Surrogate-Assisted Evolutionary Algorithm for Expensive Optimization with Equality and Inequality Constraints

The presence of equality and inequality constraints is of significant importance in expensive constrained optimization. This study aims to develop a surrogate-assisted evolutionary algorithm capable of addressing three types of constraints commonly encountered in expensive optimization problems: 1) those with only inequality constraints, 2) those with only equality constraints, and 3) those with both equality and inequality constraints. To achieve this, a radial basis function neural network is employed as a surrogate model to approximate expensive objective functions and individual constraints. Leveraging a consensus measure among all individual constraints, an improved infill sampling criterion is proposed to identify the most promising candidates. In addition, a hybrid local search strategy refines infeasible yet promising solutions via both surrogate-driven evolution and a model-free gradient-based mutation. To balance these search modes cost-effectively, a stagnation strategy enables adaptive switching between exploration and exploitation. Experimental results on 58 test instances demonstrate the efficacy of the proposed approach across all three constraint types under a strict budget of 1000 expensive function evaluations. These findings validate the methodology and show competitive performance relative to state-of-the-art methods.