Differential Evolution (DE) is arguably one of the most powerful and versatile evolutionary optimizers for the continuous parameter spaces in recent times. Almost 5 years have passed since the first comprehensive survey article was published on DE by Das and Suganthan in 2011. Several developments have been reported on various aspects of the algorithm in these 5 years and the research on and with DE have now reached an impressive state. Considering the huge progress of research with DE and its applications in diverse domains of science and technology, we find that it is a high time to provide a critical review of the latest literatures published and also to point out some important future avenues of research. The purpose of this paper is to summarize and organize the information on these current developments on DE. Beginning with a comprehensive foundation of the basic DE family of algorithms, we proceed through the recent proposals on parameter adaptation of DE, DE-based single-objective global optimizers, DE adopted for various optimization scenarios including constrained, large-scale, multi-objective, multi-modal and dynamic optimization, hybridization of DE with other optimizers, and also the multi-faceted literature on applications of DE. The paper also presents a dozen of interesting open problems and future research issues on DE.

Recent advances in differential evolution – An updated survey

This paper presents the interior search algorithm (ISA) as a novel method for solving optimization tasks. The proposed ISA is inspired by interior design and decoration. The algorithm is different from other metaheuristic algorithms and provides new insight for global optimization. The proposed method is verified using some benchmark mathematical and engineering problems commonly used in the area of optimization. ISA results are further compared with well-known optimization algorithms. The results show that the ISA is efficiently capable of solving optimization problems. The proposed algorithm can outperform the other well-known algorithms. Further, the proposed algorithm is very simple and it only has one parameter to tune.

Interior search algorithm (ISA): a novel approach for global optimization.

Chaos-enhanced accelerated particle swarm optimization

Metamodeling is becoming a rather popular means to approximate the expensive simulations in today’s complex engineering design problems since accurate metamodels can bring in a lot of benefits. The metamodel accuracy, however, heavily depends on the locations of the observed points. Adaptive sampling, as its name suggests, places more points in regions of interest by learning the information from previous data and metamodels. Consequently, compared to traditional space-filling sampling approaches, adaptive sampling has great potential to build more accurate metamodels with fewer points (simulations), thereby gaining increasing attention and interest by both practitioners and academicians in various fields. Noticing that there is a lack of reviews on adaptive sampling for global metamodeling in the literature, which is needed, this article categorizes, reviews, and analyzes the state-of-the-art single−/multi-response adaptive sampling approaches for global metamodeling in support of simulation-based engineering design. In addition, we also review and discuss some important issues that affect the success of an adaptive sampling approach as well as providing brief remarks on adaptive sampling for other purposes. Last, challenges and future research directions are provided and discussed.

A survey of adaptive sampling for global metamodeling in support of simulation-based complex engineering design

Particle Swarm Optimization (PSO) is a metaheuristic global optimization paradigm that has gained prominence in the last two decades due to its ease of application in unsupervised, complex multidimensional problems which cannot be solved using traditional deterministic algorithms. The canonical particle swarm optimizer is based on the flocking behavior and social co-operation of birds and fish schools and draws heavily from the evolutionary behavior of these organisms. This paper serves to provide a thorough survey of the PSO algorithm with special emphasis on the development, deployment and improvements of its most basic as well as some of the state-of-the-art implementations. Concepts and directions on choosing the inertia weight, constriction factor, cognition and social weights and perspectives on convergence, parallelization, elitism, niching and discrete optimization as well as neighborhood topologies are outlined. Hybridization attempts with other evolutionary and swarm paradigms in selected applications are covered and an up-to-date review is put forward for the interested reader.

Particle Swarm Optimization: A survey of historical and recent developments with hybridization perspectives

A global optimization method for continuous design variables called as Generalized Random Tunneling Algorithm is proposed. Proposed method is called as “Generalized” random tunneling algorithm because this method can treat the behavior constraints as well as the side constraints. This method consists of three phases, that is, the minimization phase, the tunneling phase, and the constraints phase. In the minimization phase, mathematical programming is used, and heuristic approach is introduced in the tunneling and constraint phases. By iterating these phases, global minimum is found. The characteristics of mathematical programming and heuristic approaches are included in the proposed method. Global minimum which may lie on the boundary of constraints is easily found by proposed method. Proposed method is applied to mathematical and structural optimization problems. Through numerical examples, the effectiveness and validity of proposed method have been confirmed.Copyright © 2003 by ASME

Generalized Random Tunneling Algorithm for Continuous Design Variables

Study on optimal impact damper using collision of vibrators

Sequential approximate optimization for discrete design variable problems using radial basis function network

This paper proposes an approach for twist springback reduction using variable blank holder force (VBHF) trajectory that the blank holder force (BHF) varies through the stroke. In addition, the blank shape is optimized. Therefore, design optimization of VBHF trajectory and blank shape for twist springback reduction is performed. Springback of U-shaped product is a simple deformation, whereas the one of S-rail-shaped product shows more complicated behavior due to twisting. As the result, compared with the springback of U-shaped product, it is difficult to evaluate the twist springback. A novel evaluation method for the twist springback is proposed, and the optimal VBHF trajectory and blank shape for the twist springback reduction are determined under several design constraints. Numerical simulation of the S-rail-shaped product is so intensive that response surface approach is valid. In particular, a sequential approximate optimization that the response surface is repeatedly constructed and optimized is used to determine the optimal VBHF and blank shape. Through numerical result, the validation of the proposed approach is examined.

Numerical optimization of variable blank holder force trajectory and blank shape for twist springback reduction using sequential approximate optimization

This paper proposes a method for determining optimal back-pressure profile in forging of aluminum alloy using a sequential approximate optimization (SAO). In forging, it is important to improve the mold filling for the product quality. In addition, it is preferable to produce a product with a minimum forming energy. To achieve these objectives simultaneously, a forging method with back-pressure profile is proposed. Here, the back-pressure profile implies that the back-pressure varies through the stroke. In this paper, a multi-objective optimization (MOO) problem is formulated. To improve the mold filling, an unfilled area is taken as the first objective function. Furthermore, a forming energy during the forging is taken as the second objective function. Numerical simulation in the forging is so expensive that the SAO using the radial basis function (RBF) network is adopted, and the pareto-frontier is identified with a small number of simulation runs. Based on the numerical result, the experiments are also conducted. It can be found from these results that, the back-pressure profile approach is valid for improving the mold filling as well as the forming energy.

Satoshi Kitayama

Papers

Generalized Random Tunneling Algorithm for Continuous Design Variables

Study on optimal impact damper using collision of vibrators

Sequential approximate optimization for discrete design variable problems using radial basis function network

Numerical optimization of variable blank holder force trajectory and blank shape for twist springback reduction using sequential approximate optimization

Determination of back-pressure profile for forward extrusion using sequential approximate optimization