A Comparative Study of Metaheuristic Optimization Algorithms for Solving Real-World Engineering Design Problems

Real-world engineering design problems with complex objective functions under some constraints are relatively difficult problems to solve.Such design problems are widely experienced in many engineering fields,such as industry,automotive,construction,machinery,and interdisciplinary research.However,there are established optimization techniques that have shown effectiveness in addressing these types of issues.This research paper gives a comparative study of the implementation of seventeen new metaheuristic methods in order to optimize twelve distinct engineering design issues.The algorithms used in the study are listed as:transient search optimization(TSO),equilibrium optimizer(EO),grey wolf optimizer(GWO),moth-flame optimization(MFO),whale optimization algorithm(WOA),slimemould algorithm(SMA),harris hawks optimization(HHO),chimp optimization algorithm(COA),coot optimization algorithm(COOT),multi-verse optimization(MVO),arithmetic optimization algorithm(AOA),aquila optimizer(AO),sine cosine algorithm(SCA),smell agent optimization(SAO),and seagull optimization algorithm(SOA),pelican optimization algorithm(POA),and coati optimization algorithm(CA).As far as we know,there is no comparative analysis of recent and popular methods against the concrete conditions of real-world engineering problems.Hence,a remarkable research guideline is presented in the study for researchersworking in the fields of engineering and artificial intelligence,especiallywhen applying the optimization methods that have emerged recently.Future research can rely on this work for a literature search on comparisons of metaheuristic optimization methods in real-world problems under similar conditions.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

Multidisciplinary Modeling and Optimization Method of Remote Sensing Satellite Parameters Based on SysML-CEA

To enhance the efficiency of system modeling and optimization in the conceptual design stage of satellite parameters,a system modeling and optimization method based on System Modeling Language and Co-evolutionary Algorithm is proposed.At first,the objectives of satellite mission and optimization problems are clarified,and a design matrix of discipline structure is constructed to process the coupling relationship of design variables and constraints of the orbit,payload,power and quality disciplines.In order to solve the problem of increasing nonlinearity and coupling between these disciplines while using a standard collaborative optimization algorithm,an improved genetic algorithm is proposed and applied to system-level and discipline-level models.Finally,the CO model of satellite parameters is solved through the collaborative simulation of Cameo Systems Modeler(CSM)and MATLAB.The result obtained shows that the method proposed in this paper for the conceptual design phase of satellite parameters is efficient and feasible.It can shorten the project cycle effectively and additionally provide a reference for the optimal design of other complex projects.

Reliability-based multidisciplinary design optimization using incremental shifting vector strategy and its application in electronic product design

Use of multidisciplinary analysis in reliabilitybased design optimization(RBDO) results in the emergence of the important method of reliability-based multidisciplinary design optimization(RBMDO). To enhance the efficiency and convergence of the overall solution process,a decoupling algorithm for RBMDO is proposed herein.Firstly, to decouple the multidisciplinary analysis using the individual disciplinary feasible(IDF) approach, the RBMDO is converted into a conventional form of RBDO. Secondly,the incremental shifting vector(ISV) strategy is adopted to decouple the nested optimization of RBDO into a sequential iteration process composed of design optimization and reliability analysis, thereby improving the efficiency significantly. Finally, the proposed RBMDO method is applied to the design of two actual electronic products: an aerial camera and a car pad. For these two applications, two RBMDO models are created, each containing several finite element models(FEMs) and relatively strong coupling between the involved disciplines. The computational results demonstrate the effectiveness of the proposed method.

Multidisciplinary Design Optimization of Vehicle Instrument Panel Based on Multi-objective Genetic Algorithm

Typical multidisciplinary design optimization（MDO） has gradually been proposed to balance performances of lightweight, noise, vibration and harshness（NVH） and safety for instrument panel（IP） structure in the automotive development. Nevertheless, plastic constitutive relation of Polypropylene（PP） under different strain rates, has not been taken into consideration in current reliability-based and collaborative IP MDO design. In this paper, based on tensile test under different strain rates, the constitutive relation of Polypropylene material is studied. Impact simulation tests for head and knee bolster are carried out to meet the regulation of FMVSS 201 and FMVSS 208, respectively. NVH analysis is performed to obtain mainly the natural frequencies and corresponding mode shapes, while the crashworthiness analysis is employed to examine the crash behavior of IP structure. With the consideration of lightweight, NVH, head and knee bolster impact performance, design of experiment（DOE）, response surface model（RSM）, and collaborative optimization（CO） are applied to realize the determined and reliability-based optimizations, respectively. Furthermore, based on multi-objective genetic algorithm（MOGA）, the optimal Pareto sets are completed to solve the multi-objective optimization（MOO） problem. The proposed research ensures the smoothness of Pareto set, enhances the ability of engineers to make a comprehensive decision about multi-objectives and choose the optimal design, and improves the quality and efficiency of MDO.

Effect of Variable Selection on Multidisciplinary Design Optimization:a Flight Vehicle Example

Different multidisciplinary design optimization （MDO） problems are formulated and compared. Two MDO formulations are applied to a sounding rocket in order to optimize the performance of the rocket. In the MDO of the referred vehicle, three disciplines have been considered, which are trajectory, propulsion and aerodynamics. A special design structure matrix is developed to assist data exchange between disciplines. This design process uses response surface method （RSM） for multidisciplinary optimization of the rocket. The RSM is applied to the design in two categories： the propulsion model and the system level. In the propulsion model, RSM determines an approximate mathematical model of the engine output parameters as a function of design variables. In the system level, RSM fits a surface of objective function versus design variables. In the first MDO problem formulation, two design variables are selected to form propulsion discipline. In the second one, three new design variables from geometry are added and finally, an optimization method is applied to the response surface in the system level in order to find the best result. Application of the first developed multidisciplinary design optimization procedure increased accessible altitude （performance index） of the referred sounding rocket by twenty five percents and the second one twenty nine.

Multidisciplinary Design Optimization of A Human Occupied Vehicle Based on Bi-Level Integrated System Collaborative Optimization

The design of Human Occupied Vehicle （HOV） is a typical multidisciplinary problem, but heavily dependent on the experience of naval architects at present engineering design. In order to relieve the experience dependence and improve the design, a new Multidisciplinary Design Optimization （MDO） method ＂Bi-Level Integrated System Collaborative Optimization （BLISCO）＂ is applied to the conceptual design of an HOV, which consists of hull module, resistance module, energy module, structure module, weight module, and the stability module. This design problem is defined by 21 design variables and 23 constraints, and its objective is to maximize the ratio of payload to weight. The results show that the general performance of the HOV can be greatly improved by BLISCO.

MULTIDISCIPLINARY ROBUST OPTIMIZATION DESIGN

Because uncertainty factors inevitably exist under multidisciplinary designenvironment, a hierarchical multidisciplinary robust optimization design based on response surfaceis proposed. The method constructs optimization model of subsystem level and system level tocoordinate the coupling among subsystems, and also the response surface based on the artificialneural network is introduced to provide information for system level optimization tool to maintainthe independence of subsystems, i.e. to realize multidisciplinary parallel design. The applicationcase of electrical packaging demonstrates that reasonable robust optimum solution can be yielded andit is a potential and efficient multi-disciplinary robust optimization approach.

Applying the disciplinary relation matrix to multidisciplinary design optimization modeling and solving

A new efficient coupling relationship description method has been developed to provide an automated and visualized way to multidisciplinary design optimization (MDO) modeling and solving. The disciplinary relation matrix (DRM) is proposed to describe the coupling relationship according to disciplinary input/output variables, and the MDO definition has been reformulated to adopt the new interfaces. Based on these, a universal MDO solving procedure is proposed to establish an automated and efficient way for MDO modeling and solving. Through a simple and convenient initial configuration, MDO problems can be solved using any of available MDO architectures with no further effort. Several examples are used to verify the proposed MDO modeling and solving process. Result shows that the DRM method has the ability to simplify and automate the MDO procedure, and the related MDO framework can evaluate the MDO problem automatically and efficiently.

APPLICATION OF HYBRID GENETIC ALGORITHM IN AEROELASTIC MULTIDISCIPLINARY DESIGN OPTIMIZATION OF LARGE AIRCRAFT

The genetic/gradient-based hybrid algorithm is introduced and used in the design studies of aeroelastic optimization of large aircraft wings to attain skin distribution,stiffness distribution and design sensitivity.The program of genetic algorithm is developed by the authors while the gradient-based algorithm borrows from the modified method for feasible direction in MSC/NASTRAN software.In the hybrid algorithm,the genetic algorithm is used to perform global search to avoid to fall into local optima,and then the excellent individuals of every generation optimized by the genetic algorithm are further fine-tuned by the modified method for feasible direction to attain the local optima and hence to get global optima.Moreover,the application effects of hybrid genetic algorithm in aeroelastic multidisciplinary design optimization of large aircraft wing are discussed,which satisfy multiple constraints of strength,displacement,aileron efficiency,and flutter speed.The application results show that the genetic/gradient-based hybrid algorithm is available for aeroelastic optimization of large aircraft wings in initial design phase as well as detailed design phase,and the optimization results are very consistent.Therefore,the design modifications can be decreased using the genetic/gradient-based hybrid algorithm.

Uncertain Multidisciplinary Design Optimization on Next Generation Subsea Production System by Using Surrogate Model and Interval Method

The innovative Next Generation Subsea Production System(NextGen SPS)concept is a newly proposed petroleum development solution in ultra-deep water areas.The definition of NextGen SPS involves several disciplines,which makes the design process difficult.In this paper,the definition of NextGen SPS is modeled as an uncertain multidisciplinary design optimization(MDO)problem.The deterministic optimization model is formulated,and three concerning disciplines—cost calculation,hydrodynamic analysis and global performance analysis are presented.Surrogate model technique is applied in the latter two disciplines.Collaborative optimization(CO)architecture is utilized to organize the concerning disciplines.A deterministic CO framework with two disciplinelevel optimizations is proposed firstly.Then the uncertainties of design parameters and surrogate models are incorporated by using interval method,and uncertain CO frameworks with triple loop and double loop optimization structure are established respectively.The optimization results illustrate that,although the deterministic MDO result achieves higher reduction in objective function than the uncertain MDO result,the latter is more reliable than the former.

Multidisciplinary Design Optimization with a New Effective Method

Collaborative optimization （CO） is one of the most widely used methods in multidisciplinary design optimization （MDO）, which is an effective methodology to solve modem complex engineering problems. CO consists of two-level optimization problems which are system optimization problem and subspace optimization problem. The architecture of CO can reserve the autonomy of individual disciplines in maximum, while providing a mechanism for coordinating design problem. However, CO has low computation efficiency and is easy to diverge. For the purpose of solving these problems, the former improved methods were studied. The relaxation factors were used to change the system consistency constraints to inequality constraints, or the response surface estimation was used to surrogate the system consistency constraints. However, these methods didn＇t avoid the computational difficulties very well, furthermore, some new problems arose. The concept of optimum constraint sensitivity was proposed, and the quadratic constraints in system level were reformed. Hence, a new collaborative optimization was developed, which is called system level dynamic constraint collaborative optimization （DCCO）. The novel method is able to increase the exchange of information between system level and disciplinary level. The optimization results of each disciplinary optimization can be feedback to system level with the optimum constraint sensitivity. On the basis of the information, the new system level linear dynamic constraints can be constructed; it is better to reflect the effect of disciplinary level optimizations. The system level optimizer can clearly capture the boundary where disciplinary objective functions become zero, and considerably enhance the convergence. Two standard MDO examples were conducted to verify the feasibility and effectiveness of DCCO. The results show that DCCO can save the solving time, and is much better in terms of convergence and robustness, hence, the new method is more efficient.

Design methodology of a mini-missile considering flight performance and guidance precision

The design of mini-missiles(MMs)presents several novel challenges.The stringent mission requirement to reach a target with a certain precision imposes a high guidance precision.The miniaturization of the size of MMs makes the design of the guidance,navigation,and control(GNC)have a larger-thanbefore impact on the main-body design(shape,motor,and layout design)and its design objective,i.e.,flight performance.Pursuing a trade-off between flight performance and guidance precision,all the relevant interactions have to be accounted for in the design of the main body and the GNC system.Herein,a multi-objective and multidisciplinary design optimization(MDO)is proposed.Disciplines pertinent to motor,aerodynamics,layout,trajectory,flight dynamics,control,and guidance are included in the proposed MDO framework.The optimization problem seeks to maximize the range and minimize the guidance error.The problem is solved by using the nondominated sorting genetic algorithm II.An optimum design that balances a longer range with a smaller guidance error is obtained.Finally,lessons learned about the design of the MM and insights into the trade-off between flight performance and guidance precision are given by comparing the optimum design to a design provided by the traditional approach.

Multidisciplinary design optimization on production scale of underground metal mine

In order to ensure overall optimization of the underground metal mine production scale, multidisciplinary design optimization model of production scale which covers the subsystem objective function of income of production, safety and environmental impact in the underground metal mine was established by using multidisciplinary design optimization method. The coupling effects from various disciplines were fully considered, and adaptive mutative scale chaos immunization optimization algorithm was adopted to solve multidisciplinary design optimization model of underground metal mine production scale. Practical results show that multidisciplinary design optimization on production scale of an underground lead and zinc mine reflect the actual operating conditions more realistically, the production scale is about 1.25 Mt/a (Lead and zinc metal content of 160 000 t/a), the economic life is approximately 14 a, corresponding coefficient of production profits can be increased to 15.13%, safety factor can be increased to 5.4% and environmental impact coefficient can be reduced by 9.52%.

Robust Multiobjective and Multidisciplinary Design Optimization of Electrical Drive Systems

Design and optimization of electrical drive systems often involve simultaneous consideration of multiple objectives that usually contradict to each other and multiple disciplines that normally coupled to each other.This paper aims to present efficient system-level multiobjective optimization methods for the multidisciplinary design optimization of electrical drive systems.From the perspective of quality control,deterministic and robust approaches will be investigated for the development of the optimization models for the proposed methods.Meanwhile,two approximation methods,Kriging model and Taylor expansion are employed to decrease the computation/simulation cost.To illustrate the advantages of the proposed methods,a drive system with a permanent magnet synchronous motor driven by a field oriented control system is investigated.Deterministic and robust Pareto optimal solutions are presented and compared in terms of several steady-state and dynamic performances(like average torque and speed overshoot)of the drive system.The robust multiobjective optimization method can produce optimal Pareto solutions with high manufacturing quality for the drive system.

Stability analysis of underground engineering based on multidisciplinary design optimization

Aiming at characteristics of underground engineering,analyzed the feasibility of Multidisciplinary Design Optimization (MDO) used in underground engineering,and put forward a modularization-based MDO method and the idea of MDO to resolve problems in stability analysis,proving the validity and feasibility of using MDO in underground engi- neering.Characteristics of uncertainty,complexity and nonlinear become bottle-neck to carry on underground engineering stability analysis by MDO.Therefore,the application of MDO in underground engineering stability analysis is still at a stage of exploration,which need some deep research.

Torpedo Overall Multidisciplinary Design Based on Collaborative Optimization

A torpedo multidisciplinary design optimization (MDO) based on the collaborative optimization is proposed. Through decomposition and coordination, some problems in torpedo design such as multidisciplinary coupling, large data volume and complex data relationships can be solved. Taking aim at some complex problems in the torpedo design, such as computation in multidisciplinary design, organization, modeling and information exchange, the collaborative optimization methods based on approximate technology are presented. An example to increase the torpedo range is also given. It demonstrates that the method can converge quickly, has higher reliability and smaller data throughput, and is a very effective MDO method.

Multidisciplinary Design and Optimization of Satellite Launch Vehicle Using Latin Hypercube Design of Experiments

The design of new Satellite Launch Vehicle （SLV） is of interest, especially when a combination of Solid and Liquid Propulsion is included. Proposed is a conceptual design and optimization technique for multistage Low Earth Orbit （LEO） bound SLV comprising of solid and liquid stages with the use of Genetic Algorithm （GA） as global optimizer. Convergence of GA is improved by introducing initial population based on the Design of Experiments （DOE） Technique. Latin Hypercube Sampling （LHS）-DOE is used for its good space filling properties. LHS is a stratified random procedure that provides an efficient way of sampling variables from their multivariate distributions. In SLV design minimum Gross Lift offWeight （GLOW） concept is traditionally being sought. Since the development costs tend to vary as a function of GLOW, this minimum GLOW is considered as a minimum development cost concept. The design approach is meaningful to initial design sizing purpose for its computational efficiency gives a quick insight into the vehicle performance prior to detailed design.

Multidisciplinary integrated design of long-range ballistic missile using PSO algorithm

In the case of the given design variables and constraint functions, this paper is concerned with the rapid overall parameters design of trajectory, propulsion and aerodynamics for long-range ballistic missiles based on the index of the minimum take-off mass.In contrast to the traditional subsystem independent design, this paper adopts the research idea of the combination of the subsystem independent design and the multisystem integration design.Firstly, the trajectory, propulsion and aerodynamics of the subsystem are separately designed by the engineering design, including the design of the minimum energy trajectory, the computation of propulsion system parameters, and the calculation of aerodynamic coefficient and dynamic derivative of the missile by employing the software of missile DATCOM. Then, the uniform design method is used to simplify the constraint conditions and the design variables through the integration design, and the accurate design of the optimized variables would be accomplished by adopting the uniform particle swarm optimization(PSO) algorithm. Finally, the automation design software is written for the three-stage solid ballistic missile. The take-off mass of 29 850 kg is derived by the subsystem independent design, and 20 constraints are reduced by employing the uniform design on the basis of 29 design variables and 32 constraints, and the take-off mass is dropped by 1 850 kg by applying the combination of the uniform design and PSO. The simulation results demonstrate the effectiveness and feasibility of the proposed hybrid optimization technique.

Application of the optimal Latin hypercube design and radial basis function network to collaborative optimization

Improving the efficiency of ship optimization is crucial for modern ship design. Compared with traditional methods, multidisciplinary design optimization (MDO) is a more promising approach. For this reason, Collaborative Optimization (CO) is discussed and analyzed in this paper. As one of the most frequently applied MDO methods, CO promotes autonomy of disciplines while providing a coordinating mechanism guaranteeing progress toward an optimum and maintaining interdisciplinary compatibility. However, there are some difficulties in applying the conventional CO method, such as difficulties in choosing an initial point and tremendous computational requirements. For the purpose of overcoming these problems, optimal Latin hypercube design and Radial basis function network were applied to CO. Optimal Latin hypercube design is a modified Latin Hypercube design. Radial basis function network approximates the optimization model, and is updated during the optimization process to improve accuracy. It is shown by examples that the computing efficiency and robustness of this CO method are higher than with the conventional CO method.