Multistate-Constrained Multiobjective Differential Evolution Algorithm With Variable Neighborhood Strategy

Multiobjective differential evolution (DE) algorithm (MODE) has been widely used in multiobjective optimization problems. However, due to the complex feasible regions, the optimization efficiency of MODE may decrease when solving constrained multiobjective problems. It is challenging to promote the evolution of population with few feasible solutions. In this article, a multistate-constrained MODE with variable neighborhood strategy (MSCMODE-VNS) is proposed to enhance the optimization effectiveness with complex feasible regions. First, a variable neighborhood DE strategy, based on a specially designed convergence indicator, is designed to accelerate the generation of feasible solutions. Second, a multistate population updating strategy with a comprehensive solution evaluation mechanism is devised to update the population of the next generation to improve the performance of solutions. Third, the convergence analysis, based on the probability theory, is derived to verify the effectiveness of the proposed MSCMODE-VNS algorithm. Finally, experimental results indicate that MSCMODE-VNS can achieve a satisfactory performance on three benchmark test suites and two real-world-constrained multiobjective problems.