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Differential evolution (DE) is a popular evolutionary algorithm inspired by Darwin’s theory of evolution and has been studied extensively to solve different areas of optimisation and engineering applications since its introduction by Storn in 1997. This study aims to review the massive progress of DE in the research community by analysing the 192 articles published on this subject from 1997 to 2021, particularly studies in the past five years. The methodology used to search for relevant DE papers and an overview of the original DE are firstly explained. Recent advances in the modifications proposed to enhance the effectiveness and efficiency of the original DE are reviewed by analysing the strengths and weaknesses of each published work, followed by the potential applications of these DE variants in solving different real-world engineering problems. In contrast to most existing DE review papers, additional analyses are performed in this survey by investigating the impacts of various parameter settings on given DE variants to identify their optimal values required for solving certain problem classes. The qualities of modifications incorporated into selected DE variants are also evaluated by measuring the performance gains achieved in terms of search accuracy and/or efficiency against the original DE. The additional surveys conducted in this study are anticipated to provide more insightful perspectives for both beginners and experts of DE research, enabling their better understanding about current research trends and new motivations to outline appropriate strategic planning for future development works.

The original particle swarm optimization (PSO) is not able to tackle constrained optimization problems (COPs) due to the absence of constraint handling techniques. Furthermore, most existing PSO variants can only perform well in certain types of optimization problem and tend to suffer with premature convergence due to the limited search operator and directional information used to guide the search process. An improved PSO variant known as the constrained multi-swarm particle swarm optimization without velocity (CMPSOWV) is proposed in this paper to overcome the aforementioned drawbacks. Particularly, a constraint handling technique is first incorporated into CMPSOWV to guide population searching towards the feasible regions of search space before optimizing the objective function within the feasible regions. Two evolution phases known as the current swarm evolution and memory swarm evolution are also introduced to offer the multiple search operators for each CMPSOWV particle, aiming to improve the robustness of algorithm in solving different types of COPs. Finally, two diversity maintenance schemes of multi-swarm technique and probabilistic mutation operator are incorporated to prevent the premature convergence of CMPSOWV. The overall optimization performances of CMPSOWV in solving the CEC 2006 and CEC 2017 benchmark functions and real-world engineering design problems are compared with selected constrained optimization algorithms. Extensive simulation results report that the proposed CMPSOWV has demonstrated the best search accuracy among all compared methods in solving majority of problems.