This paper presents a variant of particle swarm optimizers (PSOs) that we call the comprehensive learning particle swarm optimizer (CLPSO), which uses a novel learning strategy whereby all other particles' historical best information is used to update a particle's velocity. This strategy enables the diversity of the swarm to be preserved to discourage premature convergence. Experiments were conducted (using codes available from http://www.ntu.edu.sg/home/epnsugan) on multimodal test functions such as Rosenbrock, Griewank, Rastrigin, Ackley, and Schwefel and composition functions both with and without coordinate rotation. The results demonstrate good performance of the CLPSO in solving multimodal problems when compared with eight other recent variants of the PSO.

This paper presents a new particle swarm optimizer for solving multimodal multiobjective optimization problems which may have more than one Pareto-optimal solution corresponding to the same objective function value. The proposed method features an index-based ring topology to induce stable niches that allow the identification of a larger number of Pareto-optimal solutions, and adopts a special crowding distance concept as a density metric in the decision and objective spaces. The algorithm is shown to not only locate and maintain a larger number of Pareto-optimal solutions, but also to obtain good distributions in both the decision and objective spaces. In addition, new multimodal multiobjective optimization test functions and a novel performance indicator are designed for the purpose of assessing the performance of the proposed algorithms. An effectiveness validation study is carried out comparing the proposed method with five other algorithms using the benchmark functions to prove its effectiveness.

Handling constrained multi-objective optimization problems (CMOPs) is extremely challenging, since multiple conflicting objectives subject to various constraints require to be simultaneously optimized. To deal with CMOPs, numerous constrained multi-objective evolutionary algorithms (CMOEAs) have been proposed in recent years, and they have achieved promising performance. However, there has been few literature on the systematic review of the related studies currently. This article provides a comprehensive survey for evolutionary constrained multi-objective optimization. We first review a large number of CMOEAs through categorization, and analyze their advantages and drawbacks in each category. Then, we summarize the benchmark test problems and investigate the performance of different constraint handling techniques and different algorithms, followed by some emerging and representative applications of CMOEAs. Finally, we discuss some new challenges and point out some directions of the future research in the field of evolutionary constrained multi-objective optimization.