Surrogate-Assisted Differential Evolution for Expensive Equality Constrained Optimization

In recent years, surrogate-assisted evolutionary algorithms have gained considerable success in addressing expensive constrained optimization problems. While significant focus has been directed toward optimization challenges with inequality constraints, the domain of expensive equality-constrained optimization also necessitates attention, as equality constraints are frequently encountered in traditional constrained optimization problems. Recognizing this gap, this study introduces an innovative approach that integrates a multilayer perceptron regression-based surrogate with a gradient descent-based repair method and differential evolution to address these challenges effectively. Our contributions are threefold: 1) We develop a multilayer perceptron-based surrogate model that concurrently approximates the objective function and equality constraints, 2) We employ a gradient descent-based repair method to adeptly manage the challenging equality constraints, and 3) We propose a hybrid local search scheme that enhances the solution refinement process. The combined use of the multilayer perceptron-based surrogate and gradient descent-based local search works in concert with differential evolution to guide the population toward the feasible region. This approach enables the evolutionary search, supported by the surrogate model, to extensively explore potential feasible regions. Our experimental results underscore the potential and efficacy of the proposed surrogate-assisted evolutionary algorithm in solving such complex optimization problems.