A Kriging-assisted Double Population Differential Evolution for Mixed-Integer Expensive Constrained Optimization Problems with Mixed Constraints

Abstract

Many surrogate-assisted evolutionary algorithms (SAEA) with outstanding performance have been developed to handle Expensive Constrained Optimization Problems (ECOPs). But most of them are limited to solving ECOPs with continuous variables and inequality constraints. Therefore, a Kriging-assisted Double Population Differential Evolution (KDPDE) is proposed to deal with mixed-integer ECOPs with inequality and equality constraints. In particular, promising regions near the feasible region are created by Integer restriction Relaxation-based Double Population (IRDP) search framework, and then an Expected Improvement-based Classification local Search (EICS) is adopted to guide the infeasible solutions in the promising region into the feasible region. In order to improve the robustness of the algorithm, the widely distributed elite solutions are utilized by Elite solutions Retention-based Multi-directional Exploration (ERME) for diverse exploration, and the repetition rate information of individuals in the population is used by Population Diversity Maintenance Operation (PDMO) to adaptively avoid the population from falling into a local region. Therefore, KDPDE is capable of balancing the performance between convergence and robustness for mixed-integer ECOPS with mixed constraints. Experimental studies on several benchmark problems and a real-world application example demonstrate that KDPDE has excellent performance on solving such kind of problems under a limited computational budget.