An Efficient Approach for Solving Expensive Constrained Multiobjective Optimization Problems
Kamrul Hasan Rahi
TL;DR
This paper tackles expensive constrained multiobjective optimization by introducing PSCMOEA, a steady-state surrogate-assisted algorithm that explicitly accounts for surrogate uncertainty and the relative geometry of UPF and CPF. It combines adaptive normalization bounds, a probabilistic dominance-based environmental selection (PCD), an infill strategy guided by both feasibility and diversity, and an adaptive switch to unconstrained search when beneficial. Empirical results across multiple ECMOP benchmarks show PSCMOEA achieving faster identification of feasible regions and well-distributed constrained Pareto fronts, with strong performance on FFE and ST and competitive IGD/IGD+ and HV metrics. The findings indicate that uncertainty-aware, adaptive, steady-state strategies can significantly improve robustness and efficiency for ECMOPs under low evaluation budgets.
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.