A Two-Stage Hybrid Search Evolutionary Algorithm for Expensive Constrained Multi-Objective Optimization Problems

Expensive constrained multi-objective optimization problems (ECMOPs) are prevalent in engineering practice and are characterized by extremely high evaluation costs for both objective and constraint functions. These high costs pose significant challenges for traditional evolutionary algorithms, which often struggle to obtain high-quality solutions within a limited number of evaluations. To address this issue, we propose a novel population-based, two-stage surrogate-assisted hybrid evolutionary algorithm (THSAEA). The algorithm adaptively switches between two search modes-global exploration and local exploitation-based on the rate of change in the population’s ideal point. In the exploration mode, the KTA2 framework is employed to perform unconstrained search and accelerate convergence, while co-evolutionary mechanisms are used to enhance population diversity. In the exploitation mode, the PEA algorithm is incorporated to refine the search within feasible regions, improving both convergence accuracy and solution diversity. Surrogate models are dynamically constructed for the objective function and selectively for the constraint functions, depending on the population’s constraint violation status, in order to improve optimization efficiency. Experimental results on CF and WFG benchmark problems demonstrate that THSAEA significantly outperforms four state-of-the-art algorithms in convergence speed, solution quality, and constraint-handling robustness, highlighting its superior adaptability and generalization ability across diverse constrained optimization scenarios.