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

Improvement of the fuel consumption and exhaust gases have been one of the important issues in automobile Hybrid electric vehicles (HEVs) that have one internal combustion engine (ICE) and electric motors (EMs), can meet this requirement To improve them simultaneously, a well-organized energy management system (EMS) should be developed In this paper, a novel EMS considering torque control is developed, in which a function called the torque control function is introduced to control the driving mode, the target ICE torque, and the target EM torque In addition, a sequential approximate optimization using a radial basis function network is adopted to determine the torque control function CO 2 and NO x are so closely related the fuel consumption and the exhaust gases, and they are then simultaneously minimized A multi-objective design optimization is the formulated, and the torque control function is determined with a small number of simulation runs The worldwide harmonized light duty driving test cycle is used to examine the validity of the proposed EMS using the torque control function

Optimization of energy management system for parallel hybrid electric vehicles using torque control algorithm

In sheet forming, the blank holder force (BHF) has a direct influence on product quality. A high BHF leads to tearing, whereas a low one results in wrinkling. For successful sheet forming, the BHF should be adjusted. Recently, the variable BHF (VBHF) that the BHF varies through stroke is recognized as one of the advanced sheet forming technologies. On the other hand, slide velocity (SV) that controls the die velocity is rarely discussed in the literature, and the SV should also be taken into account for the successful sheet forming. A high SV can achieve the high productivity, but wrinkling occurs. The VBHF trajectory and SV are unknown in advance, and the trial and error method is widely used. In this paper, design optimization approach using computational intelligence is adopted to determine them for achieving the high productivity. The processing time is taken as the objective function to be minimized for the high productivity. Numerical simulation in sheet forming is so intensive that a sequential approximate optimization using radial basis function network is adopted to determine the optimal solution. Based on the numerical result, the experiment using AC servo press (H1F200-2, Komatsu Industries Corp.) is carried out. Through the numerical and experimental result, the validity of proposed approach is examined.

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Design optimization of variable blank holder force trajectory and slide velocity in sheet metal forming

This paper proposes a Sequential Approximate Optimization (SAO) for the discrete design variable problems using Radial Basis Function (RBF) Network. We consider that there are two important keys for SAO: One is the parameter adjustment for good approximation, and the other is to explore the sparse region for global approximation. The authors have proposed the simple estimate of the width in the Gaussian Kernel for good approximation. In addition, in order to explore the sparse region, we have developed the density function. The density function with the simple estimate of the width works well in the case of the continuous design variables. However, a simple application of the density function to the discrete design variable problems will cause some difficulties. In order to overcome these difficulties and find the sparse region of the discrete design variables with the density function, the new variables for the discrete design variables are introduced. By using the new variables, it is possible to find the sparse region of the discrete design variables. A simple sampling algorithm is shown, in which the Discrete Differential Evolution (DDE) for the discrete design variables is employed. Through typical numerical examples, the validity of proposed approach is examined.

Sequential Approximate Optimization Using Radial Basis Function Network (Application to the Discrete Design Variable Problems)

Particle Swarm Optimization is applied to the mixed discrete non-linear problems (MDNLP). PSO is mainly a method to find a global or quasiminimum for a non-convex optimization problem of continuous design variables. To handle the discrete design variables, penalty function is introduced. By using penalty function, it is possible to treat all design variables as the continuous design variables. Through typical structural optimization problem, the validity of proposed approach for MDNLP is examined.

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Satoshi Kitayama

Papers

Optimization of energy management system for parallel hybrid electric vehicles using torque control algorithm

Design optimization of variable blank holder force trajectory and slide velocity in sheet metal forming

Sequential Approximate Optimization Using Radial Basis Function Network (Application to the Discrete Design Variable Problems)

Application of Particle Swarm Optimization to the Mixed Discrete Non-Linear Problems

Optimum Back-pressure Forging Using Servo Die Cushion☆