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Constrained multi-objective optimization problems (CMOPs) are difficult to handle because objectives and constraints need to be considered simultaneously, especially when the constraints are extremely complex. Some recent algorithms work well when dealing with CMOPs with a simple feasible region; however, the effectiveness of most algorithms degrades considerably for CMOPs with complex feasible regions. To address this issue, this paper proposes a multi-stage evolutionary algorithm, where constraints are added one after the other and handled in different stages of evolution. Specifically, in the early stages, the algorithm only considers a small number of constraints, which can make the population efficiently converge to the potential feasible region with good diversity. As the algorithm moves to the later stages, more constraints are considered to search the optimal solutions based on the solutions obtained in the previous stages. Furthermore, a strategy for sorting the constraint-handling priority according to the impact on the unconstrained Pareto front is proposed, which can accelerate the convergence of the algorithm. Experimental results on five benchmark suites and three real-world applications showed that the proposed algorithm outperforms several state-of-the-art constraint multi-objective evolutionary algorithms when dealing with CMOPs, especially for problems with complex constraints. [ABSTRACT FROM AUTHOR]

Abstract: Motivated by the recent success of diverse approaches based on differential evolution (DE) to solve constrained numerical optimization problems, in this paper, the performance of this novel evolutionary algorithm is evaluated. Three experiments are designed to study the behavior of different DE variants on a set of benchmark problems by using different performance measures proposed in the specialized literature. The first experiment analyzes the behavior of four DE variants in 24 test functions considering dimensionality and the type of constraints of the problem. The second experiment presents a more in-depth analysis on two DE variants by varying two parameters (the scale factor F and the population size NP), which control the convergence of the algorithm. From the results obtained, a simple but competitive combination of two DE variants is proposed and compared against state-of-the-art DE-based algorithms for constrained optimization in the third experiment. The study in this paper shows (1) important information about the behavior of DE in constrained search spaces and (2) the role of this knowledge in the correct combination of variants, based on their capabilities, to generate simple but competitive approaches. [ABSTRACT FROM AUTHOR]