Constraint boundary pursuing-based surrogate-assisted differential evolution for expensive optimization problems with mixed constraints

Surrogate-assisted evolutionary algorithms have recently shown exceptional abilities for handling with computationally Expensive Constrained Optimization Problems (ECOPs) where the constraints can be structural performance constraints such as volume, stiffness, and stress or computational fluid simulations in real-world complex engineering problems. But most of them are limited to solving ECOPs with inequality constraints. Therefore, a constraint boundary Pursuing-based Surrogate-Assisted Differential Evolution (PSADE) is designed to solve ECOPs with mixed constraints including inequality and equality. Specifically, potential areas near feasible region are explored by Trial Vector Generation Mechanism (TVGM) according to interactive guidance between elite solutions and current population, and an Expected Improvement-based Local Search (EILS) is employed to improve the accuracies of the Kriging models in promising neighboring areas of constraint boundary. Then a specific Solution Identification-based Local Search (SILS) is put forward for guiding two kinds of elite solutions, in which an expected feasibility-based local search method is designed for moving the elite infeasible solutions that violate the equality constraints toward the feasible region. Therefore, PSADE is able to maintain a good balance between convergence and diversity when considering both constraints and objective. Experimental studies on classical test problems show that PSADE is highly competitive on solving ECOPs with mixed constraints under an acceptable computational cost.