An Efficient Approach for Solving Expensive Constrained Multiobjective Optimization Problems

TL;DR

This paper introduces PSCMOEA, an innovative evolutionary algorithm that effectively addresses expensive constrained multi-objective problems by incorporating probabilistic surrogate models and adaptive strategies to improve search efficiency and solution quality.

Contribution

The paper presents PSCMOEA, a novel probabilistic constrained evolutionary algorithm with adaptive search bounds, uncertainty-aware selection, and a balanced infill sampling strategy for ECMOPs.

Findings

PSCMEAOA outperforms five state-of-the-art algorithms on challenging ECMOPs.

The approach achieves high-quality solutions with low evaluation budgets.

Adaptive strategies enhance search efficiency and robustness.

Abstract

To solve real-world expensive constrained multi-objective optimization problems (ECMOPs), surrogate/approximation models are commonly incorporated in evolutionary algorithms to pre-select promising candidate solutions for evaluation. However, the performance of existing approaches are highly dependent on the relative position of unconstrained and constrained Pareto fronts (UPF and CPF, respectively). In addition, the uncertainty information of surrogate models is often ignored, which can misguide the search. To mitigate these key issues (among others), an efficient probabilistic selection based constrained multi-objective EA is proposed, referred to as PSCMOEA. It comprises novel elements such as (a) an adaptive search bound identification scheme based on the feasibility and convergence status of evaluated solutions (b) a probabilistic selection method backed by theoretical formulations of model mean and uncertainties to conduct search in the predicted space to identify promising solutions (c) an efficient single infill sampling approach to balance feasibility, convergence and diversity across different stages of the search and (d) an adaptive switch to unconstrained search based on certain search conditions. Numerical experiments are conducted on an extensive range of challenging constrained problems using low evaluation budgets to simulate ECMOPs. The performance of PSCMOEA is benchmarked against five competitive state-of-the-art algorithms, to demonstrate its competitive and consistent performance.