Adaptive population sizing for multi-population based constrained multi-objective optimization

Ye Tian, Ruiqin Wang, Yajie Zhang, Xingyi Zhang

Abstract: In recent years, the prevalence of constrained multi-objective optimization problems across numerous scenarios has incited a surge of interest in the advancement of constrained multi-objective evolutionary algorithms (CMOEAs). Multi-population CMOEAs have demonstrated effectiveness in balancing between objective optimization and constraint satisfaction, where auxiliary populations can mine infeasible regions to help main populations get grid of local optimums. However, the evolution of the auxiliary population often necessitates an equal or even greater number of function evaluations compared to the main population, leading to substantial expenditure of computational resources. To save function evaluations, this paper suggests an adaptive population sizing method to dynamically shrink the auxiliary population according to the current evolutionary state. Subsequently, a multi-stage evolutionary algorithm is developed, which integrates a variety of strategies to more effectively evolve the auxiliary population and ultimately eliminate it, thereby saving function evaluations for the main population. The proposed CMOEA is empirically evaluated against nine state-of-the-art algorithms on challenging test suites, which exhibits superior performance and versatility.