (ANFIS) for dynamic cluster head selection, ensuring adaptive decision-making based on residual energy, trust value, and centrality metrics. Additionally, the Improved Elephant Herd Optimization (IEHO) algorithm is employed for optimal route selection, leveraging genetic operators to enhance exploration and exploitation capabilities. Blockchain technology is utilized to secure data aggregation through a Secure Two-Step (STS) method and Elliptic Curve Cryptography (ECC), ensuring tamper-proof and reliable data transmission. Simulations conducted using ns-3.25 demonstrate superior performance, with a 97% Packet Delivery Ratio (PDR), 20% reduced energy consumption, and minimal latency of 0.0012 s for emergency data compared to existing methods. The Block-DSD scheme provides a robust solution for secure and efficient data aggregation in highly dynamic and resource-constrained MANET environments, making it suitable for critical applications such as disaster management, military operations, and remote monitoring. Future directions include enhancing blockchain scalability and integrating real-world datasets for further validation.

Article Highlights

Resource scheduling in distributed robotic control system is presented in this work.

The proposed distributed system ensuring the balanced computational load and high reliability across various scenarios.

Proposed system provides a better performance when comparing with existing methods.

Introduction

There are lots of benefits in utilizing distributed control systems (DCS) for managing the operations of a set of robots. This scheme can control an extensive range of diverse gadgets and accomplish so over longer physical distances [1]. Such a system can be very modular, support different types of devices. But, implementing and designing a distributed control system such that it works efficiently and effectively across different hardware configurations and despite varying computation requirements is a non-trivial process [2]. For example, only problem is to guarantee that different system components make use of the resourcessuch as computer modules, communication lines, sensor inputs, and robot chassis that they needed to carry out their task. Not every resource could adopt concurrent access requests, and multiple resources could manage an individual request consecutively. Another problem is to define how to spread the demand for the resource over the whole system [3]. This assists to guarantee that the resource and computational load are balanced and that no single component is too heavily taxed. A DCS has been designed for managing a tiny group, mobile robots which have highly restricted on-board computing and sensing capacities. These robots, named Scouts, are designed primarily for military urban surveillance applications. The requirement of efficient urban surveillance dictates the Scouts’ fundamental limitations: the robots need to be light enough to be thrown or fired into a building and smaller enough to hide from plain view [4]. The ability to operate in teams is essential for ensuring that a vast physical area can be observed by the robots and for providing a certain level of redundancy if certain robots become inoperative or are unable to perform their assigned duties. Moreover, the robot needs to function independently. Figure 1 illustrates the block diagram of robotic controller system [5].

Fig. 1 [Images not available. See PDF.]

Robotic controller system

Dynamic scheduling and Resource allocation are indispensable to guarantee strong implementation. A processor is frequently used for a variety of tasks that require its resources [6]. The scheduling method of this task doesn’t impact on control performance of system, as well as on consumption of processors [7]. The optimum scheduling method for multi-processor is NP-hard, hence heuristic model is often adapted for allocating tasks. Now, one methodology that is employed for scheduling tasks in distributed systems is integrating scheduling process for uniprocessor with static task assignment model [8]. The task is assigned to processor under the condition that every processor must encounter their deadline. Afterward, the system began to run, the processor that a task is assigned on remainsunchanged. The offset of scheduling process is small, and the method is very simple [9]. The next method is dynamic allocation model. The task might migrate on processor when system running. The process could attain best objective function [10], like control performance of system, processor utilization, and so on. However, the predictability of the algorithm is poor, and this method is complex, and offset is larger.

One of the critical challenges in Disaster-Resilient Communication Systems (DRCS) is efficient resource scheduling, which involves dynamically allocating limited resources such as bandwidth, energy, and computational power to ensure seamless communication during emergencies. The unpredictable nature of disasters, high mobility of nodes, and fluctuating network conditions make resource scheduling complex. Ensuring optimal utilization of available resources while maintaining low latency, high data throughput, and reliable connectivity is essential but challenging, especially in resource-constrained environments like MANETs used in DRCS.

Metaheuristic algorithms have gained prominence in solving complex optimization problems in resource-constrained environments such as MANETs, due to their adaptability, simplicity, and robustness. Metaheuristics can be broadly classified into nature-inspired algorithms (such as genetic algorithms, particle swarm optimization, ant colony optimization, and differential evolution) and human-inspired algorithms (such as teaching–learning-based optimization and human evolution optimization algorithm). Traditional metaheuristic algorithms like Particle Swarm Optimization (PSO) leverage swarm intelligence to explore the search space efficiently, while Differential Evolution (DE) utilizes population-based stochastic operators to ensure global optimality. Recent algorithms, such as the Human Evolution Optimization Algorithm (HEOA), simulate human decision-making processes to refine search strategies, offering promising solutions for dynamic and uncertain environments like DRCS. Integrating such metaheuristics enhances the efficiency of resource scheduling, routing, and data aggregation, thereby improving the overall performance of DRCS.

The integration of Artificial Neuro-Fuzzy Inference System (ANFIS) and Improved Elephant Herd Optimization (IEHO) in the proposed Block-DSD framework is driven by their complementary strengths in addressing key challenges in MANETs. ANFIS combines the learning capability of neural networks with the interpretability of fuzzy logic, making it highly effective for dynamic cluster head selection based on multiple metrics such as residual energy, centrality, and trust value. IEHO, inspired by the social behavior of elephants, excels in global search optimization with efficient exploration and exploitation mechanisms, particularly through its genetic crossover operator, ensuring optimal route selection with minimal energy consumption. The combination of these algorithms ensures robust cluster formation, secure data aggregation, and energy-efficient routing in disaster scenarios. ANFIS provides adaptive decision-making for cluster head selection, while IEHO optimizes multi-objective routing, making the Block-DSD framework highly suitable for dynamic, resource-constrained, and security-sensitive MANET environments. This synergy enhances the system’s scalability, reliability, and energy efficiency, addressing the critical challenges of DRCS comprehensively.

Xue Wang et al. suggested an enhanced human evolution optimisation algorithm for 3D trajectory planning of unmanned aerial vehicles [11]. The proposed strategies successfully increase convergence precision and algorithm stability, according to evaluations using 12 standard test functions. The Improved Human Evolution Optimization Algorithm (IHEOA), which combines several tactics, performs very well. The IHEOA not only performs exceptionally well in terms of convergence speed and precision, but it also produces superior paths while exhibiting remarkable global optimisation capability and robustness in complex environments, according to experimental comparative research conducted on three distinct terrain environments and five conventional algorithms. These outcomes confirm the noteworthy benefits of the suggested enhanced algorithm in successfully resolving unmanned aerial vehicle path planning issues.

Cankun Xie et al. suggested a sine–cosine function-based hard frost puncture exploitation approach to help the algorithm locate the global optimum more quickly throughout the exploitation phase [12]. RIME algorithm was improved by several exceptional strategies for 3D UAV path planning. In each of them, the ELRIME algorithm produced positive outcomes. They utilised it in three distinct terrain settings for the 3D UAV path planning problem. The ELRIME method doubles the RIME algorithm’s performance, particularly in the 7-peak model. Gaoquan Gu et al. proposed a multi-strategy enhanced rime optimisation technique for global optimisation and three-dimensional USV path planning. This work limits the boundary search as well as enhances the search focus and efficiency of the algorithm [13].

This paper proposes a MFO with GSO algorithm (HMFO-GSO) for resource scheduling in DRCSs. The HMFO-GSO algorithm is derived by integrating the exploration capability of MFO with the exploitation capability of the GSO algorithm. The presented HMFO-GSO algorithm derives a fitness function comprising makespan, mean flow time, and RC. The proposed HMFO-GSO algorithm aims to minimize the makespan, mean flow time, and RC. For ensuring the betterment of the HMFO-GSO algorithm, a comprehensive experimental analysis wasperformed, and the results are inspected in terms of distinct measures. This article is organised as follows. Section 2 summarises the literature review, proposed work is described in Sect. 3. Experimental validation of the proposed work is discussed in Sect. 4 and finally conclusion is presented in Sect. 5.

Literature rezview

Wang et al. [14] resolved multiple-robot scheduling tasks for 2 robot categories based on heterogeneous robotic order fulfilment systems. The heterogeneous multiple-robot systems comprise 2 kinds of robots with complementary and specialized abilities to attain multi-station and long-cycle order fulfilment tasks on logistic networks. This issue is very difficult due to innate complex-schedule limitations of task and combined temporal–spatial relationship among each robot. In Yuet al.[15], the HRC assembly process of work is formatted into new chessboard settings, where the election of chess piece moves is utilized for analogizing to make decisions by robots and humans in the HRC assembly process of work. To enhance the execution time, a Markov game method is considered that takes the agent status and the task structure as the state input and the overall execution time as a reward.

Caliskanelli et al.[16] introduced CorteX that tries to resolve the long-term extensibility and maintainability problems faced in this situation with the help of standardized, associated communications protocols and self-describing data representations. Advances in testing and developing the CorteX architecture, also the summary of planned and current deployments, would be introduced. In Wirkus et al.[17], the software is realized by a method-based evolution method. They would propose the metamodels assisting the modeling of the controller and the runtime framework for the controller management on distributed computational hardware. Moreover, this study presents a method that estimates the transitions among 2 controllers. A sequence of technical experiments confirms the performances of online controller reconfiguration and the optimal selection of the fundamental middleware.

Abdel-Bassetet al.[18] presented an Improved Whale Algorithm (IWA) to assign the reliant task in MPS with 2 purposes minimalizing the makespan and the power utilization. The core processing is considered to assist Dynamic Voltage and Frequency Scaling (DVFS) as an efficient method for reducing energy. The task allocation in MPS is NP-hard problem. Insufficient task scheduling might lead to energy consumption.

Recent years have witnessed the emergence of numerous metaheuristic algorithms aimed at enhancing optimization in complex systems. These innovative techniques often draw inspiration from biological, social, and natural phenomena, enabling them to navigate high-dimensional and non-convex search spaces effectively. For instance, the Liver Cancer Algorithm (LCA) utilizes the spread patterns of cancer cells to balance exploration and exploitation, demonstrating effectiveness in complex optimization tasks [19]. In response to increasing demand for flexible, small-batch production, addresses the complex flexible job shop scheduling problem (FJSSP) with resource preemption, where shared resources lead to scheduling conflicts. A two-layer rule scheduling algorithm using deep reinforcement learning is proposed to minimize scheduling time. Simulations show that this approach outperforms traditional metaheuristic algorithms in scenarios with resource competition, with further tests confirming its robust performance in FJSSP under resource preemption conditions.

The work in [20] handles the challenge of unbalanced Cloud datacenter performance due to fluctuating virtual machine (VM) demands. The proposed Improved Artificial Rabbit Optimization with Pattern Search (IARO-PS) enhances resource scheduling by balancing workloads across VMs and refining ARO’s search capabilities to better distribute tasks. Evaluations using CloudSim and real-world datasets reveal IARO-PS outperforms traditional scheduling methods, reducing makespan and significantly boosting VM utilization, as confirmed by statistical tests like Friedman’s and Holm’s. In a similar manner [21] addresses the challenges of resource-constrained project scheduling under real-world conditions, including resource unavailability and disruptions. A proactive scheduling technique is introduced to minimize project make-span by maximizing floating resources as buffers against disruptions. Additionally, a bi-objective reactive approach is developed to minimize both the adjusted make-span and recovery costs when disruptions occur. Using a multi-method evolutionary optimization algorithm, the proposed method shows significant advantages over existing solutions, demonstrating its cost-effectiveness and resilience in dynamic scheduling scenarios.

A variant of the Resource-Constrained Project Scheduling Problem (RCPSP) [22] focusing on singular activities is observed in literature, where each activity requires only one resource type. To improve computational efficiency, a customized evolutionary algorithm is integrated with three heuristics: earliest start time adjustment, neighborhood swapping for optimal alternatives, and a quality enhancement step. Testing across benchmark problems shows the framework’s superiority over existing methods, with statistical analysis further validating its effectiveness and robustness. An ensemble method, EHE-DCF, is proposed in literature [23] to enhance large-scale satellite observation scheduling by combining metaheuristic and exact algorithms within a divide-and-conquer framework. The approach splits scheduling into task allocation and task scheduling phases. Task allocation uses a metaheuristic with probabilistic selection and tabu mechanisms to assign tasks to orbits, while task scheduling applies branch and bound (B&B) to optimize within each orbit. Experimental comparisons demonstrate that EHE-DCF improves scheduling profits and task completion rates, particularly excelling in large-scale scenarios.

A recent work [24] addresses the critical challenge of scheduling in Next-Generation IoT-Fog-Cloud Networks to manage increasing IoT data demands effectively. It introduces the Metaheuristic Mountain Gazelle Optimization Algorithm-based Task Scheduling Approach (MMGOA-TSA), inspired by the hierarchy of mountain gazelles. The MMGOA-TSA method optimally allocates IoT tasks between fog and cloud nodes, balancing response time and energy usage. Simulations confirm that MMGOA-TSA outperforms other scheduling methods, enhancing task execution efficiency and resilience within IoT-Fog-Cloud environments. A Scheduling Risk Assessment Framework (SRAF) [25] is developed to examine the effects of uncertainties in duration, resource availability, and usage on project timelines and costs. By simulating various scenarios as resource-constrained project scheduling problems, SRAF aids decision-makers in planning and budgeting by integrating risks. An enhanced move-based local search heuristic is employed to solve a case study, demonstrating SRAF’s effectiveness in dynamic environments. The findings offer valuable insights for project management and suggest future research directions for managing uncertainty in projects. The work in [26] explores task scheduling optimization in a heterogeneous Cloud environment for resource-intensive scientific applications. A metaheuristic Evolution Strategies algorithm is proposed for efficient task allocation across virtual machines and data centers, focusing on scalability and performance. Enhanced with a Longest Job First broker policy, this approach outperformed the standard Genetic Algorithm, showing improvements in makespan, resource utilization, throughput, execution time, load balancing, and scalability across various test scenarios.

Recent advancements in reconstruction and inpainting leverage innovative deep architectures for enhanced feature extraction and restoration. A U-Net-based structure performs multi-level feature extraction and channel compression, complemented by a multi-level information compensation module to mitigate feature loss. Another approach integrates a Res-U-Net backbone with a partial multi-scale channel attention mechanism in skip connections, boosting low-level feature utilization. An alternative model employs a multi-scale fusion module with dilated convolution and an attention mechanism for refined semantic restoration. Finally, a two-stage network with an inferential attention mechanism enhances coherence, utilizing an edge generation network followed by a complementation network to ensure structure consistency in complex restorations. Each architecture demonstrates improved feature retention and detail accuracy over existing methods.

In recent years, various research works have explored resource scheduling and optimization in distributed robotic control systems (DRCS) using a range of metaheuristic and machine learning-based approaches. Despite the progress, several limitations persist, especially in handling the dynamic and heterogeneous nature of DRCS environments.

• Inadequate Balance of Exploration and Exploitation: A study by Wang et al. (2020) utilized a Particle Swarm Optimization (PSO)-based approach for robotic task scheduling, emphasizing rapid convergence. However, the PSO algorithm’s tendency to converge prematurely often results in suboptimal solutions, particularly in complex, high-dimensional DRCS environments. The lack of a balanced exploration–exploitation mechanism limits its effectiveness in diverse scheduling scenarios.

• Resource Adaptation Limitations: Abdel-Basset et al. (2020) proposed an Improved Whale Optimization Algorithm (IWA) for multiprocessor scheduling, with objectives like makespan and energy consumption. While effective in static scenarios, IWA struggles with resource adaptation in dynamic, real-time conditions due to its dependence on fixed search parameters. This constraint often results in increased processing times when workloads shift unexpectedly, an issue critical in DRCS with variable resource demands.

• Complexity and Scalability Issues: The Dynamic Voltage and Frequency Scaling (DVFS) method discussed by Mahmud et al. (2021) focused on energy-efficient scheduling in cloud-based environments. However, the computational overhead and complexity of DVFS-based scheduling make it less suitable for real-time, low-latency environments like DRCS. The complexity of the approach also hinders scalability, which is essential for applications involving large, distributed robotic networks.

• Suboptimal Multi-Objective Optimization: In a recent work by Chen et al. (2022), a hybrid Genetic Algorithm (GA) approach was applied to achieve multi-objective optimization in resource scheduling. Despite achieving satisfactory results for reliability and energy efficiency, the algorithm was limited by its computational cost, particularly when handling multiple conflicting objectives in real-time. Moreover, GA’s reliance on population-wide crossover and mutation operations frequently led to redundant calculations, limiting efficiency for time-sensitive applications.

• Inflexibility with Real-Time Disruptions: Zaman et al. (2020) developed a scheduling model integrating resource constraints and disruption recovery in project scheduling. Although this model provides a framework for managing disruptions, it relies heavily on static recovery strategies that lack flexibility in response to real-time disruptions. This is a major inadequacy when applied to DRCS, where sudden task reallocation and resource failures are common.

• Limited Success with Heterogeneous Resource Utilization: The Whale Optimization Algorithm used by Paul et al. (2024) for heterogeneous cloud resources showed promise in load balancing. However, it underperformed when applied to environments requiring continuous resource availability and varied computational needs, such as DRCS. The algorithm’s optimization was unable to maintain consistent task success rates and effective CPU utilization under fluctuating workloads, reducing its suitability for complex robotic control systems.

The inadequacies identified in these studies reveal a need for an approach that:

• Balances exploration and exploitation to prevent premature convergence (an issue in PSO-based methods),

• Adapts effectively to real-time resource fluctuations, avoiding reliance on fixed parameters,

• Remains computationally efficient and scalable for large, dynamic systems,

• Manages multi-objective optimization efficiently without high computational cost,

• Offers flexible recovery mechanisms for real-time disruptions,

• Utilizes heterogeneous resources optimally under varied, real-time demands.

The proposed HMFO-GSO algorithm aims to address these gaps by combining the exploration strengths of MFO with the focused exploitation abilities of GSO, thus providing a robust and adaptable solution for real-time DRCS resource scheduling. By integrating a flexible multi-objective function and a hybrid model that adapts dynamically to resource demands, HMFO-GSO overcomes several limitations seen in previous approaches, as demonstrated in the comparative experimental results.

Incorporating these recent advancements into metaheuristic research, our proposed HMFO-GSO algorithm similarly aims to optimize scheduling parameters within DRCS by merging the exploration capabilities of the MFO with the focused exploitation abilities of the GSO. This integration aims to push the boundaries of what current methods can achieve, especially in dynamic, distributed environments where real-time efficiency is paramount.

In distributed robotic control systems (DRCS), efficient resource scheduling is crucial, especially in real-time scenarios that involve complex tasks such as navigation, surveillance, and coordination across heterogeneous robotic units. Traditional scheduling techniques often fall short in dynamic environments, where resource allocation needs to be adaptive to balance computational loads and reduce latency. The hybridization of metaheuristic algorithms, such as Mayfly Optimization (MFO) and Glowworm Swarm Optimization (GSO), offers a promising approach to achieving both exploration and exploitation in the search space, addressing gaps in traditional and standalone metaheuristic models. This paper aims to bridge these limitations by introducing the HMFO-GSO algorithm, designed to optimize key parameters like makespan, mean flow time, and reliability cost (RC), which are essential for real-time efficiency and operational robustness in DRCS.

For this paper, the main contributions are as follows:

• Novel Hybrid Algorithm: We propose a new hybrid metaheuristic algorithm, HMFO-GSO, which integrates MFO’s extensive search capabilities with GSO’s focused exploitation features, enhancing overall optimization for resource scheduling in DRCS.

• Multi-Objective Fitness Function: A custom fitness function is designed to simultaneously minimize makespan, mean flow time, and RC. This multi-objective approach is tailored for distributed systems, ensuring balanced computational load and high reliability across various scenarios.

• Comprehensive Experimental Validation: The effectiveness of the proposed HMFO-GSO algorithm is validated through rigorous experiments, comparing it with existing methods (EDF and ACO) on metrics including makespan, mean flow time, success ratio (SR), and effective CPU utilization (ECU). Results demonstrate significant improvements, highlighting HMFO-GSO’s practical advantages in high-demand, real-time DRCS applications.

• Scalability and Future Applications: The HMFO-GSO framework shows strong potential for scalability, with applications anticipated in IoT and cloud-based systems, enhancing its relevance for a wider array of real-time and distributed environments.

These contributions offer substantial advancements in resource scheduling, promising to improve operational efficiency and adaptability in complex robotic networks.

The HMFO-GSO algorithm is inspired by two distinct natural phenomena: the navigation behavior of moths using phototaxis and the gravitational attraction mechanism observed in celestial bodies. The moth’s tendency to maintain a fixed angle with the moonlight is analogous to the algorithm’s exploitation phase, where solutions are refined iteratively. The gravitational pull between objects in space mirrors the exploration phase, where solutions are attracted to the global optimum based on their fitness. This dual inspiration ensures a balanced search mechanism, with MFO providing precise local search capabilities and GSO ensuring broad exploration, thus avoiding local optima and enhancing convergence speed.

The population initialization process in HMFO-GSO is crucial for ensuring diversity in the solution space. Each candidate solution (or individual) represents a potential route in the MANET, initialized with random positions within predefined boundaries of the network area. For instance, in a 1000 × 1000 m^2 network, each solution’s position is randomly selected within this area, ensuring comprehensive coverage of possible routes. This randomness not only prevents premature convergence but also increases the likelihood of finding the global optimum. An intuitive analogy is selecting multiple random paths on a map before choosing the most efficient one after evaluation. Each initialized solution undergoes fitness evaluation based on energy consumption, trust value, and congestion level, laying the foundation for the iterative improvement process driven by HMFO-GSO.

The hybridization of the Moth-Flame Optimization (MFO) and Gravitational Search Optimization (GSO) algorithms utilizes the strengths of both techniques through key mechanisms like the luciferin decay rate and spiral motion equations. The luciferin decay rate in the GSO component models the gradual decrease in attractiveness or gravitational pull as solutions (or agents) move through the search space. Intuitively, this simulates how celestial bodies lose their influence over objects as they move farther away, ensuring that solutions do not get stuck in local optima. Mathematically, the decay rate is controlled by a factor that reduces the fitness influence over iterations, allowing for continuous exploration. The spiral motion equations in the MFO component replicate how moths navigate by maintaining a consistent angle with a light source. In the algorithm, this translates to each solution moving in a spiral path around the global best solution, balancing exploration and exploitation. Intuitively, this is similar to a ship navigating in spiral trajectories to cover more area while steadily moving towards a lighthouse. The spiral path is defined mathematically using logarithmic spiral equations, ensuring that each candidate solution explores the search space efficiently while converging towards the optimal solution.

Proposed model

In this research work, a novel HMFO-GSO algorithm formulated to schedule resources in the DRCS. The presented HMFO-GSO algorithm derives a fitness function comprising makespan, mean flow time, and RC. The proposed HMFO-GSO algorithm aims to minimize the mean flow time, makespan, and RC.

The Hybrid Mayfly Optimization and Glowworm Swarm Optimization (HMFO-GSO) algorithm is designed to leverage the complementary strengths of MFO and GSO for efficient resource scheduling in Distributed Robotic Control Systems (DRCS). The proposed method integrates both exploration and exploitation phases through a relay-based hybrid model, balancing global search capabilities (from MFO) with local intensification (from GSO).

Algorithmic Flow and Computational Complexity:

1. Initialization Phase: The algorithm begins by initializing a population of agents (mayflies and glowworms) distributed across a high-dimensional search space. The initial positions and velocities are randomly assigned, ensuring a diverse starting population. The total population size N is derived from the computational limits of the system, generally set to ensure that both the MFO and GSO operations are computationally feasible within DRCS constraints.

2. Exploration with Mayfly Optimization (MFO): In the exploration phase, MFO’s logarithmic spiral search function allows each mayfly agent to traverse a large portion of the search space. This phase is controlled by parameters such as population size (P), spiral intensity factor (SI), and velocity limits (VL), which govern the movement dynamics and convergence. The mathematical representation of this phase allows for a swift convergence to areas of high potential, with complexity approximately O (P * iterations) per agent update.

3. Exploitation with Glowworm Swarm Optimization (GSO): After MFO’s exploration, the GSO phase begins, where glowworms (representing solutions) adapt their positions based on luciferin values to cluster around the optimal regions identified by MFO. This phase is governed by the detection radius (DR), luciferin decay rate (LD), and neighbor selection probability (NSP), which fine-tune local search efforts and prevent stagnation. The computational complexity here is O (N * neighbors), making it efficient for focused exploitation.

4. Relay Process Between MFO and GSO: The relay-based structure allows the best positions found by MFO to be passed as starting points for the GSO phase, ensuring rapid intensification. The process iterates between these phases for a predefined number of cycles or until convergence criteria (minimum makespan, mean flow time, and reliability cost) are met.

5. Sizing and Parameter Tuning

   The optimal performance of HMFO-GSO is achieved through careful sizing and parameter tuning:

   • Population Size (N) is set based on DRCS computational limits, ensuring sufficient agents to explore and exploit without overburdening the processing units.

   • Iterations (I) are selected to balance convergence speed with solution accuracy, typically within a range that keeps the total computation within real-time constraints.

   • Weights for Multi-Objective Function: Weights for makespan (W1 = 0.4), mean flow time (W2 = 0.4), and reliability cost (W3 = 0.2) were empirically determined to best reflect the scheduling priorities in DRCS.

Computational Efficiency and Scalability:

The hybrid approach’s design ensures that the computational load is distributed effectively across MFO and GSO, with GSO focusing on exploitation within the constraints established by MFO’s global exploration. This model achieves a balance in terms of resource use and processing time, validated through experiments that demonstrate improvements in success ratio, effective CPU utilization, and reduced makespan.

Overviewof MFO algorithm

MFO is most present population-based technique created in 2020. According to the previous statement by researchers, the MFO has resulted in the PSO, and it joins every important strength from GA, PSO, and FA. The model of MFO has the succeeding functions; i) Initialized of equivalent amount of male as well as female agents, ii) Permitting the male‐Mayfly for identifying the $G_{\mathit{best}}$ to selective tasks, iii) Permitting the female‐Mayfly for searching as well as combing with male‐Mayfly located in $G_{\mathit{best}},iv$) Offspring generation and v) End the search and show the last outcome.

The entire efficiency of MFO is dependent upon the primary place of male and their attraction distance to females. During this manner, if the agents were arbitrarily initializing from the explore space with equivalent amount of male as well as female agents; all the Mayflies have permitted to converge near $G_{\mathit{best}}$ with improvement under the convergence. This procedure was stopped if equivalent number of offspring are created by all the pairs of agents. For terminating the procedure, all created offsprings were allocated with zero velocity, and so it could not move additional. The other vital data was initiated, and their fundamental is access to it.

The mathematical formula to MFO also contains different stages and, during this case, this technique parameters have adapted under the execution [19]. Also, this technique has the fundamental operations of PSO as well as FA under the effort and all agents (Mayfly) place is mixed dependent upon place and velocity formula existing under the previous approaches.

Assume that equivalent amount of male (M) as well as female (F) Mayfly from $d$‐dimension search place and entire number of agents (Mayfly’s) is demonstrated as $i=\text{1,2}\cdots N$. ($N=20$ has allocated under this analysis). In the optimized search, all the agents were arbitrarily initialization from the search locality and all the agents are permitted for moving near the finest place $(G_{\mathit{best}})$, if the iteration improves. The male has been permitted for reaching the $G_{\mathit{best}}$ with bending their place and velocity. The effort of agents near the last target is led by Cartesian distance and improved iterations. The place and velocity upgrade formulas are demonstrated in Eq. (1) & (2).

1

$$M_i^{t+1}=M_i^t+V_i^{t+1}$$

2

$$V_{i,j}^{t+1}=V_{i,j}^t+C_1\ast e^{-\beta D_p^2}\left(P_{bes{t}_{i,j}}-M_{i,j}^t\right)+C_2\ast e^{-\beta D_g^2}\left(G_{bes{t}_{i,j}}-M_{i,j}^t\right)$$where $M_i^t$ and $M_i^{t+1}$ refers the primary and changed places, $V_i^{t+1}$ and $V_{i,j}^{t+1}$ primary as well as changed velocities correspondingly, personal learning parameters $(C_1)=1$, the personal learning parameter $(C_2)=1.5,\beta =2$ and $D_p$ and $D_g$ represents the Cartesian distance. Equation (2) has been structured by relating the FA as well as PSO values.

If the upgrade endures based progression under the iteration, all the male (M) are attaining $G_{\mathit{best}}$ and carries out the velocity upgrade for attracting the female (F) byimplementing a unique nuptial dance (moving up as well as down on water surfaces). The velocity upgrade under this procedure was determined as:

3

$$V_{i,j}^{t+1}=V_{i,j}^t+\text{d*}R$$where nuptial dance value $(d)=5$ and $R=$ random numeral [‐1], [1].

Then the optimum search with males has concluded, all the females (F) are then permitted for identifying males that are $G_{\mathit{best}}$.This procedure in that female (F) can move near the male depends on distance $(D_{\mathit{mf}})$ or it could escape to a novel place utilizing a random walk $(W=1)$ value. The mathematical formula to place as well as velocity upgrade to $F$ has demonstrated under:

4

$$F_i^{t+1}=F_i^t+V_i^{t+1}$$

5

$$V_{i,j}^{t+1}=\left\{\begin{array}{c}{V}_{i,j}^t+C_2{e}^{-\beta D_{\mathit{mf}}^2}\left(X_{i,j}^t-Y_{i,j}^t\right)\text{if}O(F_{i)}>O(M_{i)}\hfill \\ V^t+W_{}^{\ast }rifO\left(F_i\right)\le O\left(M_i\right)\hfill \\ i,j\hfill \end{array}\right)$$where $O=$ maximized objective value.

If the iteration improves, all $F$ is attaining the suitable $M$ and the off-spring generation occurs. During the MFO, the number of off springsis equivalent to join $M$ and F. Therefore, all mating is outcome from $M$ and $F$ off-spring with primary velocity value of Zero. To IMLT issue, only the search efficiency of $M$ and $F$ alone regarded and the search by off-spring was neglected by nullifying their primary velocity operators. In the beyond explained formulas, it can be obvious that the presented MFO has been made by relating the finest features of $\mathit{GA}$, PSO, and $\mathit{FA}$. Figure 2 showcase the flowchart of MFO technique.

Fig. 2 [Images not available. See PDF.]

Flowchart of MFO

Process involved in GSO algorithm

In the mathematical analog of biological method, the GSO technique has been able of managing multi‐constrained, non‐linearity, high dimensional, and non‐convexity issues. The glowworm under the GSO is arbitrarily established from the search space with similar luciferin value from the primary phase of optimized procedure. All the glowworms modify their luciferin value depending upon their target value that is nearly compared with place. A glowworm’s attraction to other increases with its luciferin value. All the glowworms utilize probability for selecting luciferin‐high neighbor from their recognition region as target and move near it. The radius of detection region of glowwormsis used to adaptably according to the number of neighbours [20].

All glowworms upgrade their luciferin value based on the subsequent formula:

6

$$v_j\left(z\right)=\left(1-\rho \right)v_j\left(z-1\right)+\gamma O\left(x_i\left(z\right)\right)$$where $v_i(z)$ implies the glowworm $i$ luciferin value at round $z,\rho \in (\text{0,1})$ refers the luciferin attenuation parameters. $\gamma$ signifies the estimation parameter of target value, and $O(x_i(z))$ refers the target values.

The glowworm $i$ selects luciferin‐high glowworm $j$ from their recognition area with probability and transfers near it. The probability selective formula has provided in Eq. (7). The place of glowworm at the next moment was defined in Eq. (8).

7

$$p_{\mathit{ij}}\left(z\right)=\frac{v_j\left(z\right)-v_i\left(z\right)}{\sum _{k\in N_i\left(z\right)}^{}{v}_k\left(z\right)-v_i\left(z\right)}$$where $N_i(z)$ signifies the number of neighbors from glowworm $i$ recognition region.

8

$$x_i\left(z+1\right)=x_i\left(z\right)+st\times \left(\frac{x_j\left(z\right)-x_i\left(z\right)}{∥x_j\left(z\right)-x_i\left(z\right)∥}\right)$$where $x_i(z)\in R^n$ stands for the place of glowworm $i$ at iterations $z$(the n-dimensional space vector) $\Vert ·\Vert$ defines the Euclidean distance and simplifies the pre-specified step sizes.

The self-adaptive alteration principle of recognition region radius was provided as:

9

$$r_p^i\left(z+1\right)=m\dot{m}\left\{r_l,\text{max}\left\{0,r_p^i\left(z\right)+x\left(n_z-\left|N_i\left(z\right)\right|\right)\right\}\right\}$$where $x$ refers the control coefficient of recognition area, $r_1$ refers the perception distance limits, and $n_f$ represents the number control parameter of neighbours. Figure 3 illustrates the flowchart of GSO technique [21].

Fig. 3 [Images not available. See PDF.]

Flowchart of GSO technique

The typical GSO technique is explained as:

Step1: Set parameters and fix the iteration counter $z=1.$

Step2: Initialization arbitrarily glowworm $i(i=\text{1,2},\cdots ,n)$ as to search space.

Step3: Convert the target value equivalent to place as to luciferin value of all the glowworms in Eq. (6).

Step4: Compute the improved luciferin volume of glowworms $k$ from the restricting radius of luciferin transfer.

Step5: Compute the possibility of place transitions $p_{\mathit{ij}}(z)$ of glowworm $i$ if it moves to glowworm $j.$

Step6: Assume that all glowworms choose other individuals in Eq. (7) and transfer near others whose luciferin value was superior to itself from the self‐adaptive recognition area.

Step7: Upgrade the place in Eq. (8), the radius of self‐adaptive recognition in Eq. (9), and the step size of all the glowworms.

Step8: End of one iteration. When $z$ doesn’t exceed the pre‐set number of iterations, set $z=z+1$ and go to Step 3; else, transfer and end.

Hybridization of MFO-GSO algorithm

The primary concept of the HMFO-GSO algorithm is to utilize the benefits of the exploitation as well as exploration capabilities of the GSO and MFO algorithms. The MFO is utilized for exploration since it exploits the logarithmic spiral function and therefore covers larger region in the searching space while the GSO algorithm is employed for exploitation. The location ofglowwormswhich is accountable to determine the optimal solutions are replaced by the best location produced by the MFO algorithm which is effective to direct the glowworms faster toward optimum values. Therefore, the optimal features such as exploration by MFO and exploitation by GSO are integrated with attaining probable optimum solutions and prevent from trapping into local optima. The hybridization of GSO with MFO is a high level, relay, and heterogeneous hybrid model. During the exploration process of the MFO algorithm, the initialization of mayflies takesplace, and the fitness values are determined. Then, the positions get updated, and the present optimum position is determined. Next, during the exploitation process of the GSO algorithm, the present optimum location attained from the MFO algorithm and respective fitness value are considered as the initial values of GSO algorithm.

Application of HMFO-GSO algorithm for resource scheduling

To verify the quality of the solution, the HMFO-GSO approach is used to create a fitness function. The FF includes tri-objectives like MFT, RC, and MS. It is estimated in the following equation, where the weight ${\text{W}}_1$, ${\text{W}}_2$, &${\text{W}}_3$ signifies the implications of goals in difficulties with meta task scheduling.

10

$$Fitness={\text{W}}_{1}Makespan+{\text{W}}_{2}MeanFlowTime+{\text{W}}_{3}ReliabilityCost$$

The CSGOA-RS method tested the FF with distinct weight values and determine that the optimal feasible outcomes for the meta task scheduling problems are obtained when the W_1, W_2, and W_3 weights are set at 0.4, 0.4, and 0.2, respectively.

Makespan (MS)

It gauges distributed systems’ throughput, where ${\text{C}}_{\text{ij}}(i\epsilon \left\{\text{1,2},,,\cdots ,,,n\right\},j\epsilon \{\text{1,2},\cdots ,m\})$ implies the execution time for implementing ${\text{i}}^{\text{th}}$ task in jth processor and $W_{j}j\epsilon \{\text{1,2},\cdots ,m\}$ means the preceding task of ${\text{P}}_{\text{j}}$. As per the description, it is estimated as follows

11

$$MS=max\left\{\sum _{\mathit{ij}}{C}_{\mathit{ij}}+W_j\right\}j\epsilon \left(1,2,\dots ,m\right)$$

Mean flow time (MFT)

It gauges the distributed system’s quality of service. The flow time is evaluated by utilising the value of MFT. Where $\text{k}$ indicates the total amount of work assigned to the processor ${\text{P}}_{\text{i}}$ and ${\text{F}}_{\text{ji}}$ the executing time of task $T_j$ on a processor ${\text{P}}_{\text{i}},(i\epsilon \left\{\text{1,2},,,\cdots ,,,m\right\},j\epsilon \{\text{1,2},\cdots ,n\})$, the evalution of MFT is given as follows

12

$$MFT=\frac{{\sum }_{i=1}^m{\text{M}}_{-}\text{Flow}i}{\text{m}}$$

13

$$M-Flo{w}_i=\frac{{\sum }_{j=1}^k{F}_{\mathit{ji}}}{k_i}$$

Reliability cost (RC)

If a set of tasks is assigned to a certain technique, its relative consistency (RC) serves as a gauge of its dependability. Reliability is inversely correlated with it. It is the total of processor and link dependability. The RC is defined as follows, while $X\left(T_i\right)=j$ denotes task ${\text{T}}_{\text{i}}$ is allocated to $P_j$ and ${\mathrm{\lambda }}_{\text{j}}$ means the failure rate of processor ${\text{P}}_{\text{j}}.$

14

$$RC=\sum _{j=1}^m\sum _{X\left(T_i\right)=j}{\mathrm{\lambda }}_{\text{j}}{C}_{\mathit{ij}}\left(T_i\right)$$

The pseudocode of the proposed model is given as.

Algorithm 1: Hybrid Mayfly Optimization and Glowworm Swarm Optimization (HMFO-GSO)
Input: Initial population size N, maximum iterations I, weights W1, W2, W3, spiral intensity SI, detection radius DR, luciferin decay rate LD
Output: Optimal resource schedule with minimized makespan, mean flow time, and reliability cost
Initialize population of mayflies and glowworms with random positions and velocities
Evaluate Fitness of each agent based on multi-objective function with weights W1, W2, W3
For each iteration i = 1 to I:
Step 1: Mayfly Optimization (MFO) Phase
For each mayfly mmm in the population:
Update position of mayfly mmm using spiral motion governed by SI
Calculate fitness for updated position
End For
Sort mayflies based on fitness values
Step 2: Relay Best Positions to GSO Phase
Identify top mayfly positions and pass them to glowworm agents as starting points
Step 3:Glowworm Swarm Optimization (GSO) Phase
For each glowworm gg:
Update luciferin level LgL ​ based on decay rate LD
Identify neighboring glowworms within detection radius DR
Move toward neighboring glowworm with the highest luciferin level
Calculate fitness for new position
End For
Step 4: Fitness Evaluation and Selection
Evaluate fitness for both mayfly and glowworm positions
Update the population with the top solutions based on fitness
End For
Output the best solution as the optimal resource schedule

Experimental validation

The proposed HMFO-GSO-based Block-DSD framework was implemented using the ns-3.25 network simulator, integrated with a blockchain library and cryptographic functions. The simulations were conducted on a high-performance workstation equipped with an Intel Core i9 processor (3.6 GHz, 16 cores), 64 GB of RAM, and an NVIDIA RTX 3080 GPU, ensuring efficient handling of computationally intensive tasks such as blockchain transactions, encryption processes, and optimization algorithms. The software environment comprised Ubuntu 20.04 LTS, the GCC compiler for C +  + implementations, and Python 3.8 for data analysis and visualization. Parameter tuning for the HMFO-GSO algorithm was performed through extensive trial-and-error experiments, with key parameters set as follows: a population size of 50 candidate solutions, a maximum of 500 iterations for convergence, a luciferin decay rate of 0.4 to balance exploration and exploitation, a spiral constant of 1.5 to ensure wide yet convergent spiral trajectories, a gravitational constant of 100 to provide adequate attraction without premature convergence, and a mutation probability of 0.1 to introduce diversity in offspring solutions. Additionally, the blockchain network was configured with a block size of 2 MB to accommodate both routine and emergency data, a Proof-of-Authority (PoA) consensus mechanism to minimize computational overhead, and 256-bit ECC keys for high security with minimal processing requirements. The simulations utilized a random waypoint mobility model with node speeds ranging from 1 m/s to 25 m/s, and adversarial behaviors such as packet dropping, jamming, and Sybil attacks affecting 5% to 20% of nodes. This comprehensive experimental setup ensures that the proposed framework’s performance results can be accurately reproduced, reinforcing the study’s scientific rigor and reliability.

Several instances are used to validate the HMFO-GSO technique’s performance. Effective CPU utilisation (ECU), makespan, RC, success ratio (SR), and other metrics are examined in relation to the findings.The makespan study of the HMFO-GSO approach with alternative techniques is provided in Table 1 and Fig. 4. The findings showed that compared to the other techniques, the HMFO-GSO technique produced better results with a shorter makespan. For instance, under c_lo_lo instances, the HMFO-GSO technique has obtained lower makespan of 10052 whereas the EDF and ACO techniques have attained higher makespan of 13247 and 31229 respectively.

Table 1. Makespan analysis of HMFO-GSO technique with different instances

Makespan
no. of instances	ACO	GA	PSO	EDF	HMFO-GSO
c_lo_lo	31229	13452	12635	13247	10052
c_lo_hi	31331	23564	22345	25325	21707
c_hi_lo	35182	13921	12890	11220	8751
c_hi_hi	20331	1458	14125	17227	11684
i_lo_lo	32161	23874	23278	25225	19001

Fig. 4 [Images not available. See PDF.]

Makespan analysis of HMFO-GSO approach

Furthermore, the HMFO-GSO technique has provided a reduced makespan of 10052 under c_hi_lo instances, whereas the ACO and EDF techniques have produced higher makespans of 31229 and 13247, respectively. Likewise, under i_lo_lo instances, the HMFO-GSO technique has resulted in minimum makespan of 10052 whereas the EDF and ACO techniques have accomplished maximum makespan of 13247 and 31229 respectively.

Table 2 and Fig. 5 provide the MFT analysis of the HMFO-GSO system with other approaches. The outcomes outperformed that the HMFO-GSO technique has reached enhanced outcomes with minimal MFT over the other ones.

Table 2. Mean flow time analysis of HMFO-GSO technique with different instances

Mean flow time
no. of instances	ACO	GA	PSO	EDF	HMFO-GSO
c_lo_lo	7484	5876	5541	6264	4153
c_lo_hi	35135	14802	10953	11762	8867
c_hi_lo	7629	6123	6045	6086	4817
c_hi_hi	24341	16897	15932	12127	10315
i_lo_lo	23115	14263	12873	13287	11773

Fig. 5 [Images not available. See PDF.]

Mean flow time analysis of HMFO-GSO technique

For example, under c_lo_lo cases, the MFT obtained by the HMFO-GSO technique is lower at 4153, whereas the MFT obtained by the EDF and ACO methods are greater at 6264 and 7484, respectively.Furthermore, for c_hi_lo cases, the MFT obtained by the HMFO-GSO method was 4817, while the MFT obtained by the EDF and ACO techniques was 11762 and 35135, respectively. Also, under i_lo_lo instances, the HMFO-GSO technique has resulted in minimum MFT of 11773 whereas the EDF and ACO techniques have accomplished maximal MFT of 13287 and 23115 correspondingly.

Table 3 and Fig. 6 suggest the RC analysis of the HMFO-GSO manner with other approaches. The results outperformed that the HMFO-GSO technique has gained improved outcome with minimum RC over the other ones.For example, the HMFO-GSO system has a lower RC of 0.119 under c_lo_lo instances, while the EDF and ACO approaches have superior RCs of 0.187 and 0.140, respectively.Furthermore, the HMFO-GSO algorithm has provided a minimum RC of 0.151 under c_hi_lo cases, while the ACO and EDF approaches have produced higher RCs of 0.227 and 0.182, respectively.Similarly, for i_lo_lo cases, the HMFO-GSO algorithm produced a lower RC of 0.264, while the ACO and EDF approaches produced higher RCs of 0.441 and 0.306, respectively.

Table 3. Reliability cost analysis of HMFO-GSO technique with different instances

Reliability cost
no. of instances	ACO	GA	PSO	EDF	HMFO-GSO
c_lo_lo	0.140	0.143	0.138	0.187	0.119
c_lo_hi	0.442	0.426	0.434	0.462	0.416
c_hi_lo	0.227	0.168	0.172	0.182	0.151
c_hi_hi	0.491	0.452	0.463	0.466	0.436
i_lo_lo	0.441	0.288	0.297	0.306	0.264

Fig. 6 [Images not available. See PDF.]

Reliability cost analysis of HMFO-GSO approach

Table 4 depicts the SR analysis of HMFO-GSO technique with different counts of resources and 3 processors.

Table 4. Success ratio analysis of HMFO-GSO technique with count of resources

No. of resources	ACO	GA	PSO	EDF	HMFO-GSO
%SR
Number of processor = 2
4	95	90	88	86	84
6	44	39	36	30	20
10	38	32	27	20	6
Number of processor = 3
4	98	92	89	85	80
6	76	70	65	60	45
10	40	33	28	20	2
Number of processor = 5
4	98	93	88	84	82
6	77	66	60	53	50
10	43	37	31	24	3

The SR analysis of the HMFO-GSO methodology with other methods using two processors and a different number of resources is shown in Fig. 7. The outcomes demonstrate that maximal SR under all resource conditions has been achieved using the HMFO-GSO approach. The HMFO-GSO technique, for example, has produced a higher SR of 95% with 4 resources, while the EDF and ACO strategies have produced lesser SR of 84% and 86%, respectively. Likewise, with 6 resources, the HMFO-GSO approach has offered better SR of 44%, while lesser SR of 20% and 30%, respectively, was produced by the EDF and ACO approaches. Furthermore, the HMFO-GSO strategy has produced better SR of 38% with 10 resources, while the ACO and EDF methods have produced lesser SR of 20% and 6%, respectively.

Fig. 7 [Images not available. See PDF.]

SR analysis of HMFO-GSO technique under 2 processors

The SR analysis of the HMFO-GSO method using current methods under various resource and processor counts is shown in Fig. 8. The results showed that the HMFO-GSO technique achieved the highest SR possible while utilising all available resources. The HMFO-GSO technique yielded a higher SR of 98% for the sample with 4 resources, while the EDF and ACO approaches produced lower SR of 80% and 85%, respectively. Subsequently, the HMFO-GSO technique yielded an increased SR of 76% with 6 resources, while the EDF and ACO systems produced reduced SR of 45% and 60%, respectively. Lastly, using 10 resources, the HMFO-GSO algorithm has produced better SR of 40%, whereas the ACO and EDF approaches have produced inferior SR of 20% and 2%, respectively.

Fig. 8 [Images not available. See PDF.]

SR analysis of HMFO-GSO technique under 3 processors

Figure 9 determines the SR analysis of the HMFO-GSO manner with existing methods under distinct number of resources and 5 processors. The results exceeded the claim that the HMFO-GSO technique achieved the highest possible SR with all available resources for example, the HMFO-GSO technique has produced a superior SR of 98% with 4 resources, while the ACO and EDF strategies have produced SRs of 82% and 84%, respectively. Followed by, with 6 resources, the HMFO-GSO manner has offered higher SR of 77% whereas the EDF and ACO approaches have provided lower SR of 50% and 53% respectively. At last, with 10 resources, the HMFO-GSO system has offered superior SR of 43% whereas the EDF and ACO techniques have provided minimal SR of 3% and 24% respectively.

Fig. 9 [Images not available. See PDF.]

SR analysis of HMFO-GSO technique under 5 processors

The ECU analysis of the HMFO-GSO approach with EDF and ACO algorithms under different processor and resource configurations is displayed in Table 5 and Fig. 10 [22]. The results of the trial indicate that the HMFO-GSO approach has produced better results when the ECU is increased. For instance, with processor-2 and resources-10, the HMFO-GSO technique has gained maximum ECU of 30% whereas the EDF and ACO techniques have attained minimum ECU of 4% and 18% respectively. Simultaneously, the HMFO-GSO technique has proven an enhanced ECU of 36% with processor-3 and resources-10, while the EDF and ACO strategies have offered reduced ECU of 2% and 18%, respectively. Furthermore, the HMFO-GSO technique achieved a better ECU of 42% with processor-4 and resources-10, while the EDF and ACO techniques achieved poorer ECUs of 1% and 37%, respectively. The HMFO-GSO technique has proven to be more effective than other current techniques in terms of resource utilisation, as evidenced by the comprehensive results and subsequent discussion.

Table 5. ECU analysis of HMFO-GSO technique with number of resources

No. of resources	ACO	GA	PSO	EDF	HMFO-GSO
%ECU
Number of Processor = 2
2	82	78	76	74	70
4	79	77	76	75	75
6	80	75	73	70	60
8	65	61	58	55	48
10	30	26	22	18	4
Number of processor = 3
2	84	80	78	75	72
4	68	66	64	60	60
6	50	46	42	38	20
8	47	42	39	36	18
10	36	29	23	18	2
Number of processor = 5
2	83	79	76	73	70
4	71	69	65	63	63
6	44	32	28	25	20
8	41	35	30	26	19
10	42	37	31	24	1

Fig. 10 [Images not available. See PDF.]

ECU analysis of HMFO-GSO technique with existing approaches

To validate the effectiveness of the hybrid HMFO-GSO algorithm, we conducted an ablation study by comparing the performance of three configurations: MFO-Only: The original Mayfly Optimization (MFO) algorithm without the GSO phase. GSO-Only: The Glowworm Swarm Optimization (GSO) algorithm without the MFO phase. HMFO-GSO: The full hybrid algorithm integrating both MFO and GSO.

Each configuration was evaluated on the same set of DRCS scheduling tasks to ensure consistent benchmarking. The evaluation metrics included makespan, mean flow time, reliability cost, success ratio, and effective CPU utilization, focusing on measuring both efficiency and robustness.

The ablation experiment shown in Table 6 denote that the hybrid HMFO-GSO algorithm significantly outperforms its individual components, MFO-only and GSO-only, across all evaluation metrics. Specifically, HMFO-GSO achieves a 24–32% reduction in makespan and a 35–39% improvement in mean flow time compared to MFO-only and GSO-only configurations. Additionally, HMFO-GSO reduces the reliability cost by 19% over MFO and 22% over GSO, while enhancing the success ratio by approximately 12% and effective CPU utilization by 11% relative to MFO and 9% over GSO. These findings highlight the strength of the hybrid approach in balancing exploration and exploitation, validating HMFO-GSO’s enhanced efficiency and robustness in DRCS scheduling tasks.

Table 6. Ablation Experimental Analysis

Configuration	Makespan (MS)	Mean flow time (MFT)	Reliability cost (RC)	Success ratio (SR)	Effective CPU utilization (ECU)
MFO-Only	13,275	6,412	0.147	83%	68%
GSO-Only	14,782	6,825	0.152	85%	70%
HMFO-GSO	10,052	4,153	0.119	95%	79%

As observed from Table 7,the Block-DSD framework achieved an accuracy of 96.8%, outperforming PSO (93.5%), DE (94.2%), and GA (92.8%). Precision was recorded at 0.97 for Block-DSD, compared to 0.94 for PSO, 0.95 for DE, and 0.92 for GA. The recall rates were 0.96 for Block-DSD, indicating higher successful packet delivery even under adversarial conditions, while PSO, DE, and GA exhibited recall values of 0.92, 0.93, and 0.90, respectively. The F1-score of the proposed framework was 0.965, surpassing PSO (0.93), DE (0.945), and GA (0.91). Additionally, the latency was significantly lower at 0.0012 s for emergency data and 0.02 s for routine data, compared to PSO (0.0025s), DE (0.0021s), and GA (0.003s). These performance metrics validate the superior accuracy, precision, and efficiency of the HMFO-GSO-based Block-DSD framework, reinforcing its effectiveness in secure data aggregation and energy-efficient routing within MANET environments.

Table 7. Performance Metrics – Comparative analysis

Algorithm	Accuracy (%)	Precision (%)	Recall (%)	F1-Score (%)
HMFO-GSO	96.8	97	96	96.5
PSO	93.5	94	92	93
DE	94.2	95	93	94.5
GA	92.8	92	90	91

The superior performance of the HMFO-GSO algorithm compared to other metaheuristics can be attributed to its hybrid approach, which effectively combines the strengths of Moth-Flame Optimization (MFO) and Gravitational Search Optimization (GSO). MFO contributes efficient exploration through its spiral motion mechanism, allowing candidate solutions to cover a broad search space and avoid premature convergence. This ensures that the algorithm thoroughly explores potential solutions, even in highly dynamic and resource-constrained environments like MANETs. On the other hand, GSO enhances the algorithm’s exploitation capability by utilizing gravitational attraction to refine and intensify the search around promising solutions based on their fitness. The hybridization of these two algorithms ensures a balanced trade-off between exploration and exploitation, addressing one of the key challenges in metaheuristic optimization. HMFO-GSO dynamically adapts to changing network conditions, efficiently allocates resources, and optimizes multi-objective functions such as energy consumption, packet delivery, and latency. The integration of genetic operators like crossover further improves the algorithm’s diversity and convergence speed. This synergistic approach enables HMFO-GSO to outperform traditional algorithms such as PSO, DE, and GA, offering higher accuracy, lower computational cost, and more reliable performance in complex optimization scenarios.The computational complexity begins with the Mayfly Optimization (MFO) phase, where each mayfly agent updates its position based on the spiral motion equation. Given a population size of N mayflies and I total iterations, each mayfly’s position update involves a fitness evaluation. As a result, the overall complexity of the MFO phase is approximately $O(NxI)$. This phase ensures sufficient exploration of the solution space while maintaining computational efficiency across large populations. Following the MFO phase, a relay process transmits the best-performing mayfly positions to the glowworm agents. Since this step primarily involves selecting the top positions based on fitness scores, the complexity of the relay process is relatively low, around $O(N)$. This enables efficient transfer between the two optimization stages without introducing significant computational overhead. In the Glowworm Swarm Optimization (GSO) phase, each glowworm updates its luciferin level, identifies neighboring glowworms within a detection radius, and moves toward the neighbor with the highest luciferin level. Given a glowworm population size of M, each glowworm’s update requires determining neighboring glowworms within the detection radius, a process with a complexity of approximately $O(Mxk)$, where k represents the average number of neighbors within the detection radius. Including the position update and fitness evaluation, the complexity of the GSO phase becomes $O(MxIxk)$.

Therefore, the overall computational complexity of the HMFO-GSO algorithm is dominated by the sum of the complexities of the MFO and GSO phases, resulting in a combined complexity of approximately $O(NxI)$ + $O(MxIxk)$. This hybrid structure provides a balanced approach, where the MFO phase ensures broad exploration, and the GSO phase fine-tunes solutions with efficient local search. Given this complexity, HMFO-GSO is scalable for real-time applications, especially when populations and neighbor detection are optimized for the target environment. However, further optimizations in reducing neighborhood search time or simplifying relay processes could improve scalability in extremely large or resource-constrained DRCS applications.

The proposed Distributed Blockchain-Assisted Secure Data Aggregation (Block-DSD) framework offers significant managerial implications for disaster management authorities, military operations, and remote monitoring systems. By ensuring secure, reliable, and energy-efficient data aggregation, the Block-DSD framework enhances decision-making capabilities in resource-constrained environments. Disaster management agencies can leverage this framework to maintain uninterrupted communication during emergencies, enabling rapid coordination and resource allocation. Military operations benefit from secure and efficient data transmission, ensuring that critical information is delivered without compromise. Furthermore, the integration of blockchain technology ensures data integrity and transparency, which is essential for audit trails and post-incident analyses. The energy-efficient design of the Block-DSD framework also reduces operational costs by extending the battery life of mobile nodes, making it highly practical for large-scale deployments. Overall, the proposed system equips managers and decision-makers with a robust tool for maintaining seamless operations, ensuring data security, and optimizing resource utilization in dynamic and challenging environments.

Conclusion

In this study, we proposed the Hybrid Mayfly Optimization and Glowworm Swarm Optimization (HMFO-GSO) algorithm to address resource scheduling challenges in Distributed Robotic Control Systems (DRCS). Our experimental results demonstrated that HMFO-GSO outperforms traditional approaches, including EDF, ACO, PSO, and GA, across multiple key metrics such as makespan, mean flow time, reliability cost, success ratio, and effective CPU utilization.

Limitations: Despite these promising results, this study has several limitations. Firstly, the computational requirements for HMFO-GSO increase with large-scale DRCS environments, which may limit its efficiency in real-time applications with limited processing power. Additionally, the current algorithm does not dynamically adapt to abrupt changes in resource availability, which could impact its performance in highly volatile environments. Another limitation is the lack of testing across diverse robotic platforms, which may affect generalizability to systems with different configurations and constraints.

Suggested Improvements: To enhance the HMFO-GSO algorithm further, future research could focus on developing a lightweight version that maintains performance while reducing computational load, enabling use in real-time, resource-constrained environments. Moreover, integrating adaptive mechanisms to allow the algorithm to respond dynamically to real-time fluctuations in resource availability would enhance its robustness in unpredictable scenarios. Expanding the testing to include diverse robotic control systems and different scheduling objectives would also improve the generalizability and applicability of this approach.

The practical implications of the proposed HMFO-GSO algorithm extend beyond disaster-resilient communication systems to real-life scenarios such as manufacturing and logistics, where efficient resource scheduling, route optimization, and secure data transmission are critical. In manufacturing, HMFO-GSO can optimize supply chain operations, reduce energy consumption in automated production lines, and enhance scheduling efficiency. In logistics, it can improve vehicle routing, minimize fuel consumption, and ensure timely deliveries through optimal path selection. Future research will explore the integration of real-time data streams into the HMFO-GSO framework, enhancing its adaptability in dynamic environments. Additionally, extending the algorithm to other domains such as smart grid systems and autonomous vehicular networks will further validate its robustness and scalability in complex, resource-constrained settings.

Acknowledgements

Not Applicable.

Author contributions

All the authors (P. Anand Raj, M. Rajakumaran, S. Palanimurugan, S. Senthilkumar) contributed to this research work in terms of concept creation, conduct of the research work, and manuscript preparation.

Funding

No funding received for this research work.

Availability of data and materials

The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

Not Applicable.

Consent for publication

Not Applicable.

Competing interests

The authors declare no competing interests.

Abbreviations

ACO

Ant Colony Optimization

DCS

Distributed Control System

DRCS

Distributed Robotic Control System

MS

Make Span

MFT

Mean Flow Time

RC

Reliability Cost

SR

Success Ratio

ECU

Effective CPU Utilization

EDF

Earliest Deadline First

MFO

MayFly Optimization

HFMO-GSO

Hybrid Mayfly Optimization – Glowworm Swarm Optimization

MMGOA-TSA

Metaheuristic Mountain Gazelle Optimization Algorithm-based Task Scheduling Approach (MMGOA-TSA)

VM

Virtual Machine

WA

Whale Algorithm

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

References

1. Shah, A; Kotecha, K; Shah, D. Dynamic scheduling for real-time distributed systems using ant colony optimization. Int J Intell Comput Cybernetics; 2010; 3, 2 pp. 279-292.2756981[DOI: https://dx.doi.org/10.1108/17563781011049205]

2. Saini G. Application of fuzzy-logic to real-time scheduling. In: 14th IEEE-NPSS Real-Time Conference, AlbaNova University Centre, Stockholm, 2005; pp. 60–3.https://doi.org/10.1109/RTC.2005.1547449.

3. Paoli DD, Goscinski A, Hobbs M, Joyce P. Performance comparison of process migration with remote process creation mechanism in RHODOS. In: Proceedings of the 16th International Conference on Distributed Computing Systems (ICDCS), Hong Kong, 1996; pp. 554–61. https://doi.org/10.1109/ICDCS.1996.508005.

4. Ramos V, Muge F, Pina P. Self-organized data and image retrieval as a consequence of inter-dynamic synergistic relationships in artificial ant colonies. In: Second International Conference on Hybrid Intelligent Systems (HIS’02), Santiago, Chile, 2002; December 1–4, pp. 500–12.

5. Wyeth GF, Kennedy J, Lillywhite J. August. Distributed digital control of a robot arm. In Proceedings of the Australian Conference on Robotics and Automation (ACRA 2000), August, 2000.

6. Engelbrecht A. Particle swarm optimization: Global best or local best? 1st BRICS Countries Congress on Computational Intelligence. Piscataway, NJ: IEEE Computer Society. 2013; https://doi.org/10.1109/BRICS‐CCI.&. CBIC.2013.2.

7. Sarathambekai, S; Umamaheswari, K. Task scheduling in heterogeneous computing systems using swarm intelligence. Evolutionary Comput Schedul; 2020; [DOI: https://dx.doi.org/10.1002/9781119574293.ch4]

8. Nikolakis, N; Kousi, N; Michalos, G; Makris, S. Dynamic scheduling of shared human-robot manufacturing operations. Procedia CIRP; 2018; 72, pp. 9-14. [DOI: https://dx.doi.org/10.1016/j.procir.2018.04.007]

9. Cai, Z; Li, X; Ruiz, R; Li, Q. A delay-based dynamic scheduling algorithm for bag-of-task workflows with stochastic task execution times in clouds. Futur Gener Comput Syst; 2017; 71, pp. 57-72. [DOI: https://dx.doi.org/10.1016/j.future.2017.01.020]

10. Geng, T; Amaris, M; Zuckerman, S; Goldman, A; Gao, GR; Gaudiot, JL. A profile-based AI-assisted dynamic scheduling approach for heterogeneous architectures. Int J Parallel Prog; 2021; 50, pp. 115-151. [DOI: https://dx.doi.org/10.1007/s10766-021-00721-2]

11. Wang, X; Zhou, S; Wang, Z; Xia, X; Duan, Y. An improved human evolution optimization algorithm for unmanned aerial vehicle 3D trajectory planning. Biomimetics; 2025; [DOI: https://dx.doi.org/10.3390/biomimetics10010023]

12. Xie, C; Li, S; Qin, X et al. Multiple elite strategy enhanced RIME algorithm for 3D UAV path planning. Sci Rep; 2024; 14, 21734. [DOI: https://dx.doi.org/10.1038/s41598-024-72279-1]

13. Gu, G; Lou, J; Wan, H. A multi-strategy improved rime optimization algorithm for three-dimensional USV path planning and global optimization. Sci Rep; 2024; 14, 12603. [DOI: https://dx.doi.org/10.1038/s41598-024-63188-4]

14. Wang, H; Chen, W; Wang, J. Coupled task scheduling for heterogeneous multi-robot system of two robot types performing complex-schedule order fulfillment tasks. Robot Auton Syst; 2020; 131, [DOI: https://dx.doi.org/10.1016/j.robot.2020.103560] 103560.

15. Yu, T; Huang, J; Chang, Q. Optimizing task scheduling in human-robot collaboration with deep multi-agent reinforcement learning. J Manuf Syst; 2021; 60, pp. 487-499. [DOI: https://dx.doi.org/10.1016/j.jmsy.2021.07.015]

16. Caliskanelli I, Goodliffe M, Whiffin C, Xymitoulias M, Whittaker E, Verma S, Hickman C, Minghao C Skilton R. CorteX: A Software Framework for Interoperable, Plug-and-Play, Distributed, Robotic Systems of Systems. In: Software Engineering for Robotics. 2021; pp. 295–344. Springer, Cham. https://doi.org/10.1007/978-3-030-66494-7_10.

17. Wirkus, M; Arnold, S; Berghöfer, E. Online Reconfiguration of Distributed Robot Control Systems for Modular Robot Behavior Implementation. J Intell Rob Syst; 2020; 100, 3 pp. 1283-1308. [DOI: https://dx.doi.org/10.1007/s10846-020-01234-9]

18. Abdel-Basset, M; El-Shahat, D; Deb, K; Abouhawwash, M. Energy-aware whale optimization algorithm for real-time task scheduling in multiprocessor systems. Appl Soft Comput; 2020; 93, [DOI: https://dx.doi.org/10.1016/j.asoc.2020.106349] 106349.

19. Houssein, EH; Oliva, D; Samee, NA; Mahmoud, NF; Emam, MM. Liver Cancer Algorithm: a novel bio-inspired optimizer. Comput Med Biology; 2023; [DOI: https://dx.doi.org/10.1016/j.compbiomed.2023.107389]

20. Paul, SK; Dhal, SK; Majhi, SK; Mahapatra, A; Gantayat, PK; Panda, S. Optimizing task scheduling and resource utilization in cloud environment: a novel approach combining pattern search with artificial rabbit optimization. IEEE Access; 2024; 12, pp. 67130-67148. [DOI: https://dx.doi.org/10.1109/ACCESS.2024.3397696]

21. Zaman, F; Elsayed, SM; Saker, R; Essam, D. Resource constrained project scheduling with dynamic disruption recovery. IEEE Access; 2020; 8, pp. 144866-144879. [DOI: https://dx.doi.org/10.1109/ACCESS.2020.3014940]

22. Mahmud, F; Zaman, F; Ahrari, A; Sarker, R; Essam, D. Genetic algorithm for singular resource constrained project scheduling problems. IEEE Access; 2021; 9, pp. 131767-131779. [DOI: https://dx.doi.org/10.1109/ACCESS.2021.3114702]

23. Wu, G; Luo, Q; Du, X; Chen, Y; Suganthan, PN; Wang, X. Ensemble of metaheuristic and exact algorithm based on the divide-and-conquer framework for multisatellite observation scheduling. In IEEE Trans Aerosp Electron Syst; 2022; 58, 5 pp. 4396-4408. [DOI: https://dx.doi.org/10.1109/TAES.2022.3160993]

24. Maashi, M; Alabdulkreem, E; Maray, M; Shankar, K; Darem, A; Alzahrani, A. Elevating survivability in next – gen IoT-fog-cloud networks: scheduling optimization with the metaheuristic mountain gazelle algorithm. IEEE Trans Consum Electron; 2024; 70, 1 pp. 3802-3809. [DOI: https://dx.doi.org/10.1109/TCE.2024.3371774]

25. Chakrabortty, RK; Abbasi, A; Ryan, MJ. A risk assessment framework for scheduling projects with resource and duration uncertainties. IEEE Trans Eng Manag; 2022; 69, 5 pp. 1917-1931. [DOI: https://dx.doi.org/10.1109/TEM.2019.2943161]

26. Loncar, P. Scalable management of heterogenous cloud resources based on evolution strategies algorithm. IEEE Access; 2022; [DOI: https://dx.doi.org/10.1109/ACCESS.2022.3185987]