A Preference Model-Based Surrogate-Assisted Constrained Multi-Objective Evolutionary Algorithm for Expensively Constrained Multi-Objective Problems

Abstract

In the context of expensive constraint multi-objective problems, it is evident that the feasible domain shapes and sizes of different problems vary considerably. The difficulty in finding optimal solutions presents a significant challenge in ensuring the surrogate-assisted evolutionary algorithm’s feasibility, convergence, and diversity. To more effectively address the distinctive characteristics of the feasible domain and objective function across a range of problems, we have developed a Kriging-based surrogate-assisted evolutionary algorithm tailored to the current population’s preferences. The algorithm can optimize the population according to the current population’s requirements. Additionally, considering the varying degrees of accuracy observed in the surrogate models at different stages, this paper employs a dynamic approach to the number of surrogate model evaluations, contingent on the accuracy of the current surrogate model. Two types of Pareto frontier search are distinguished: unconstrained and constrained. Moreover, distinct fill sampling strategies are devised in accordance with the specific optimization requirements of the current population. After assessing the proposed solutions, the discrepancy between the actual fitness value and the surrogate model’s prediction is calculated.The discrepancy is used to modify the number of evaluations conducted on the surrogate model. In order to illustrate the algorithm’s efficacy, it is benchmarked against the current state-of-the-art algorithms on various test problems. The experimental results demonstrate that the proposed algorithm performs better than other advanced methods.