A population-oriented hybrid search surrogate-assisted evolutionary algorithm for expensive constrained optimization multi-objective problems with small feasible regions

Abstract

Multi-objective optimization problems with expensive objectives and constraints frequently arise in real industries, such problems are called expensive constrained multi-objective optimization problems(ECMOPs). Due to the expensive cost of actual fitness calculations, constructing suitable surrogates for objectives and constraints is crucial for finding potentially feasible solutions. To enhance the search efficiency of surrogate-assisted multi-objective optimization algorithms in complex, small feasible regions with many decision variables, a population-oriented hybrid search surrogate-assisted evolutionary algorithm is proposed, called PHSEA. In PHSEA, the state of the current population is determined by relevance of the objective optimization and constraint violation reduction, as well as the ideal point change rate. Three search strategies are used: unconstrained, weakly constrained and strongly constrained surrogate-assisted search strategy, to search for feasible solutions. Furthermore, according to different search requirements, three archives with separate update criteria were used to construct the surrogate model for constraint functions. On this basis, we propose a population-oriented hybrid search framework that enhances the algorithm’s ability to search for potential solutions in small feasible regions. The proposed method was compared against two surrogate-assisted algorithms and three surrogate-free algorithms on 33 benchmark problems and 6 real-world engineering problems. Experimental results demonstrate that PHSEA exhibits strong competitiveness in solving ECMOPs characterized by small feasible regions and a large number of decision variables.