Multidisciplinary Design Problems Research Articles

Optimization of electric vehicle design problems using improved electric eel foraging optimization algorithm

Abstract This paper introduces a novel approach, the Modified Electric Eel Foraging Optimization (EELFO) algorithm, which integrates artificial neural networks (ANNs) with metaheuristic algorithms for solving multidisciplinary design problems efficiently. Inspired by the foraging behavior of electric eels, the algorithm incorporates four key phases: interactions, resting, hunting, and migrating. Mathematical formulations for each phase are provided, enabling the algorithm to explore and exploit solution spaces effectively. The algorithm’s performance is evaluated on various real-world optimization problems, including weight optimization of engineering components, economic optimization of pressure handling vessels, and cost optimization of welded beams. Comparative analyses demonstrate the superiority of the MEELFO algorithm in achieving optimal solutions with minimal deviations and computational effort compared to existing metaheuristic methods.

Optimization Framework for Early Conceptual Design of Helicopters

This work illustrates how a proposed method can be used to create optimization frameworks for early conceptual design studies and to increase overall knowledge at an early design stage. The method is intended to facilitate concept selection in challenging domains that typically involve multidisciplinary design problems with contradictory requirements. The main focus of the work presented here is on the conceptual design of helicopters; however, the method is intended to be applicable to early design studies in other domains as well. In short, statistics about existing helicopters are collected and compiled to provide a basis for various regression analyses. The purpose of this is to unravel relationships in the data and to obtain simple estimation models from statistical regressions that can be used in conjunction with existing formulas and equations to generate an initial helicopter design estimate. Models for each discipline, such as aerodynamics, are then created using the outcomes of the regression analyses and existing equations. Lastly, the method is used to define a multidisciplinary design optimization framework incorporating all the models obtained from the different disciplines. A case study based on search and rescue operations is used to test the proposed framework in order to obtain possible first suggestions for the baseline design of a new general-purpose search and rescue helicopter.

Topology optimization with automated derivative computation for multidisciplinary design problems

Topology optimization with automated derivative computation for multidisciplinary design problems

Data-Driven Set Based Concurrent Engineering Method for Multidisciplinary Design Optimization

<div class="section abstract"><div class="htmlview paragraph">In the development of multi-disciplinary systems, many experts in different discipline fields need to collaborate with each other to identify a feasible design where all multidisciplinary constraints are satisfied. This paper proposes a novel data-driven set-based concurrent engineering method for multidisciplinary design optimization problems by using machine learning techniques. The proposed set-based concurrent engineering method has two advantages in the concurrent engineering process. The first advantage is the decoupling ability of multidisciplinary design optimization problems. By introducing the probabilistic representation of multidisciplinary constraint functions, feasible regions of each discipline sub-problem can be decoupled by the rule of product. The second advantage is an efficient concurrent study to explore feasible regions. A batch sampling strategy is introduced to find feasible regions based on Bayesian Active Learning (BAL). In the batch BAL, Gaussian Process models of each multi-disciplinary constraint are trained. Based on the posterior distributions of trained Gaussian Process models, an acquisition functions that combine Probability of Feasibility and Entropy Search are evaluated. In order to generate new sampling points in and around feasible regions, optimization problems to maximize the acquisition function are solved by assuming that the constraint function is Lipschitz continuous. To show the effectiveness of the proposed method, a practical numerical example of a multi-disciplinary vehicle design problem is demonstrated.</div></div>

A boosted chimp optimizer for numerical and engineering design optimization challenges.

Chimp optimization algorithm (ChoA) has a wholesome attitude roused by chimp’s amazing thinking and hunting ability with a sensual movement for finding the optimal solution in the global search space. Classical Chimps optimizer algorithm has poor convergence and has problem to stuck into local minima for high-dimensional problems. This research focuses on the improved variants of the chimp optimizer algorithm and named as Boosted chimp optimizer algorithms. In one of the proposed variants, the existing chimp optimizer algorithm has been combined with SHO algorithm to improve the exploration phase of the existing chimp optimizer and named as IChoA-SHO and other variant is proposed to improve the exploitation search capability of the existing ChoA. The testing and validation of the proposed optimizer has been done for various standard benchmarks and Non-convex, Non-linear, and typical engineering design problems. The proposed variants have been evaluated for seven standard uni-modal benchmark functions, six standard multi-modal benchmark functions, ten standard fixed-dimension benchmark functions, and 11 types of multidisciplinary engineering design problems. The outcomes of this method have been compared with other existing optimization methods considering convergence speed as well as for searching local and global optimal solutions. The testing results show the better performance of the proposed methods excel than the other existing optimization methods.

An effective solution to numerical and multi-disciplinary design optimization problems using chaotic slime mold algorithm.

Slime mold algorithm (SMA) is a recently developed meta-heuristic algorithm that mimics the ability of a single-cell organism (slime mold) for finding the shortest paths between food centers to search or explore a better solution. It is noticed that entrapment in local minima is the most common problem of these meta-heuristic algorithms. Thus, to further enhance the exploitation phase of SMA, this paper introduces a novel chaotic algorithm in which sinusoidal chaotic function has been combined with the basic SMA. The resultant chaotic slime mold algorithm (CSMA) is applied to 23 extensively used standard test functions and 10 multidisciplinary design problems. To check the validity of the proposed algorithm, results of CSMA has been compared with other recently developed and well-known classical optimizers such as PSO, DE, SSA, MVO, GWO, DE, MFO, SCA, CS, TSA, PSO-DE, GA, HS, Ray and Sain, MBA, ACO, and MMA. Statistical results suggest that chaotic strategy facilitates SMA to provide better performance in terms of solution accuracy. The simulation result shows that the developed chaotic algorithm outperforms on almost all benchmark functions and multidisciplinary engineering design problems with superior convergence.

Multidisciplinary free-form optimization of solid structures for mean compliance minimization and time-dependent temperature control

A parameter-free free-form optimization method to solve multidisciplinary shape optimization problems of solid structures is presented in this paper. The design objective is both to minimize the mean compliance of linear elastic structures and to control the temperature at arbitrary locations and time periods for arbitrary loadings and under volume constraint, simultaneously. The multidisciplinary design problem is formulated as a distributed-parameter shape optimization problem based on the variational method, and the global objective function is defined using an original normalized weighted sum method. The shape gradient density functions with respect to the shape variation are derived based on the material derivative and the adjoint variable methods. The shape gradient density functions theoretically derived are applied to the H1 gradient method, a gradient method in the function space, to obtain the optimal shape while maintaining the smoothness of the shape. Numerical examples are considered to demonstrate the validity and the effectiveness of the developed optimization method.

Optimal design of blade in pump as turbine based on multidisciplinary feasible method.

In order to make the pump as turbine (PAT) run efficiently and safely, a multidisciplinary optimization design method for PAT blade, which gives consideration to both the hydraulic and intensity performances, is proposed based on multidisciplinary feasibility (MDF) optimization strategy. This method includes blade parametric design, Latin Hypercube Sampling (LHS) experimental design, CFD technology, FEA technology, GA-BP neural network and NSGA-II algorithm. Specifically, a parameterized PAT blade with cubic non-uniform B-spline curve is adopted, and the control point of blade geometry is taken as the design variable. The LHS experimental design method obtains the sample points of training GA-BP neural network in the design space of variables. The hydraulic performance of each sample point (including the hydraulic pressure load on the blade surface) and the strength performance analysis of blades are completed by CFD and FEA technology respectively. In order to save calculation time of the whole optimization design, the multi-disciplinary performance analysis of each sample in the optimization process is completed by single-coupling method. Then, GA-BP neural network is trained. Finally, the multi-disciplinary optimization design problem of PAT blade is solved by the optimization technology combining GA-BP neural network and NSGA-II algorithm. Based on this optimization method, the PAT blade is optimized and improved. The efficiency of the optimized PAT is improved by 1.71% and the maximum static stress on the blade is reduced by 7.98%, which shows that this method is feasible.

A symbiotic organisms search algorithm-based design optimization of constrained multi-objective engineering design problems

PurposeIn line with computational technological advances, obtaining optimal solutions for engineering problems has become attractive research topics in various disciplines and real engineering systems having multiple objectives. Therefore, it is aimed to ensure that the multiple objectives are simultaneously optimized by considering them among the trade-offs. Furthermore, the practical means of solving those problems are principally concentrated on handling various complicated constraints. The purpose of this paper is to suggest an algorithm based on symbiotic organisms search (SOS), which mimics the symbiotic reciprocal influence scheme adopted by organisms to live on and breed within the ecosystem, for constrained multi-objective engineering design problems.Design/methodology/approachThough the general performance of SOS algorithm was previously well demonstrated for ordinary single objective optimization problems, its efficacy on multi-objective real engineering problems will be decisive about the performance. The SOS algorithm is, hence, implemented to obtain the optimal solutions of challengingly constrained multi-objective engineering design problems using the Pareto optimality concept.FindingsFour well-known mixed constrained multi-objective engineering design problems and a real-world complex constrained multilayer dielectric filter design problem are tackled to demonstrate the precision and stability of the multi-objective SOS (MOSOS) algorithm. Also, the comparison of the obtained results with some other well-known metaheuristics illustrates the validity and robustness of the proposed algorithm.Originality/valueThe algorithmic performance of the MOSOS on the challengingly constrained multi-objective multidisciplinary engineering design problems with constraint-handling approach is successfully demonstrated with respect to the obtained outperforming final optimal designs.

An Extended Artificial Neural Network Assisted Hybrid Harris Hawks and Whale Optimizer to Find Optimal Solution for Engineering Design Problems

The algorithms that have been developed recently have decorous behavior to solve and find optimum solution to various optimization problems in search space. Withal such calculations stuck in issues nearby quest space for compelled engineering problems. In succession to achieve an optimal solution a hybrid algorithmic approach is proffered. Artificial Neural Network (ANN) is considered as better solution for the known outputs. A hybrid variant of applying ANN on Harris Hawks and Whale Optimization Algorithm (ANNHHOWOA) is proposed to achieve effective solution for engineering problems. The effectiveness of proposed algorithm is tested for various non-linear, non-convex and standard engineering problems and to approve consequences of proposed algorithm standard benchmarks and multidisciplinary design problems have been considered. The validation endorsed that the results shown by ANNHHOWOA showed much better results than individual ANN, HHO and WOA and its effectiveness on multidisciplinary engineering problems.

Design Optimization for Mass Sizing of LEO Communication Satellites

This paper focuses on the design optimization of communication satellites for the constellation in low earth orbit (LEO). The optimization starts with defining an objective function, which is the total mass of satellites, as a function of their orbit altitude, antenna transmit diameter, and nominal data rates. The optimization routine was done in order to minimize the total mass of satellites in order to reduce the total launch mass and the total cost. The use of three different design parameters has led to a genetic algorithm (GA) as an optimization method to find the best value for each design parameter. The results show that the optimization process using a genetic algorithm is successfully applied in solving complex multidisciplinary design problems such as the design of a communication satellite system with acceptable error.

An Enhanced Reliability Index Method and Its Application in Reliability-Based Collaborative Design and Optimization

When designing complex mechanical equipment, uncertainties should be considered to enhance the reliability of performance. The Reliability Index Method (RIM) is a powerful tool which has been widely utilized in engineering design under uncertainties. To reduce computational cost in RIM, first or second order Taylor approximation is introduced to convert nonlinear probability constraint to the equivalent linear constraint during optimization process. Generally, this approximation process is performed at Most Probable Point (MPP) to reduce the loss of reliability analysis accuracy. However, it is difficult for the original RIM to be utilized in the situation that MPP is collinear and RIM has the same direction with the gradient of performance function at MPP. To tackle the above challenges, an Enhanced RIM (ERIM) is proposed in this study. The Collaborative Optimization (CO) strategy is combined with ERIM. The formula of CO using ERIM is given to solve reliability-based multidisciplinary design and optimization problems. A design problem of the speed reducer is utilized in this study to show the effectiveness of the proposed method.

Topology optimization in OpenMDAO

Recently, topology optimization has drawn interest from both industry and academia as the ideal design method for additive manufacturing. Topology optimization, however, has a high entry barrier as it requires substantial expertise and development effort. The typical numerical methods for topology optimization are tightly coupled with the corresponding computational mechanics method such as a finite element method and the algorithms are intrusive, requiring an extensive understanding. This paper presents a modular paradigm for topology optimization using OpenMDAO, an open-source computational framework for multidisciplinary design optimization. This provides more accessible topology optimization algorithms that can be non-intrusively modified and easily understood, making them suitable as educational and research tools. This also opens up further opportunities to explore topology optimization for multidisciplinary design problems. Two widely used topology optimization methods—the density-based and level-set methods—are formulated in this modular paradigm. It is demonstrated that the modular paradigm enhances the flexibility of the architecture, which is essential for extensibility.

Overview of control-centric integrated design for hypersonic vehicles

Hypersonic vehicles (HSVs) exhibit significant advantages over other vehicles, including the wide range of velocity and large airspace types, and these features have contributed to the rapid development of HSVs in the last 20 years. Moreover, hypersonic technologies have become a multidisciplinary research topic in the fields of aerodynamics, propulsion, structure, material, and control. Different types of re-entry gliding, air-breathing cruise, and aerospace vehicles have been designed to realize ambitious tasks, which in turn influenced the technological advancements and process change in the military. This paper summarizes the control-oriented integrated design of HSVs. First, the status of current research on the distinct characteristics and technique issues of HSVs is introduced. Then, the progresses made on complex modeling, guidance and control, and trajectory optimization are elaborated to exhibit the significant research interest in hypersonic technologies. The control-integrated design of HSVs is emphasized to solve the multidisciplinary design problems associated with the model and its control and trajectory. Various strategies regarding the multidisciplinary optimization design are also proposed to solve the integrated design problem. Finally, suggestions are provided for the control-oriented integrated design of HSVs.

Structural reliability analysis and uncertainties‐based collaborative design and optimization of turbine blades using surrogate model

AbstractIn power and energy systems, both the aerodynamic performance and the structure reliability of turbine equipment are affected by utilized blades. In general, the design process of blade is high dimensional and nonlinear. Different coupled disciplines are also involved during this process. Moreover, unavoidable uncertainties are transported and accumulated between these coupled disciplines, which may cause turbine equipment to be unsafe. In this study, a saddlepoint approximation reliability analysis method is introduced and combined with collaborative optimization method to address the above challenge. During the above reliability analysis and design optimization process, surrogate models are utilized to alleviate the computational burden for uncertainties‐based multidisciplinary design and optimization problems. Smooth response surfaces of the performance of turbine blades are constructed instead of expensively time‐consuming simulations. A turbine blade design problem is solved here to validate the effectiveness and show the utilization of the given approach.

陽的縮約に基づくマルチフィデリティ解析モデルによる複合領域配置設計最適化法（放熱特性を考慮した配置設計問題への適用）

Multi-fidelity analysis has been used for reducing the calculation cost of evaluating the design solution, which is the most costly process in design optimization. In general, multi-fidelity analysis is applied to problems with continuous design variables, which are suitable to construct an approximate model of design space such as the response surface. On the other hand, combinatorial optimization problems, e.g., layout design, are difficult to apply the conventional multi-fidelity analysis, since the response surface cannot be constructed due to the property of the design variables. In this paper, we propose a multi-fidelity optimization method independent of the response surface and a simple analysis model for the method, and apply them to multi-disciplinary optimal layout design problem which is a complicated combinatorial optimization problem. The proposed analytical model, which adopts the concept of the explicit method, realizes for reducing the calculation time by simplifying the physical phenomenon. Then, the multi-fidelity optimization method is constructed by combining the proposed analysis model with the thermal network method which is a well-known thermal analysis method. We confirm that there is a strong correlation between the calculation result of the proposed analysis model and of a CAE software, and show that the proposed analysis model is suitable as a low fidelity model. The effectiveness of the proposed optimization method is demonstrated through numerical experiments.

A non-nested collaborative optimization method for multidisciplinary design optimization and its application in satellite designs

As a decomposition-based multidisciplinary design optimization (MDO) method, collaborative optimization (CO) has been widely applied in aerospace design systems. During the execution process of CO method, subsystem optimizations are nested into the system optimization, and numerous subsystem analyses are thus required to achieve the consistency for entire system. For this problem, a non-nested collaborative optimization (NNCO) method is presented in this paper. In this method, system and subsystem optimizations are conducted sequentially and repeatedly, and system consistency is then coordinated with the use of a loop process by updating penalty parameters. The feasibility of this method was firstly tested in solving common analytical problems, and it was further applied in two MDO problems of an observation satellite as well as a maneuver satellite. All of the results have demonstrated the efficacy of this proposed NNCO method, which indicates that it is effective and suitable for dealing with practical multidisciplinary design problems.

Expert-guided evolutionary algorithm for layout design of complex space stations

ABSTRACTThe layout of a space station should be designed in such a way that different equipment and instruments are placed for the station as a whole to achieve the best overall performance. The station layout design is a typical nondeterministic polynomial problem. In particular, how to manage the design complexity to achieve an acceptable solution within a reasonable timeframe poses a great challenge. In this article, a new evolutionary algorithm has been proposed to meet such a challenge. It is called as the expert-guided evolutionary algorithm with a tree-like structure decomposition (EGEA-TSD). Two innovations in EGEA-TSD are (i) to deal with the design complexity, the entire design space is divided into subspaces with a tree-like structure; it reduces the computation and facilitates experts’ involvement in the solving process. (ii) A human–intervention interface is developed to allow experts’ involvement in avoiding local optimums and accelerating convergence. To validate the proposed algorithm, the layout design of one-space station is formulated as a multi-disciplinary design problem, the developed algorithm is programmed and executed, and the result is compared with those from other two algorithms; it has illustrated the superior performance of the proposed EGEA-TSD.

Convergence Study of Local Continuum Sensitivity Method Using Spatial Gradient Reconstruction

Gradient-based optimization for large-scale, multidisciplinary design problems requires accurate and efficient sensitivity analysis to compute design derivatives. The local continuum shape sensitivity method with spatial gradient reconstruction is a nonintrusive design sensitivity analysis method that was previously published for linear and nonlinear structural analysis. The numerical behavior, accuracy, and convergence for this method are studied using benchmark problems. The benchmark problems include finite element analysis of an axial bar and finite element analysis of a rectangular membrane using unstructured grids. The results are used to establish general guidelines for conducting mesh refinement and selecting the parameters associated with spatial gradient reconstruction calculations. Lastly, design derivatives are calculated for the potential flow solution around a Joukowsky airfoil. The analytic design derivative solutions are used to calculate the true errors associated with the local continuum design derivative results.

Matrix-free aerostructural optimization of aircraft wings

In structural optimization subject to failure constraints, computing the gradients of a large number of functions with respect to a large number of design variables may not be computationally practical. Often, the number of constraints in these optimization problems is reduced using constraint aggregation at the expense of a higher mass of the optimal structural design. This work presents results of structural and coupled aerodynamic and structural design optimization of aircraft wings using a novel matrix-free augmented Lagrangian optimizer. By using a matrix-free optimizer, the computation of the full constraint Jacobian at each iteration is replaced by the computation of a small number of Jacobian-vector products. The low cost of the Jacobian-vector products allows optimization problems with thousands of failure constraints to be solved directly, mitigating the effects of constraint aggregation. The results indicate that the matrix-free optimizer reduces the computational work of solving the optimization problem by an order of magnitude compared to a traditional sequential quadratic programming optimizer. Furthermore, the use of a matrix-free optimizer makes the solution of large multidisciplinary design problems, in which gradient information must be obtained through iterative methods, computationally tractable.