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In 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.

Though 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.

Four 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.

The 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.

The computational drawbacks of existing numerical methods have forced researchers to rely on heuristic algorithms. Heuristic methods are powerful in obtaining the solution of optimization problems. Although they are approximate methods (i.e. their solution are good, but not provably optimal), they do not require the derivatives of the objective function and constraints. Also, they use probabilistic transition rules instead of deterministic rules. The purpose of this paper is to present an improved ant colony optimization (IACO) for constrained engineering design problems.

IACO has the capacity to handle continuous and discrete problems by using sub‐optimization mechanism (SOM). SOM is based on the principles of finite element method working as a search‐space updating technique. Also, SOM can reduce the size of pheromone matrices, decision vectors and the number of evaluations. Though IACO decreases pheromone updating operations as well as optimization time, the probability of finding an optimum solution is not reduced.

Utilizing SOM in the ACO algorithm causes a decrease in the size of the pheromone vectors, size of the decision vector, size of the search space, the number of function evaluations, and finally the required optimization time. SOM performs as a search‐space‐updating rule, and it can exchange discrete‐continuous search domain to each other.

The suitability of using ACO for constrained engineering design problems is presented, and applied to optimal design of different engineering problems.

This paper aims to represent an improved whale optimization algorithm (WOA) based on a Lévy flight trajectory and called the LWOA algorithm to solve engineering optimization problems. The LWOA makes the WOA faster, more robust and significantly enhances the WOA. In the LWOA, the Lévy flight trajectory enhances the capability of jumping out of the local optima and is helpful for smoothly balancing exploration and exploitation of the WOA. It has been successfully applied to five standard engineering optimization problems. The simulation results of the classical engineering design problems and real application exhibit the superiority of the LWOA algorithm in solving challenging problems with constrained and unknown search spaces when compared to the basic WOA algorithm or other available solutions.

In this paper, an improved WOA based on a Lévy flight trajectory and called the LWOA algorithm is represented to solve engineering optimization problems.

It has been successfully applied to five standard engineering optimization problems. The simulation results of the classical engineering design problems and real application exhibit the superiority of the LWOA algorithm in solving challenging problems with constrained and unknown search spaces when compared to the basic WOA algorithm or other available solutions.

An improved WOA based on a Lévy flight trajectory and called the LWOA algorithm is first proposed.

Highly non-linear optimization problems exist in many practical engineering applications. To deal with these problems, this study aims to propose an improved optimization algorithm, named, adaptive resistance and stamina strategy-based dragonfly algorithm (ARSSDA).

To speed up the convergence, ARSSDA applies an adaptive resistance and stamina strategy (ARSS) to conventional dragonfly algorithm so that the search step can be adjusted appropriately in each iteration. In ARSS, it includes the air resistance and physical stamina of dragonfly during a flight. These parameters can be updated in real time as the flight status of the dragonflies.

The performance of ARSSDA is verified by 30 benchmark functions of Congress on Evolutionary Computation 2014’s special session and 3 well-known constrained engineering problems. Results reveal that ARSSDA is a competitive algorithm for solving the optimization problems. Further, ARSSDA is used to search the optimal parameters for a bucket wheel reclaimer (BWR). The aim of the numerical experiment is to achieve the global optimal structure of the BWR by minimizing the energy consumption. Results indicate that ARSSDA generates an optimal structure of BWR and decreases the energy consumption by 22.428% compared with the initial design.

A novel search strategy is proposed to enhance the global exploratory capability and convergence speed. This paper provides an effective optimization algorithm for solving constrained optimization problems.

The purpose of this article is to analyze the optimization process in depth, elaborating on the components of the entire process and the techniques used. Researchers have been drawn to the expanding trend of optimization since the turn of the century. The rate of research can be used to measure the progress and increase of this optimization procedure. This study is phenomenal to understand the optimization process and different algorithms in addition to their application by keeping in mind the current computational power that has increased the implementation for several engineering applications.

Two-dimensional analysis has been carried out for the optimization process and its approaches to addressing optimization problems, i.e. computational power has increased the implementation. The first section focuses on a thorough examination of the optimization process, its objectives and the development of processes. Second, techniques of the optimization process have been evaluated, as well as some new ones that have emerged to overcome the above-mentioned problems.

This paper provided detailed knowledge of optimization, several approaches and their applications in civil engineering, i.e. structural, geotechnical, hydraulic, transportation and many more. This research provided tremendous emerging techniques, where the lack of exploratory studies is to be approached soon.

Optimization processes have been studied for a very long time, in engineering, but the current computational power has increased the implementation for several engineering applications. Besides that, different techniques and their prediction modes often require high computational strength, such parameters can be mitigated with the use of different techniques to reduce computational cost and increase accuracy.

Bat algorithm (BA) is a global optimization method, but has a worse performance on engineering optimization problems. The purpose of this study is to propose a novel chaotic bat algorithm based on catfish effect (CE-CBA), which can effectively deal with optimization problems in real-world applications.

Incorporating chaos strategy and catfish effect, the proposed algorithm can not only enhance the ability for local search but also improve the ability to escape from local optima traps. On the one hand, the performance of CE-CBA has been evaluated by a set of numerical experiment based on classical benchmark functions. On the other hand, five benchmark engineering design problems have been also used to test CE-CBA.

The statistical results of the numerical experiment show the significant improvement of CE-CBA compared with the standard algorithms and improved bat algorithms. Moreover, the feasibility and effectiveness of CE-CBA in solving engineering optimization problems are demonstrated.

This paper proposed a novel BA with two improvement strategies including chaos strategy and catfish effect for the first time. Meanwhile, the proposed algorithm can be used to solve many real-world engineering optimization problems with several decision variables and constraints.

As an advanced calculation methodology, reliability-based multidisciplinary design optimization (RBMDO) has been widely acknowledged for the design problems of modern complex engineering systems, not only because of the accurate evaluation of the impact of uncertain factors but also the relatively good balance between economy and safety of performance. However, with the increasing complexity of engineering technology, the proposed RBMDO method gradually cannot effectively solve the higher nonlinear coupled multidisciplinary uncertainty design optimization problems, which limits the engineering application of RBMDO. Many valuable works have been done in the RBMDO field in recent decades to tackle the above challenges. This study is to review these studies systematically, highlight the research opportunities and challenges, and attempt to guide future research efforts.

This study presents a comprehensive review of the RBMDO theory, mainly including the reliability analysis methods of different uncertainties and the decoupling strategies of RBMDO.

First, the multidisciplinary design optimization (MDO) preliminaries are given. The basic MDO concepts and the corresponding mathematical formulas are illustrated. Then, the procedures of three RBMDO methods with different reliability analysis strategies are introduced in detail. These RBMDO methods were proposed for the design optimization problems under different uncertainty types. Furtherly, an optimization problem for a certain operating condition of a turbine runner blade is introduced to illustrate the engineering application of the above method. Finally, three aspects of future challenges for RBMDO, namely, time-varying uncertainty analysis; high-precision surrogate models, and verification, validation and accreditation (VVA) for the model, are discussed followed by the conclusion.

The scope of this study is to introduce the RBMDO theory systematically. Three commonly used RBMDO-SORA methods are reviewed comprehensively, including the methods' general procedures and mathematical models.

The purpose of this paper is to propose a novel improved teaching and learning-based algorithm (TLBO) to enhance its convergence ability and solution accuracy, making it more suitable for solving large-scale optimization issues.

Utilizing multiple cooperation mechanisms in teaching and learning processes, an improved TBLO named CTLBO (collectivism teaching-learning-based optimization) is developed. This algorithm introduces a new preparation phase before the teaching and learning phases and applies multiple teacher–learner cooperation strategies in teaching and learning processes. Applying modularization idea, based on the configuration structure of operators of CTLBO, six variants of CTLBO are constructed. For identifying the best configuration, 30 general benchmark functions are tested. Then, three experiments using CEC2020 (2020 IEEE Conference on Evolutionary Computation)-constrained optimization problems are conducted to compare CTLBO with other algorithms. At last, a large-scale industrial engineering problem is taken as the application case.

Experiment with 30 general unconstrained benchmark functions indicates that CTLBO-c is the best configuration of all variants of CTLBO. Three experiments using CEC2020-constrained optimization problems show that CTLBO is one powerful algorithm for solving large-scale constrained optimization problems. The application case of industrial engineering problem shows that CTLBO and its variant CTLBO-c can effectively solve the large-scale real problem, while the accuracies of TLBO and other meta-heuristic algorithm are far lower than CLTBO and CTLBO-c, revealing that CTLBO and its variants can far outperform other algorithms. CTLBO is an excellent algorithm for solving large-scale complex optimization issues.

The innovation of this paper lies in the improvement strategies in changing the original TLBO with two-phase teaching–learning mechanism to a new algorithm CTLBO with three-phase multiple cooperation teaching–learning mechanism, self-learning mechanism in teaching and group teaching mechanism. CTLBO has important application value in solving large-scale optimization problems.

In multidisciplinary design optimization (MDO), if the relationships between design variables and some output parameters, which are important performance constraints, are complex implicit problems, plenty of time should be spent on computationally expensive simulations to identify whether the implicit constraints are satisfied with the given design variables during the optimization iteration process. The purpose of this paper is to propose an ensemble of surrogates-based analytical target cascading (ESATC) method to tackle such MDO engineering design problems with reduced computational cost and high optimization accuracy.

Different surrogate models are constructed based on the sample point sets obtained by Latin hypercube sampling (LHS) method. Then, according to the error metric of each surrogate model, the repeated ensemble of surrogates is constructed to approximate the implicit objective functions and constraints. Under the framework of analytical target cascading (ATC), the MDO problem is decomposed into several optimization subproblems and the function of analysis module of each subproblem is simulated by repeated ensemble of surrogates, working together to find the optimum solution.

The proposed method shows better modeling accuracy and robustness than other individual surrogate model-based ATC method. A numerical benchmark problem and an industrial case study of the structural design of a super heavy vertical lathe machine tool are utilized to demonstrate the accuracy and efficiency of the proposed method.

This paper integrates a repeated ensemble method with ATC strategy to construct the ESATC framework which is an effective method to solve MDO problems with implicit constraints and black-box objectives.

Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly degrade the overall performance of engineering systems and change the feasibility of the obtained solutions. This paper aims to propose a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) to obtain the robust Pareto set under the interval uncertainty.

In K-MORO, the nested optimization structure is reduced into a single loop optimization structure to ease the computational burden. Considering the interpolation uncertainty from the Kriging metamodel may affect the robustness of the Pareto optima, an objective switching and sequential updating strategy is introduced in K-MORO to determine (1) whether the robust analysis or the Kriging metamodel should be used to evaluate the robustness of design alternatives, and (2) which design alternatives are selected to improve the prediction accuracy of the Kriging metamodel during the robust optimization process.

Five numerical and engineering cases are used to demonstrate the applicability of the proposed approach. The results illustrate that K-MORO is able to obtain robust Pareto frontier, while significantly reducing computational cost.

The proposed approach exhibits great capability for practical engineering design optimization problems that are multi-objective and constrained and have uncertainties.

A K-MORO approach is proposed, which can obtain the robust Pareto set under the interval uncertainty and ease the computational burden of the robust optimization process.