A systematic review of MDO methods applied to launch vehicle design and their contributions to concurrent engineering

Abstract

The purpose of this paper is to review recent advances in Multidisciplinary Design Optimization (MDO) methods applied to the conceptual design of launch vehicles. The data search includes the words: MDO, launch vehicle and concurrent engineering, and it was carried out using the Scopus search engine, with access provided by the Brazilian database Periódicos/CAPES. The authors found that existing MDO publications focus only on optimizing some aspects of the design, mainly related to mass (65.22%), followed by trajectory (19.13%), cost (9.56%), and propulsion (3.48%). In terms of the disciplines involved in each of the studies, the authors typically work with four primary disciplines: trajectory (94%), propulsion (91%), weights and sizing (84%), and aerodynamics (79%). The studies focused primarily on disciplines related to vehicle performance. Cost is mentioned in only 12% of the results, indicating that it is usually considered a secondary aspect of the design. It was expected that the analysis of costs and business models would become more important in the design of launch vehicles, especially with the New Space Economy in full swing. The vast majority of architectures found in publications are still monolithic, and the main technique used to obtain the solution are evolutionary algorithms. In the end, the authors observed that MDO studies do not cover all the disciplines required for the entire lifecycle of launch vehicles, which is a premise of the broader concept of concurrent engineering to include technical, programmatic and support disciplines in its methodology.

Introduction

Several survey papers on MDO methods and their applications in aerospace and launch vehicle design have been published over the last 30 years. They provide a comprehensive overview of the state of MDO research and its implications for engineering design. While some focus on describing of architectures (Martins and Lambe [1], Wang et al. [2]), others emphasize the benefits and limitations of MDO methods commonly used in launch vehicle design (Rowell et al. [3], Balesdent et al. [4]) and in many other applications such as missiles, rockets, and satellite systems Chen et al. [5].

MDO can be described as an approach to the design of complex systems and their components that effectively explores the interactions between related domains (Giesing and Barthelemy [6]). It is a process that considers the impact of interactions among various engineering disciplines. It is well known that in the development of complex systems, there have always been multiple competing objectives related to satisfying design requirements. However, MDO methods suggest a way to organize the interaction between different domains to maximize or minimize these objectives, taking into account the constraints of each discipline and facilitating trade-offs between them. It is an environment in which mathematical methods are supported by computational tools in an organized way for the development of complex systems. Hammond [7].

MDO methods provide a tool for addressing the inherent interdependencies and trade-offs within complex systems, which is a constant in the aerospace industry, enabling more efficient and integrated solutions across multiple engineering disciplines. The process of designing space-related systems such as satellites, launch vehicles, ground support systems, and the interfaces between the various stakeholders in a mission architecture requires a large number of specialists from different fields of knowledge. There are many arrangements that can support a design process through all life cycle phases. However, for complex space systems, the world is moving toward concurrent engineering. The definition looks very similar to the one provided by Hammond [7]. The vast majority of references on Concurrent Engineering use a definition from a December 1988 publication by the Institute of Defense Analyses (IDA) (Syan and Menon [8], Stjepandić et al. [9]). It is described as:

Concurrent engineering is a systematic approach to the integrated, concurrent design of products and their related processes, including manufacture and support. This approach is intended to cause the developers, from the outset, to consider all elements of the product life cycle from conception through disposal, including quality, cost, schedule, and user requirements.

IDA Report R-338 (Winner et al. [10]) goes on to say that this approach can be done in three main ways: in project management, in product development, or in the overall business plan of the organization. It also states that there are several ways to implement this approach, using different methodologies and techniques. However, there are three general elements to the approach:

• Reliance on multifunctional teams to integrate the designs of a product and its manufacturing and support processes;

• Use of computer-aided tools that support integration, system development, and sharing of system information; and

• The application of various analytical techniques to optimize the design of a product and its related processes.

Comparing the two concepts, we can see that the concurrent engineering concept is more comprehensive because it refers to the entire lifecycle of a project, including its programmatic and support disciplines. In addition, project management disciplines can also benefit from these collaborative methodologies.

There are several studies that seek to develop methodologies to integrate different domains during the project lifecycle, with the purpose of facilitating collaboration in the face of great multidisciplinarity. (Lawson and Karandikar [11]; Jo et al. [12]). These facts have motivated MDO as a mechanism to contribute to the concurrent engineering process, acting as an essential link between engineering domains. The rapid advancement of computer technology and optimization algorithms makes it possible to quickly and accurately identify optimal designs for various structures, disciplines, and systems. The motivation for using MDO methods in engineering processes is related to improving product performance, as well as providing benefits related to cost savings and anticipation of system commissioning (Blachut and Eschenauer [13]).

The objective of this study is to map the application of MDO algorithms and verify how they can support the conceptual design of launch vehicles through a systematic review (Page et al. [14]). This work will analyze which architectures and algorithms are commonly used, as well as detail the disciplines involved in each of the studies and the fidelity of the analysis. The goal is to verify whether the MDO problems in the literature permeate the entire design development cycle of a launch vehicle, including its programmatic and support disciplines, following the broader concept of concurrent engineering. It should be noted that this paper does not intend to describe the various existing MDO methods which can be found in specific books (Papalambros and Wilde [15], Vanderplaats [16], Steuer [17]).

Methods

For this research, the authors performed a data search with the following terms: launch vehicle, MDO and concurrent engineering, and it was carried out using the Scopus search engine, with access provided by the Brazilian database Periódicos/CAPES.

The Periódicos/CAPES portal has established itself as an important tool for teaching and research activities in Brazil, providing an up-to-date digital scientific collection with a high impact factor. The business model developed by CAPES is unique in the world, where the Foundation negotiates subscription fees directly with publishers and makes the content available to many institutions in the country through a single virtual environment. This entire process facilitates and ensures user access to a vast and diverse collection of publications (Capes [18]).

When conducting a systematic review, the risk of bias is directly related to the number of databases and records collected. In this case, the Scopus search engine is considered to be one of the largest curated abstract and citation databases, with broad global and regional coverage of scientific journals, conference proceedings, and books (Baas et al. [19]). It includes sources from Elsevier, Springer, SAGE, IEEE, and others (Scopus [20]).

By selecting this database, the authors believe that the most important publications on the topic have been included in this systematic review. Each source was last searched on January $4^{\mathit{th}}$, 2025.

The abstracts were used to select (or not) the articles to be cited in this research. If the publication contained information related to the design of launch vehicles using MDO methods, the article was selected.

The database search was performed by Alexandre Oliveira and subsequently reviewed by Christopher Cerqueira. In conducting this systematic review, the authors did not use any automated tools to assist in the search process.

To synthesize the data obtained for this paper, the authors chose to list six sets of information for each outcome:

1. Publications with single, multiple single or multi-objective functions for the optimization problem;

2. Disciplines related to each one of the publications;

3. Cost function variables;

4. Type of architecture;

5. Type of algorithm used to find the solution; and

6. Fidelity of analysis;

The information was presented in charts to summarize the data in an easy-to-understand form. The authors obtained all the information by analyzing the data presented in the publications, which is very common in any multidisciplinary optimization problem.

Systematic reviews usually perform sensitivity analysis, identify the presence and extent of statistical heterogeneity, sources of heterogeneity among study results, and others. In the case of this paper, these types of analyses are not indicated because the variables are classified as qualitative and not quantitative variables.

No risk of bias due to missing results is expected in the analysis. The disciplines and variables included in each publication were double-checked. Missing results should only occur if the authors do not describe (with figures or text) the optimization objective function or the disciplines involved. In terms of certainty assessment, there is no cause-effect analysis in this study that could benefit from this type of analysis.

The publications were classified according to whether they addressed single, multiple single or multi-objective problems. The cost function variable aspects of each study were also described.

Regarding the type of architecture, the literature divides the problem into three types: monolithic, distributed, and hybrid.

In terms of the fidelity of analysis in each of the publications, they were separated by analytical, numerical and surrogate models.

With regard to the algorithms chosen to find the solution, the studies were divided into three groups: evolutionary algorithms, gradient-based algorithms and mixed algorithms.

The authors found 101 publications in the Scopus search engine from 1995 to 2024, of which 81 were related to this study. Publications related to other space activities (atmospheric aircraft, satellites and space missions), not related to launch vehicles, were excluded from the research.

Tables 1, 2 and 3 provide a comprehensive list of all publications with single objective, multiple single objective and multi-objective problems, as well as the corresponding cost function aspects and algorithms used to find the solution.

Table 1. Publications found with single objective problems with the corresponding cost function variables and algorithm

Authors	Year	Cost function variable aspects	Algorithm
Olds [21]	1994	Mass	Others
Braun et al. [22]	1995	Mass	GB
Gee et al. [23]	2004	Trajectory	EA
Qu et al. [24]	2004	Trajectory	Others
Akhtar and Linshu [25]	2005	Mass	EA + GB
Jodei et al. [26]	2006	Mass	GB
Qazi and Linshu [27]	2006	Mass	EA + GB
Akhtar and Linshu [28]	2006	Mass	EA
Roshanian and Keshavarz [29]	2007	Trajectory	GB
Briggs et al. [30]	2007	Mass	EA
Kalden [31]	2007	Mass	GB
Jodei et al. [32]	2009	Mass	GB
Rafique et al. [33]	2009a	Mass	EA
Rafique et al. [34]	2009b	Mass	EA
Rafique et al. [35]	2010	Mass	GB
Roshanian et al. [36]	2010	Mass	EA
Adami et al. [37]	2011	Mass	EA
Rafique et al. [38]	2011	Mass	EA
Carr et al. [39]	2012	Mass/Trajectory	GB
Ebrahimi et al. [40]	2012	Mass	EA
Roshanian and Ebrahimi [41]	2013	Mass	GB
Adami et al. [42]	2015	Mass	EA + GB
Bataleblu et al. [43]	2015	Mass	EA + GB
Villanueva and Abbas [44]	2015	Mass	EA
Villanueva [45]	2016	Mass	EA
Fujikawa et al. [46]	2017	Mass	GB
Afilipoae et al. [47]	2018	Mass/Trajectory	EA
Onel et al. [48]	2018	Mass/Trajectory	EA
Villanueva [49]	2018	Mass aspects	EA + GB
Zhang and Zhang [50]	2020	Mass/Trajectory	EA
Hao et al. [51]	2020	Mass	EA + GB
McCammon et al. [52]	2020	Mass/Trajectory	EA + GB
Wang et al. [53]	2020	Mass	EA
Brevault and Balesdent [54]	2021	Mass	EA
Balesdent et al. [55]	2022	Mass	GB
Onel and Chelaru [56]	2022	Mass/Trajectory	EA + GB
Alimohammadi et al. [57]	2023	Propulsive	Others
Balesdent et al. [58]	2023	Mass	EA
Messinger et al. [59]	2023	Mass	EA
Montella et al. [60]	2025	Mass	EA

EA evolutionary algorithms, GB gradient-based methods

Table 2. Publications found with multiple single objective problems with the corresponding cost function variables and algorithm

Authors	Year	Cost function variable aspects	Algorithm
Braun et al. [61]	1996	Mass/Propulsive/Cost	GB
Cormier et al. [62]	2000	Mass/Trajetory/ Propulsive	GB
Duranté et al. [63]	2004	Mass/Cost	EA
Brown and Olds [64]	2005	Mass/Propulsive	GB
Gang et al. [65]	2005	Mass/Trajetory	EA + GB
Jean-Marius [66]	2006	Mass/Cost	EA
Bayley and Hartfield [67]	2007	Mass/Cost	EA
Bayley et al. [68]	2008	Mass/Trajectory	EA
Delattre and Mongrard [69]	2007	Mass/Cost	EA
Perrot [70]	2007	Mass	GB
Balesdent et al. [71]	2010a	Mass	EA + GB
Balesdent et al. [72]	2010b	Mass/Trajectory	EA + GB
Geethaikrishnan et al. [73]	2010	Mass/Trajectory	EA + GB
Hosseini et al. [74]	2011	Mass/Trajectory/ Propulsive	EA
Jamilnia and Naghash [75]	2012	Mass/Trajectory	GB
Balesdent et al. [76]	2016	Mass	EA + GB
Liu and Chen [77]	2016	Mass/Trajectory/ Propulsive	GB
Lugo et al. [78]	2016	Mass	GB
Dupont et al. [79]	2019	Mass/Cost	EA + GB
Maddock et al. [80]	2018	Mass/Trajectory	GB
Morovat et al. [81]	2019	Mass	GB
Dresia et al. [82]	2021	Mass	EA
Wang et al. [83]	2021	Mass/Trajectory	EA
Wang et al. [84]	2022	Mass/Trajectory	EA + GB
Borwankar et al. [85]	2024	Mass	EA + GB

EA evolutionary algorithms, GB gradient-based methods

Table 3. Publications found with multi-objective problems with the corresponding cost function variables and algorithm

Authors	Year	Cost function variable aspects	Algorithm
Villeneuve et al. [86]	2004	Mass/Cost	Others
Luo and Tang [87]	2004	Mass	EA + GB
Castellini et al. [88]	2010	Mass/Cost/ Reliability	EA
Castellini et al. [89]	2011	Mass/Cost	EA
Kosugi et al. [90]	2011	Mass/Trajectory	EA
Zafar et al. [91]	2013	Mass/Trajectory	EA
Castellini et al. [92]	2014	Mass/Cost/ Reliability	GB
Gong et al. [93]	2014	Mass/Trajectory	GB
Kanazaki et al. [94]	2015	Mass/Trajectory	EA
Yoda et al. [95]	2015	Mass/Trajectory	EA
Brevault et al. [96]	2019	Mass	EA
Brevault et al. [97]	2020	Mass	EA
Priyadarshi et al. [98]	2020	Mass/Propulsive	EA
LI et al. [99]	2021	Mass/Trajectory/Cost	EA
Yan and Zhang [100]	2023	Propulsive	EA
Takao et al. [101]	2024	Mass/Trajectory	EA

EA evolutionary algorithms. GB gradient-based methods

Results and discussions

Figure 1 shows the percentage of publications separated by the type of optimization problem. Although the majority of studies related to MDO use many constraints across various disciplines, half of them (49.4%) optimize the design using only one cost function, with constraints related to other disciplines. The second most common approach is to perform multiple single optimization problems (30.9%), typically at the system and subsystem levels in distributed architectures. Lastly, only 19.7% of the studies focus on multi-objective problems.

[See PDF for image]

Fig. 1

Type of optimization problem separated in single, multiple single and multi objective problems

Multi-objective problems optimize more than one function simultaneously by constructing Pareto frontiers and identifying a set of optimized solutions. In contrast, single objective problems have been optimized using a variety of approaches, with constraints related to various disciplines. Within this approach, it is possible to provide some guidance through the optimization process. However, the design is always optimized for only one cost function.

In a multiple single objective problem, each discipline can be optimized separately at the subsystem level using predefined optimization algorithms, followed by optimization at the system level. This technique, however, does not guarantee finding a global minimum or maximum solution.

Finally, regarding multi-objective problems, searching the design space for these solutions may not be computationally efficient, especially as the problem complexity increases with additional disciplines and cost functions.

Figure 2 illustrates the disciplines associated with each one of the publications. Considering the disciplines involved in each of the optimization studies, the authors typically work with four primary disciplines: trajectory (94%), propulsion (91%), weights and sizing (84%), and aerodynamics (79%). The percentage represents the ratio of the number of publications citing the discipline to the total number of publications. It can be seen that the four primary disciplines are related to the analysis of launch vehicle performance. Cost is mentioned in only 12% of the results, indicating that it is usually considered as a secondary aspect for the conceptual project. This finding indicates that programmatic disciplines are not typically considered from the beginning of the launch vehicle design.

[See PDF for image]

Fig. 2

Disciplines related in each outcome of this systematic review

Figure 3 represents the aspects related to each of the disciplines that are used as the objective function cost. In other words, the design variable that will be minimized or maximized. For understanding the attributes of Fig. 3, Table 4 describes each aspect. It can be noted that the existing publications focus mostly on the optimization of some aspects of the design, mainly connected to mass aspects (65.22%), trajectory (19.13%), costs (9.56%), and propulsion (3.48%). The growing importance of cost analysis and business models in launch vehicle design was expected, particularly as the New Space Economy continues to flourish. This evolving space sector, driven by private companies and commercial ventures, places a greater emphasis on affordability and sustainability than traditional government-led space programs. As competition intensifies and more players enter the market, developing cost-effective solutions has become critical to success. In this environment, companies must not only focus on technological innovation, but also ensure that their business models are financially viable and scalable to meet the growing demand for space-related services. This shift underscores the need to balance technical advances with sound business strategies to succeed in the competitive landscape of space exploration and commercialization.

[See PDF for image]

Fig. 3

Objective function optimization aspects

Table 4. Type of objective functions and their description

Type of Objective Function	Description
Mass aspects	Minimum lift-off weight, maximum payload, maximum motor mass, minimum dry weight, mass ratio, stage sizing, minimum propellant mass.
Trajectory aspects	Minimum time-to-orbit, maximum range, maximum altitude, orbit positioning parameters.
Propulsion aspects	Propulsive parameters, fuel consumption.
Cost aspects	Development cost, cost per weight.
Other aspects	Reliability and thermal disciplines.

Figure 4 illustrates the percentage of publications according to each architecture definition.

Monolithic architectures describe the problem at a single level, analyzing all constraints and interactions in a single cycle. This form of the design optimization problem includes all coupling variables, coupling variable copies, state variables, consistency constraints, and residuals of the governing equations directly in the problem statement (Martins and Lambe [1]).

Distributed architectures, on the other hand, divide the optimization problem into multiple lower-level problems, each with its own set of design variables and associated constraints. A global optimization algorithm coordinates the entire process, optimizing an overall objective that encompasses each of the problems. The key advantage of distributed architectures is that domain experts can independently investigate lower-level problems without being impacted or restricted by others (Balesdent et al. [4]).

Finally, hybrid architectures work with a mixture of the two concepts, either working in monolithic structures or using distributed techniques. Each discipline involved in the problem can take advantage of each architecture implementation, depending on the context of use and domain analysis (Martins and Lambe [1]).

[See PDF for image]

Fig. 4

MDO architecture separated in monolithic, distributed and hybrid

In the analysis of monolithic architectures, the MDF technique is the most widely used (58% of publications on monolithic architecture). MDF solves the multidisciplinary analysis directly, without decomposing the problem. However, the technique can be computationally expensive, since a complete multidisciplinary analysis must be performed at each iteration. If the value of one variable changes, all other variables must be recalculated.

All-at-Once (AAO) is the most basic MDO method, but it appears in only 12% of the publications on monolithic architectures. In this type of architecture, control of the process is given to a system level optimizer that aims to optimize a global objective and calls subsystem evaluations. The optimizer handles all design, coupling, and state variables at once (Balesdent et al. [4]).

The same percentage appears for IDF architectures, which coupling variables and constraints must be added to the problem so that the consistency of the systemic solution is maintained at the end of the optimization. This is one way to reduce the computational cost compared to the MDF architecture. However, dealing with coupling may not be easy due to the multidisciplinary nature of the problems (Balesdent et al. [4]).

In about 19%, there is no actual description of the architecture used. However, the text of the publication mentions that the optimization process is performed at a single level, which is characteristic of monolithic architectures. Figure 5 illustrates the results.

[See PDF for image]

Fig. 5

Type of monolithic architectures

In the analysis of distributed architectures, 16 publications were found that use this approach. Half of them use the Collaborative Optimization (CO) strategy to organize the problem. The Bi-Level Integrated System Synthesis (BLISS) and Object Coordination Methodology (OCM) architectures were used only once, and the Analytical Target Cascading (ATC) architecture was used twice. Finally, there are 6 publications that describe bi-level and multi-level architectures but do not characterize them.

CO has several advantages over single-level optimization methods. It does not require changing the disciplinary codes to add a discipline to the CO optimization scheme, which indicates that the method is more modular. It also allows using the most appropriate optimization methods for each sub-problem, with possible actions by disciplinary experts. It also allows adding or modifying some subsystems without changing the whole design process. In this context, flexibility may be the most important feature of CO architecture. Unfortunately, the high number of coupling variables can cause difficulties in the convergence process, making the method less efficient. This fact leads to the use of this architecture for optimization problems with a small number of couplings (Balesdent et al. [4]).

In general, all of these statements are true for distributed architectures compared to monolithic architectures. The advantages of OCM are that the optimization process matches the modern organizational structure of the launcher. The method uses coordination variables that relate only the couplings between the different domains. This strategy greatly reduces the possibility of having an inflated system, which typically occurs in problems where there are many upper-level system design variables scattered throughout the lower-level problems (Liu and Chen [77]). In a complementary way, the major strength of the BLISS method is that it decouples the system level from the lower-level optimization problems. In this sense, there is no need to know which algorithm is being run in the lower-level problems, since the system level only has access to their outputs. Each problem can then be optimized using the most efficient tool for its domain, making it easier for experts to use their familiar tools (Balesdent et al. [4]). The Analytical Target Cascade (ATC) breaks down the entire system into various levels, with each level consisting of multiple independent elements. Within each level, design optimizations are conducted concurrently, taking advantage of parallel computing. The exchange of information between independent elements across adjacent levels is the central concept of the ATC approach. (Wang et al. [83, 84]).

Figure 6 shows the results for the distributed architecture descriptions.

[See PDF for image]

Fig. 6

Type of distributed architectures

Figure 7 illustrates the fidelity of the analysis in each of the publications.

Most problems in mechanics have their dynamic equations that are well known and modeled. In this context, most of the works found in this systematic review use analytical methods, indicating this characteristic. Analytical models involve deriving exact solutions through closed-form mathematical expressions, relying on established theories and formulas. Solutions are precise within the assumptions of the problem and the results are given as explicit equations or expressions (Kreyszig [102]).

In addition, the solution of some complex problems requires numerical methods (finite elements, Runge–Kutta numerical integrators, among others), especially in the disciplines of trajectory, aerodynamics, structures, thermal, among others, in order to facilitate the obtaining of the results. In this case, numerical models approximate solutions to problems using computational algorithms, often by iteration (Chapra and Canale [103]).

For very complex problems with multiple disciplines, design variables, and design constraints, it is possible to use surrogate models to reduce the computational load of the solution. They use simpler models (often statistical) to reduce computational cost by avoiding full model evaluations. Machine learning, response surface models, and reduced-order approaches are types of surrogate models (Forrester et al. [104]). These methods are particularly valuable when performing an initial exploration of the design space (Hammond [7]).

A detailed description of fidelity analysis with these types of modeling the problem can be seen in Kreyszig [102], Chapra and Canale [103], Forrester et al. [104].

[See PDF for image]

Fig. 7

Fidelity of analysis divided in analytical, numerical and surrogate models

Figure 8 illustrates the type of algorithm used to solve the MDO problem in each of the publications. As we can see, evolutionary algorithms are widely used to solve complex MDO problems because of their ability to handle the challenges posed by such problems, which include nonlinearity, high dimensionality, and the presence of multiple conflicting objectives (Rajwar et al. [105]). The growing computing power of modern computers also contributes to the use of this technique in complex projects, such as the design of launch vehicles. For example, evolutionary algorithms have a greater capacity to explore the search space, avoiding local minima by exploring different regions of the problem. In addition, unlike gradient-based methods, there is usually no need to insert initial conditions close to the optimal solution of the problem, which makes obtaining results faster. Nearly half of the papers use evolutionary techniques, the vast majority of which are Genetic Algorithms, followed by Particle Swarm Optimization, Simulated Annealing and Ant Colony Optimization.

[See PDF for image]

Fig. 8

Type of algorithm used to solve the MDO problem

Hybrid algorithms tend to take advantage of both evolutionary and gradient-based techniques. First, evolutionary algorithms are used to find the best solution region in the design space. Then, gradient-based methods are used to refine the solution in that region, further improving the solution obtained. All mixed-algorithm solutions found in this study use this approach, which indicates a good advantage for searching the solution.

By presenting this analysis, the authors have obtained an up-to-date picture of the scenario of the use of MDO algorithms, portraying the type of problem, the main architectures, the main cost functions used to solve the problems, the main disciplines used to model the problems, the fidelity of the analysis and the type of algorithm used to search for the solution.

From the publications found, it was clear that the majority of studies applying MDO methods to the conceptual design of launch vehicles tended to focus primarily on evaluating vehicle performance, without considering the programmatic and support disciplines.

This fact shows that there is still a lot of room for research on issues related to solving MDO problems when examining the complete project life cycle, following the more comprehensive concept of concurrent engineering. Six publications addressed the concept of concurrent engineering, but they did not describe the process, the computational tools, the multidisciplinary team, or the methodology that are fundamental elements of concurrent engineering theory (Bandecchi et al. [106]). They will be briefly described below.

Stevenson et al. [107] presented the integration of a suite of software tools designed to improve hypersonic and launch vehicle conceptual design and analysis. The paper also highlighted the benefits of using the software suite in an environment distributed across five different organizations. The Adaptive Modeling Language (AML) was selected as the design modeling environment for the study. Although the paper develops a collaborative framework, it presents a use case that relates the same common launch vehicle design performance disciplines: weights and sizing, propulsion, trajectory, and aerodynamics.

Kui and Chuan-jin [108] presented a framework for multidisciplinary design of launch vehicles. The paper describes the integration of many disciplines such as system parameters, control, dynamics, pneumatics, structure, load, ballistics, and others, with 5 main capabilities: integration of multidisciplinary design tools, system modeling and integration, design of experiments capability, common search capability of design optimization, and centralized data management. The framework was divided into several layers with many different functionalities, separated into user layer, collaborative service layer, data layer, and analysis service layer. Finally, the authors describe three types of personnel needed to implement the framework: general designers, disciplinary designers, and collaborative environment experts.

Braukhane et al. [109] presented a comparison of three studies conducted at the DLR Concurrent Engineering Facility related to launch vehicle design: a kickstage for launch vehicles, the VENUS-II project to improve VEGA performance, and the ANGELA project for a launch vehicle with a cost-effective solution. The study identified that the general characteristics of rockets imply adaptations for the design process compared to classical space system and mission design with the need to execute modifications for models, tools, iterations, and the team set-up. In this context, despite the existence of a known infrastructure and framework for the development of space missions, the development of launch vehicles must be tailored to the specific needs of launch design.

Clark et al. [110] presented an initiative from DLR titled Collaborative Launch Vehicle Analysis (CLaVA), which aimed to provide a new, flexible design environment to foster collaboration between experts in Space Transportation Systems design. The study mentions the previous experience with the collaborative platform in the Concurrent Engineering Facility (CEF) at DLR and describes a collaborative process chain divided into three loops to guide the design process. As with previous studies, the disciplines used are: weights and sizing, propulsion, aerodynamics, trajectory, control, stability and thermal disciplines.

Brevault et al. [111] described some limitations of concurrent engineering approaches related to the selection of correct design margins, the difficulty of implementing the process at the system level, and the difficulty of performing analysis under uncertainty. The author presented two groups of MDO methods to support launch vehicle design: deterministic methods and methods under uncertainty, in order to improve concurrent engineering sessions. However, there are no details on the concurrent engineering process to be followed for the design of the launch vehicle.

Fischer et al. [112] complemented CLaVA’s earlier DLR study by describing the use of metamodels to improve concurrent engineering studies. This metamodel, often referred to as a conceptual data model, provided a user interface for instantiating and sharing the system model within the design team. The article focuses more on explaining the tools and how the system works, while not detailing user interaction or disciplines.

Conclusions

The study yielded several notable findings regarding the methodology for solving multidisciplinary optimization problems. First, it was found that the majority of problems still involve the optimization of a single cost function. Despite advances in computing power, multi-objective problems that simultaneously optimize more than one cost function are less common in studies. Nevertheless, distributed architectures bring flexibility and modularity to MDO problems and optimize more than one objective function at different levels within the architecture.

With regard to the disciplines employed in the studies, the preponderance continues to operate within the domain of vehicle performance. It was expected that the discipline of costs would be more extensively utilized in studies with the emerging New Spatial Economy. Concepts related to the disciplines of logistics, AIT, Risks and Schedule were not mentioned among the MDO problems found in this review. In this context, these domains of knowledge provide a number of opportunities for further study. Launch vehicle development goes through all of these disciplines that are not related to vehicle performance, which could help reduce design changes later in the development cycle, saving costs and improving the project schedule. Looking at the broader concept of concurrent engineering, no publication was found that described the process, computational tools, multidisciplinary team, or methodology for launch vehicle design. Given the critical role that launch vehicles play in space missions and the growing demand for more efficient and cost-effective solutions in the space industry, the lack of extensive research on the application of concurrent engineering using MDO techniques to this area suggests a gap that could benefit from further exploration.

When selecting design variables for the objective function, there is a strong tendency to focus on vehicle mass, as it is logical to aim for a vehicle with lower dry mass due to its cost implications. However, as shown by Braun et al. [61], this assumption is not necessarily valid, even when a weight-based cost model is applied. By integrating both cost and schedule considerations into MDO problems, new insights can be gained into which technologies should be used for development, along with their associated costs and development timelines. As a result, different technologies may be selected for the conceptual design of the launcher, depending on the optimization variables chosen.

When considering the choice of algorithms, it is noticeable that more evolutionary algorithms are used than gradient-based methods. Much of this is due to the high complexity of launch vehicle design problems, the size of the design space, and the difficulty of providing representative initial conditions for the solution. As a result, meta-heuristics built around evolutionary algorithms are able to explore the problem more efficiently. Mixed-algorithms that combine both evolutionary algorithms and gradient-based methods are emerging and are now being published at nearly the same volume as papers that focus exclusively on gradient-based methods. This indicates a preference for using evolutionary algorithms in complex MDO studies.

Finally, the Brazilian Aeronautics Institute (ITA) intends to analyze the combination of MDO and concurrent engineering methodologies in future research related to the development of launch vehicles to support the activities of the Brazilian space sector.

Acknowledgements

The authors acknowledge the support of CAPES and the Brazilian Aeronautics Institute of Technology (ITA).

Author contributions

The database search was performed by A.M. Oliveira and subsequently reviewed by C.S. Cerqueira. Figures were prepared by A.M. Oliveira. All authors reviewed the manuscript.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Data availability

No datasets were generated or analysed during the current study.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

On behalf of all authors, the corresponding author states that there is no Competing interests.

Publisher's Note

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

References

1. Martins, JRRA; Lambe, AB. Multidisciplinary design optimization: a survey of architectures. AIAA J; 2013; 51, pp. 2049-2075. [DOI: https://dx.doi.org/10.2514/1.J051895]

2. Wang, Z; Huang, W; Yan, L. Multidisciplinary design optimization approach and its application to aerospace engineering. Chin Sci Bull; 2014; 59, pp. 5338-5353. [DOI: https://dx.doi.org/10.1007/s11434-014-0671-1]

3. Rowell L, Olds J, Unal R. Recent experiences in multidisciplinary conceptual design optimization for launch vehicles. In: 6th Symposium on Multidisciplinary Analysis and Optimization. American Institute of Aeronautics and Astronautics, Bellevue, WA, 1996. https://doi.org/10.2514/6.1996-4050.

4. Balesdent, M; Bérend, N; Dépincé, P; Chriette, A. A survey of multidisciplinary design optimization methods in launch vehicle design. Struct Multidiscip Optim; 2012; 45, pp. 619-642.2913433 [DOI: https://dx.doi.org/10.1007/s00158-011-0701-4]

5. Chen X, Yan L, Luo W, Xu L, Zhao Y, Wang Z. Research on theory and application of multidisciplinary design optimization of flying vehicles. In: 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 14th AIAA/ASME/AHS Adaptive Structures Conference 7th. American Institute of Aeronautics and Astronautics, Newport, RI 2006. https://doi.org/10.2514/6.2006-1721.

6. Giesing J, Barthelemy J-F. A summary of industry mdo applications and needs. In: 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. American Institute of Aeronautics and Astronautics, St. Louis, MO 1998. https://doi.org/10.2514/6.1998-4737.

7. Hammond WE. Design Methodologies for Space Transportation Systems. AIAA Education. American Institute of Aeronautics and Astronautics, Reston, VA 2001. https://doi.org/10.2514/4.861734.

8. Syan, CS; Menon, U. Concurrent Engineering; 1994; Dordrecht, Netherlands, Springer: [DOI: https://dx.doi.org/10.1007/978-94-011-1298-7]

9. Stjepandić, J; Wognum, N; Verhagen, WJC. Concurrent Engineering in the 21st Century; 2015; 1 Cham, Springer: 839. [DOI: https://dx.doi.org/10.1007/978-3-319-13776-6]

10. Winner RI, Pennell JP, Bertrand HE, Slusarczuk MM. The role of concurrent engineering in weapons system acquisition. IDA Report R-338 1988.

11. Lawson, M; Karandikar, HM. A survey of concurrent engineering. Concurr Eng; 1994; 2, pp. 1-6. [DOI: https://dx.doi.org/10.1177/1063293X9400200101]

12. Jo, HH; Parsaei, HR; Sullivan, WG. Principles of concurrent engineering; 1993; Boston, Springer: pp. 3-23. [DOI: https://dx.doi.org/10.1007/978-1-4615-3062-6_1]

13. Blachut, J; Eschenauer, HA. Emerging methods for multidisciplinary optimization; 2001; Vienna, Springer: [DOI: https://dx.doi.org/10.1007/978-3-7091-2756-8]

14. Page, MJ; McKenzie, JE; Bossuyt, PM; Boutron, I; Hoffmann, TC; Mulrow, CD; Shamseer, L; Tetzlaff, JM; Akl, EA; Brennan, SE; Chou, R; Glanville, J; Grimshaw, JM; Hróbjartsson, A; Lalu , MM; Li, T; Loder, EW; Mayo-Wilson, E; McDonald, S; McGuinness, LA; Stewart, LA; Thomas, J; Tricco, AC; Welch, VA; Whiting, P; Moher, D. statement: an updated guideline for reporting systematic reviews. BMJ; 2020; [DOI: https://dx.doi.org/10.1136/bmj.n71]

15. Papalambros, PY; Wilde, DJ. Principles of optimal design: modeling and computation; 2000; 2 Cambridge, Cambridge University Press: [DOI: https://dx.doi.org/10.1017/CBO9780511626418]

16. Vanderplaats, GN. Numerical optimization techniques for engineering design; 2001; 3 Colorado Springs, Vanderplaats Research and Development Inc: 449.

17. Steuer, RE. Multiple criteria optimization; theory, computation, and application; 1986; Hoboken, Wiley: 546. [DOI: https://dx.doi.org/10.1002/oca.4660100109]

18. Capes: Homepage. https://periodicos.capes.gov.br/index.php/sobre/nossa-historia.html. Accessed 4 Jan 2025.

19. Baas, J; Schotten, M; Plume, A; Côté, G; Karimi, R. Scopus as a curated, high-quality bibliometric data source for academic research in quantitative science studies. Quant Sci Stud; 2020; 1, pp. 377-86. [DOI: https://dx.doi.org/10.1162/qss_a_00019]

20. Scopus: Blog. https://blog.scopus.com/posts/peer-reviewed-publication-about-scopus-scopus-as-a-curated-high-quality-bibliometric-data. Accessed 4 Jan 2025.

21. Olds, JR. Results of a rocket-based combined-cycle SSTO design using parametric MDO methods. SAE Trans; 1994; [DOI: https://dx.doi.org/10.4271/941165]

22. Braun, RD; Powell, RW; Lepsch, RA; Stanley, DO; Kroo, IM. Comparison of two multidisciplinary optimization strategies for launch-vehicle design. J Spacecr Rocket; 1995; 32, pp. 404-410. [DOI: https://dx.doi.org/10.2514/3.26629]

23. Gee K, Tang C, Lawrence S. Rlv aerodynamic and trajectory analysis using an agent-based framework. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. American Institute of Aeronautics and Astronautics, Albany, NY 2004. https://doi.org/10.2514/6.2004-4329.

24. Qu M, Gage P, Sohn J, Bradford J, Starr B. Generalized vehicle performance closure model for two-stage-to-orbit launch vehicles. In: AIAA Paper, 2004. p. 9815–9821. https://doi.org/10.2514/6.2004-1221.

25. Akhtar S, Linshu H. Simulation-based optimization strategy for liquid fueled multi-stage space launch vehicle. In: Sixth International Conference on Parallel and Distributed Computing Applications and Technologies (PDCAT’05), 2005. p. 359–365. IEEE, Dalian, China. https://doi.org/10.1109/PDCAT.2005.215.

26. Jodei J, Ebrahimi M, Roshanian J. An automated approach to multidisciplinary system design optimization of small solid propellant launch vehicles. In: 2006 1st International Symposium on Systems and Control in Aerospace and Astronautics, 2006. p. 1401–1406. IEEE, Harbin, China. https://doi.org/10.1109/ISSCAA.2006.1627501.

27. Qazi, MUD; Linshu, H. Nearly-orthogonal sampling and neural network metamodel driven conceptual design of multistage space launch vehicle. CAD Comput Aided Des; 2006; 38, pp. 595-607. [DOI: https://dx.doi.org/10.1016/j.cad.2006.02.001]

28. Akhtar S, Linshu H. Support vector regression-driven multidisciplinary design optimization for multi-stage space launch vehicle considering throttling effect. Collection of Technical Papers - 44th AIAA Aerospace Sciences Meeting. 2006;6:4089–102. https://doi.org/10.2514/6.2006-341.

29. Roshanian, J; Keshavarz, Z. Effect of variable selection on multidisciplinary design optimization: a flight vehicle example. Chin J Aeronaut; 2007; 20, 1 pp. 86-96. [DOI: https://dx.doi.org/10.1016/S1000-9361(07)60012-0]

30. Briggs GP, Ray T, Milthorpe JF. Evolutionary algorithm use in optimisation of a launch vehicle stack model. In: Collection of Technical Papers - 45th AIAA Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics Inc., Reno, NV. 2007; vol. 7: pp. 4504–4513 https://doi.org/10.2514/6.2007-364.

31. Kalden O. Multidisciplinary design trajectory optimization of the reusable launch vehicle concept hopper. In: 2007 3rd international conference on recent advances in space technologies, IEEE, Istanbul, Turkey, 2007; p. 213–218. https://doi.org/10.1109/RAST.2007.4283979.

32. Jodei, J; Ebrahimi, M; Roshanian, J. Multidisciplinary design optimization of a small solid propellant launch vehicle using system sensitivity analysis. Struct Multidiscip Optim; 2009; 38, pp. 93-100. [DOI: https://dx.doi.org/10.1007/s00158-008-0260-5]

33. Rafique A, LinShu H, Zeeshan Q, Kamran A, Nisar K, Wang X. Hybrid optimization method for multidisciplinary design of air launched satellite launch vehicle. In: 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference Exhibit. American Institute of Aeronautics and Astronautics, Denver, CO 2009. https://doi.org/10.2514/6.2009-5535.

34. Rafique AF, LinShu H, Zeeshan Q, Kamran A. Multidisciplinary design of air-launched satellite launch vehicle using particle swarm optimization. In: 18th World IMACS/MODSIM Congress. Cairns, Australia. 2009.

35. Rafique, AF; Linshu, H; Kamran, A; Zeeshan, Q. Multidisciplinary design of air launched satellite launch vehicle: performance comparison of heuristic optimization methods. Acta Astronaut; 2010; 67, pp. 826-844. [DOI: https://dx.doi.org/10.1016/j.actaastro.2010.05.016]

36. Roshanian, J; Jodei, J; Mirshams, M; Ebrahimi, R; Mirzaee, M. Multi-level of fidelity multi-disciplinary design optimization of small, solid-propellant launch vehicles. Trans Japan Soc Aeronaut Space Sci; 2010; 53, pp. 73-83. [DOI: https://dx.doi.org/10.2322/tjsass.53.73]

37. Adami A, Nosratollahi M, Mortazavi M, Hosseini M. Multidisciplinary design optimization of a manned reentry mission considering trajectory and aerodynamic configuration. In: Proceedings of 5th International Conference on Recent Advances in Space Technologies - RAST2011, IEEE, Istanbul, Turkey. 2011; p. 598–603 https://doi.org/10.1109/RAST.2011.5966908.

38. Rafique, AF; He, L; Kamran, A; Zeeshan, Q. Hyper heuristic approach for design and optimization of satellite launch vehicle. Chin J Aeronaut; 2011; 24, pp. 150-163. [DOI: https://dx.doi.org/10.1016/S1000-9361(11)60019-8]

39. Carr RW, Jorris TR, Paulson EJ. Multidisciplinary design optimization for a reusable launch vehicle using multiple-phase pseudospectral optimization. In: Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012. https://doi.org/10.2514/6.2012-1350.

40. Ebrahimi, M; Roshanian, J; Barzinpour, F. Multidisciplinary design optimization approach for a small solid propellant launch vehicle conceptual design using hybrid simulated annealing. Appl Mech Mater; 2012; 110–116, pp. 4765-4771. [DOI: https://dx.doi.org/10.4028/www.scientific.net/AMM.110-116.4765]

41. Roshanian, J; Ebrahimi, M. Latin hypercube sampling applied to reliability-based multidisciplinary design optimization of a launch vehicle. Aerosp Sci Technol; 2013; 28, pp. 297-304. [DOI: https://dx.doi.org/10.1016/j.ast.2012.11.010]

42. Adami, A; Mortazavi, M; Nosratollahi, M. A new approach in multidisciplinary design optimization of upper-stages using combined framework. Acta Astronaut; 2015; 114, pp. 174-183. [DOI: https://dx.doi.org/10.1016/j.actaastro.2015.04.011]

43. Bataleblu AA, Roshanian J, Ebrahimi M. Hybrid search multi-discipline feasible design optimization of a typical space launch vehicle. In: 2015 7th International Conference on Recent Advances in Space Technologies (RAST), IEEE, Istanbul, Turkey, 2015. p. 455–460. https://doi.org/10.1109/RAST.2015.7208388.

44. Villanueva FM, Abbas H. Small launch vehicle optimal design configuration from ballistic missile components. In: 2015 12th International Bhurban Conference on Applied Sciences and Technology (IBCAST), IEEE, Islamabad, Pakistan. 2015; p. 228–234. https://doi.org/10.1109/IBCAST.2015.7058509.

45. Villanueva FM. Solid propellant launch vehicle development program for peru. In: 2016 IEEE Aerospace Conference. IEEE, Big Sky, MT. 2016. p. 1–15. https://doi.org/10.1109/AERO.2016.7500724.

46. Fujikawa, T; Tsuchiya, T; Tomioka, S. Multidisciplinary design optimization of a two-stage-to-orbit reusable launch vehicle with ethanol-fueled rocket-based combined cycle engines. Trans Japan Soc Aeronaut Space Sci; 2017; 60, pp. 265-275. [DOI: https://dx.doi.org/10.2322/tjsass.60.265]

47. Afilipoae, TP; Neculǎescu, AM; Onel, AI; Pricop, MV; Marin, A; Persinaru, AG; Cismilianu, AM; Munteanu, CE; Toader, A; Sirbi , A; Bennani, S; Chelaru, TV. Launch vehicle - MDO in the development of a microlauncher. Transp Res Proced; 2018; 29, pp. 1-11. [DOI: https://dx.doi.org/10.1016/j.trpro.2018.02.001]

48. Onel, AI; Afilipoae, TP; Neculaescu, AM; Pricop, MV. MDO approach for a two-stage microlauncher. INCAS Bull; 2018; 10, pp. 127-138. [DOI: https://dx.doi.org/10.13111/2066-8201.2018.10.3.11]

49. Villanueva FM. Design of mobile solid propellant launch vehicle using hybrid optimization approach. In: 2018 IEEE Aerospace Conference, IEEE, Big Sky, MT. 2018;p. 1–9. https://doi.org/10.1109/AERO.2018.8396566.

50. Zhang, D; Zhang, Y. Multidisciplinary design and optimization of an innovative nano air launch vehicle with a twin-fuselage uav as carrier aircraft. Acta Astronaut; 2020; 170, pp. 397-411. [DOI: https://dx.doi.org/10.1016/j.actaastro.2019.11.012]

51. Hao, Z; Haowen, L; Pengcheng, W; Guobiao, C; Feng, H. Uncertainty analysis and design optimization of solid rocket motors with finocyl grain. Struct Multidiscip Optim; 2020; 62, pp. 3521-3537. [DOI: https://dx.doi.org/10.1007/s00158-020-02728-8]

52. McCammon D, Khan S, Lindsay S. Multidisciplinary optimization for nano-satellite launch vehicles. In: IAC 2020 Congress Proceedings, 71st International Astronautical Congress (IAC) - IAC CyberSpace Edition 2020. 2020.

53. Wang, P; Tian, H; Zhu, H; Cai, G. Multi-disciplinary design optimization with fuzzy uncertainties and its application in hybrid rocket motor powered launch vehicle. Chin J Aeronaut; 2020; 33, pp. 1454-1467. [DOI: https://dx.doi.org/10.1016/j.cja.2019.11.002]

54. Brevault, L; Balesdent, M. Uncertainty quantification for multidisciplinary launch vehicle design using model order reduction and spectral methods. Acta Astronaut; 2021; 187, pp. 295-314. [DOI: https://dx.doi.org/10.1016/j.actaastro.2021.06.040]

55. Balesdent, M; Brevault, L; Valderrama-Zapata, JL; Urbano, A. All-at-once formulation integrating pseudo-spectral optimal control for launch vehicle design and uncertainty quantification. Acta Astronaut; 2022; 200, pp. 462-477. [DOI: https://dx.doi.org/10.1016/j.actaastro.2022.08.032]

56. Onel, AI; Chelaru, TV. Parametric analysis of a two-stage small launcher using a MDO approach. INCAS Bull; 2022; 14, pp. 79-96. [DOI: https://dx.doi.org/10.13111/2066-8201.2022.14.1.7]

57. Alimohammadi, HR; Naseh, H; Ommi, F. An integrated methodology applied for reliability based multi-disciplinary design optimization in epfe with lox/kerosene. Reliab Eng Syst Saf; 2023; [DOI: https://dx.doi.org/10.1016/j.ress.2023.109570]

58. Balesdent, M; Brevault, L; Paluch, B; Thépot, R; Wuilbercq, R; Subra, N; Defoort, S; Bourgaie, M; Vieille, B. Multidisciplinary design and optimization of winged architectures for reusable launch vehicles. Acta Astronaut; 2023; 211, pp. 97-115. [DOI: https://dx.doi.org/10.1016/j.actaastro.2023.05.041]

59. Messinger, TL; Corbiell, MS; Johansen, CT. Optimization and parametric studies of two-stage-to-orbit liquid oxygen/paraffin hybrid rocket vehicles. Aerospace Sci Technol; 2023; [DOI: https://dx.doi.org/10.1016/j.ast.2023.108495]

60. Montella, N; Iuspa, L; Vio, GA; Aprovitola, A; Pezzella, G; Viviani, A. Aeroshape design and low speed aerodynamic analysis of a crew return vehicle. Aerospace Sci Technol; 2025; [DOI: https://dx.doi.org/10.1016/j.ast.2024.109876]

61. Braun R, Moore A, Kroo I. Use of the collaborative optimization architecture for launch vehicle design. In: 6th Symposium on Multidisciplinary Analysis and Optimization. American Institute of Aeronautics and Astronautics, Bellevue,WA 1996. https://doi.org/10.2514/6.1996-4018.

62. Cormier T, Scott A, Ledsinger L, McCormick D, Way D, Olds J. Comparison of collaborative optimization to conventional design techniques for a conceptual rlv. In: 8th Symposium on Multidisciplinary Analysis and Optimization. American Institute of Aeronautics and Astronautics, Long Beach,CA 2000. https://doi.org/10.2514/6.2000-4885.

63. Duranté N, Dufour A, Pain V, Baudrillard G, Schoenauer M. Multidisciplinary analysis and optimisation approach for the design of expendable launchers. In: Collection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. American Institute of Aeronautics and Astronautics Inc., Albany, NY. 2004; vol. 3: p. 1597–1611. https://doi.org/10.2514/6.2004-4441 .

64. Brown NF, Olds JR. Evaluation of multidisciplinary optimization (mdo) techniques applied to a reusable launch vehicle. In: 43rd AIAA Aerospace Sciences Meeting and Exhibit - Meeting Papers, 2005. p. 8151–8171. https://doi.org/10.2514/6.2005-707.

65. Gang C, Min X, Zi-Ming W, Chen S-L. Multidisciplinary design optimization of rlv reentry trajectory. In: AIAA/CIRA 13th International Space Planes and Hypersonics Systems and Technologies, Capua, Italy 2005. https://doi.org/10.2514/6.2005-3270.

66. Jean-Marius T. Multidisciplinary optimization for early system design for expandable launchers. In: Collection of Technical Papers - 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2006. vol. 4, pp. 2573–2583. https://doi.org/10.2514/6.2006-7125.

67. Bayley DJ, Hartfield RJ. Design optimization of space launch vehicles for minimum cost using a genetic algorithm. In: Collection of Technical Papers - 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 2007. vol. 8, p. 8357–8372. https://doi.org/10.2514/6.2007-5852.

68. Bayley, DJ; Hartfield, RJ; Burkhalter, JE; Jenkins, RM. Design optimization of a space launch vehicle using a genetic algorithm. J Spacecr Rocket; 2008; 45, pp. 733-740. [DOI: https://dx.doi.org/10.2514/1.35318]

69. Delattre N, Mongrard O. The use of multi-disciplinary optimization for the design of expendable launchers. In: 2nd European Conference for Aero-Space Sciences - EUCASS 2007, Brussels, Belgium 2007.

70. Perrot L. Optimisation of reusable launchers trajectory by coordination of optimal control problems. In: 2nd European Conference for Aero-Space Sciences - EUCASS 2007, Brussels, Belgium 2007.

71. Balesdent, M; Bérend, N; Dépincé, P; Chriette, A. Multidisciplinary design optimization of multi-stage launch vehicle using flight phases decomposition. Int J Simul Multi Design Optim; 2010; 4, pp. 117-125. [DOI: https://dx.doi.org/10.1051/ijsmdo/2010015]

72. Balesdent M, Bérendy N, Dépincé P. Optimal design of expendable launch vehicles using stage-wise mdo formulation. In: 13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 2010. 2010. https://doi.org/10.2514/6.2010-9324.

73. Geethaikrishnan C, Mujumdar PM, Sudhakar K, Adimurthy V. A hybrid mdo architecture for launch vehicle conceptual design. In: Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2010. https://doi.org/10.2514/6.2010-2757.

74. Hosseini M, Toloie A, Nosratollahi M, Adami A. Multidisciplinary design optimization of an expendable launch vehicle. In: Proceedings of 5th International Conference on Recent Advances in Space Technologies - RAST2011, IEEE, Istanbul, Turkey. 2011; p. 702–707. https://doi.org/10.1109/RAST.2011.5966932.

75. Jamilnia, R; Naghash, A. Simultaneous optimization of staging and trajectory of launch vehicles using two different approaches. Aerosp Sci Technol; 2012; 23, pp. 85-92. [DOI: https://dx.doi.org/10.1016/j.ast.2011.06.013]

76. Balesdent, M; Brevault, L; Price, NB; Defoort, S; Le Riche, R; Kim, N-H; Haftka, RT; Bérend, N. Advanced space vehicle design taking into account multidisciplinary couplings and mixed epistemic/aleatory uncertainties; 2016; Cham, Springer: pp. 1-48. [DOI: https://dx.doi.org/10.1007/978-3-319-41508-6_1]

77. Liu Y, Chen W. Multidisciplinary design optimization of launch vehicle using objective coordination methodology. In: 2016 IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC). IEEE, Xi’an, China. 2016; p. 925–930. https://doi.org/10.1109/IMCEC.2016.7867346.

78. Lugo R, Litton D, Qu M, Shidner J, Powell R. A robust method to integrate end-to-end mission architecture optimization tools. In: 2016 IEEE Aerospace Conference, IEEE, Big Sky, MT. 2016; p. 1–8. https://doi.org/10.1109/AERO.2016.7500621.

79. Dupont, C; Tromba, A; Missonnier, S. New strategy to preliminary design space launch vehicle based on a dedicated MDO platform. Acta Astronaut; 2019; 158, pp. 103-110. [DOI: https://dx.doi.org/10.1016/j.actaastro.2018.04.013]

80. Maddock, CA; Ricciardi, L; West, M; West, J; Kontis, K; Rengarajan, S; Evans, D; Milne, A; McIntyre, S. Conceptual design analysis for a two-stage-to-orbit semi-reusable launch system for small satellites. Acta Astronaut; 2018; 152, pp. 782-792. [DOI: https://dx.doi.org/10.1016/j.actaastro.2018.08.021]

81. Morovat, F; Mozaffari, A; Roshanian, J; Zare, H. A novel aspect of composite sandwich fairing structure optimization of a two-stage launch vehicle (safir) using multidisciplinary design optimization independent subspace approach. Aerosp Sci Technol; 2019; 84, pp. 865-879. [DOI: https://dx.doi.org/10.1016/j.ast.2018.10.033]

82. Dresia, K; Jentzsch, S; Waxenegger-Wilfing, G; Hahn, RDS; Deeken, J; Oschwald, M; Mota, F. Multidisciplinary design optimization of reusable launch vehicles for different propellants and objectives. J Spacecr Rocket; 2021; 58, pp. 1017-1029. [DOI: https://dx.doi.org/10.2514/1.A34944]

83. Wang, P; Zhu, H; Tian, H; Cai, G. Analytic target cascading with fuzzy uncertainties based on global sensitivity analysis for overall design of launch vehicle powered by hybrid rocket motor. Aerospace Sci Technol; 2021; [DOI: https://dx.doi.org/10.1016/j.ast.2021.106680]

84. Wang, P; Xu, W; Zhu, H; Tian, H; Cai, G. An application of analytical target cascading for a hierarchical multidisciplinary system: the preliminary design of a launch vehicle powered by hybrid rocket motors. Aerospace; 2022; [DOI: https://dx.doi.org/10.3390/aerospace9120778]

85. Borwankar P, Kapania RK, Inoyama D, Stoumbos T. Multidisciplinary design analysis and optimization of space vehicle structures. In: AIAA SciTech Forum and Exposition, 2024. American Institute of Aeronautics and Astronautics Inc, AIAA, Orlando, FL 2024. https://doi.org/10.2514/6.2024-2898.

86. Villeneuve F, Osburg J, Mavris DN. A probabilistic conceptual design analysis of multi-stage launch vehicles. In: Collection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2004;vol. 1: pp. 62–72. https://doi.org/10.2514/6.2004-4305.

87. Luo Y, Tang G. Near-optimal low-thrust orbit transfer generated by parallel simulated annealing. In: 55th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law. American Institute of Aeronautics and Astronautics, Vancouver, Canada 2004. https://doi.org/10.2514/6.IAC-04-A.6.10.

88. Castellini F, Lavagna MR, Riccardi A, Büskens C. Multidisciplinary design optimization models and algorithms for space launch vehicles. In: 13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 2010. 2010. https://doi.org/10.2514/6.2010-9086.

89. Castellini F, Riccardi A, Lavagna M, Büskens C. Global and local multidisciplinary design optimization of expendable launch vehicles. In: Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2011. https://doi.org/10.2514/6.2011-1901.

90. Kosugi Y, Oyama A, Fujii K, Kanazaki M. Multidisciplinary and multi-objective design exploration methodology for conceptual design of a hybrid rocket. In: AIAA Infotech at Aerospace Conference and Exhibit 2011. 2011. https://doi.org/10.2514/6.2011-1634.

91. Zafar N, He LS, Xu D. A multiobjective, multidisciplinary design optimization of solid propellant based space launch vehicle. In: 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 2013. https://doi.org/10.2514/6.2013-1464.

92. Castellini, F; Lavagna, MR; Riccardi, A; Büskens, C. Quantitative assessment of multidisciplinary design models for expendable launch vehicles. J Spacecr Rocket; 2014; 51, pp. 343-359. [DOI: https://dx.doi.org/10.2514/1.A32527]

93. Gong C, Chen B, Gu L. Design and optimization of rbcc powered suborbital reusable launch vehicle. In: AIAA AVIATION 2014 -19th AIAA International Space Planes and Hypersonic Systems and Technologies Conference. American Institute of Aeronautics and Astronautics Inc., Atlanta, GA 2014. https://doi.org/10.2514/6.2014-2361.

94. Kanazaki, M; Ariyairt, A; Chiba, K; Kitagawa, K; Shimada, T. Durga, R. Conceptual design of single-stage rocket using hybrid rocket bymeans of genetic algorithm. Procedia engineering; 2015; Shanghai, Elsevier Ltd: pp. 198-207. [DOI: https://dx.doi.org/10.1016/j.proeng.2014.12.526]

95. Yoda H, Ito S, Kanazaki M, Kitagawa K, Shimada T, Chiba K. Evolutionary algorithm applied to ballistic launch vehicle design using hybrid rocket engine evaluated by enhanced flight simulation. In: 2015 IEEE Congress on Evolutionary Computation (CEC), IEEE, Sendai, Japan. 2015; p. 618–625https://doi.org/10.1109/CEC.2015.7256948.

96. Brevault L, Balesdent M, Hebbal A, Mirand APD. Surrogate model-based multi-objective mdo approach for partially reusable launch vehicle design. In: AIAA Scitech 2019 Forum. American Institute of Aeronautics and Astronautics Inc, AIAA, San Diego, CA 2019. https://doi.org/10.2514/6.2019-0704.

97. Brevault, L; Balesdent, M; Hebbal, A. Multi-objective multidisciplinary design optimization approach for partially reusable launch vehicle design. J Spacecr Rocket; 2020; 57, pp. 373-390. [DOI: https://dx.doi.org/10.2514/1.A34601]

98. Priyadarshi, P; Joseph, L; Saroha, K. Optimal two-stage parachute and retro motor sizing for launch vehicle stage recovery. Sādhanā; 2020; 45, 241. [DOI: https://dx.doi.org/10.1007/s12046-020-01420-3]

99. Li, Y; Fang, J; Sun, B; Li, K; Cai, G. Index allocation for a reusable lox/ch4 rocket engine. Chin J Aeronaut; 2021; 34, pp. 432-440. [DOI: https://dx.doi.org/10.1016/j.cja.2020.04.017]

100. Yan, H; Zhang, X. A self-adaptive local diversity-preserving NSGA-ii for the multidisciplinary design optimization of a miniaturized supersonic rocket. Aerospace Sci Technol; 2023; [DOI: https://dx.doi.org/10.1016/j.ast.2023.108230]

101. Takao Y, Ozawa T, Yeo SH, Suenaga K, Bandera AY, Ogawa H. Multidisciplinary system design optimization for lunar transportation missions via surrogate-assisted evolutionary algorithms. In: AIAA SciTech Forum and Exposition, 2024. American Institute of Aeronautics and Astronautics Inc, AIAA, Orlando, FL 2024. https://doi.org/10.2514/6.2024-0206.

102. Kreyszig, E. Advanced engineering mathematics; 2011; 10 Hoboken, Wiley:

103. Chapra, SC; Canale, RP. Numerical methods for engineers; 2021; 8 New York, McGraw-Hill:

104. Forrester, A; Sobester, A; Keane, A. Engineering design via surrogate modelling: a practical guide; 2008; Chichester, Wiley: [DOI: https://dx.doi.org/10.1002/9780470770801]

105. Rajwar, K; Deep, K; Das, S. An exhaustive review of the metaheuristic algorithms for search and optimization: taxonomy, applications, and open challenges. Artif Intell Rev; 2023; 56, pp. 13187-13257. [DOI: https://dx.doi.org/10.1007/s10462-023-10470-y]

106. Bandecchi M, Melton B, Gardini B. The esa/estec concurrent design facility. In: Proceedings of the 2nd European Systems Engineering Conference (EuSEC), Munich, Germany 2000.

107. Stevenson MD, Hartong AR, Zweber JV, Bhungalia AA, Grandhi RV. Collaborative Design Environment for Space Launch Vehicle Design and Optimization. U.S. Department of Defense - DTIC. 1993. https://apps.dtic.mil/sti/tr/pdf/ADP014189.pdf. Accessed 16 Jan 2025.

108. Kui W, Chuan-jin G. A study on the multidisciplinary collaborative optimization platform solution of launch vehicles. In: 2009 Third International Symposium on Intelligent Information Technology Application, IEEE, Nanchang, China. 2009; p. 677–680. https://doi.org/10.1109/IITA.2009.187.

109. Braukhane A, Dumont E, Koch AD, Joumier H. Launch vehicle design applying concurrent engineering. In: AIAA SPACE 2013 Conference and Exposition. American Institute of Aeronautics and Astronautics, San Diego, CA 2013. https://doi.org/10.2514/6.2013-5430.

110. Clark V, Johannsson M, Martelo A. Process chain development for iterative, concurrent design of advanced space transportation systems. In: Proceedings of the 6th European Conference for Aerospace Sciences, Kraków, Poland 2015.

111. Brevault, L; Balesdent, M; Defoort, S. Preliminary study on launch vehicle design: applications of multidisciplinary design optimization methodologies. Concurr Eng; 2018; 26, pp. 93-103. [DOI: https://dx.doi.org/10.1177/1063293X17737131]

112. Fischer PM, Deshmukh M, Koch AD, Mischke R, Gomez AM, Schreiber A, Gerndt A. Enabling a conceptual data model and workflow integration environment for concurrent launch vehicle analysis. In: Proceedings of the 69th International Astronautical Congress (IAC), International Astronautical Federation (IAF), Bremen, Germany. 2018; p. 1–11.