A Two-Phase Kriging-Assisted Evolutionary Algorithm for Expensive Constrained Multiobjective Optimization Problems

TL;DR: A two-phase Kriging-assisted evolutionary algorithm (TEA) is designed to tackle expensive constrained multiobjective optimization problems (CMOPs). The algorithm considers objectives and constraints in two phases, finds feasible solutions in the first phase, and improves the solutions in the second phase.

Abstract: This article devises a two-phase Kriging-assisted evolutionary algorithm (named TEA) to tackle expensive constrained multiobjective optimization problems (CMOPs). In the first phase, only objectives are considered, which can help the population to cross infeasible obstacles and to evolve toward the unconstrained Pareto front. Since the unconstrained Pareto front is in front of the feasible region in the objective space, the first phase can find some feasible solutions during the evolution. In the second phase, both objectives and constraints are considered. In this article, we also propose two transition conditions to judge whether the search should be switched from the first phase to the second phase, by making use of the candidates evaluated by the original objectives and constraints in the first phase. These two transition conditions aim at maintaining some high-quality feasible solutions when the first phase ends, which is able to motivate the population to converge toward the constrained Pareto front with good diversity in the second phase. Furthermore, in both phases, we design a new Pareto dominance relationship (called PDPD) by incorporating the probability distribution information derived from the Kriging models. PDPD is further generalized to handle constraints in expensive CMOPs, Constrained PDPD (CPDPD), which provides high credibility for the comparison between two individuals with respect to both objectives and constraints. Finally, three benchmark test suites and a real-world application confirm the superiority of TEA.