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.

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Constrained multi-objective optimization problems (CMOPs) exist widely in the real world, which simultaneously contain multiple constraints to be satisfied and multiple conflicting objectives to be optimized. Therefore, the challage in addressing CMOPs is how to better balance constraints and objectives. To remedy this issue, this paper proposes a novel dual-population based constrained multi-objective evolutionary algorithm to solve CMOPs, in which two populations with different functions are employed. Specifically, the main population considers both objectives and constraints for solving the original CMOPs, while the auxiliary population is used only for optimization of objectives without considering constraints. In addition, a dynamic population size reducing mechanism is proposed, which is used to adjust the size of the auxiliary population, so as to reduce the consumption of computing resoruces in the later stage. Moreover, an independent external archive is set to store feasible solutions found by the auxiliary population, so as to provide high-quality feasible solutions for the main population. The experimental results on 55 benchmark functions show that the proposed algorithm exhibits superior or at least competitive performance compared to other state-of-the-art algorithms.

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