A surrogate-assisted differential evolution for expensive optimization with equality constraints

Surrogate-assisted evolutionary algorithms have achieved notable success in expensive optimization. While significant attention has been given to expensive optimization scenarios without constraints or only with inequality constraints, equality constraints also commonly emerge in constrained optimization problems. Thus, there is a pressing need for surrogate-assisted evolutionary algorithms tailored for expensive optimization problems with equality constraints. This study integrates a multilayer perceptron as a surrogate with gradient descent-based local search in differential evolution to tackle the challenges caused by equalities in expensive constrained optimization. Our contributions encompass: 1) deploying a multilayer perceptron-based cheap surrogate that simultaneously fits the expensive objective function and equality constraints, 2) an enhanced gradient descent local search to manage challenging equality constraints, and 3) an individual update strategy aiming to strike a balance between objective optimization and constraint satisfaction. The proposed multilayer perceptron-based surrogate, along with the gradient descent-based local search, collaboratively navigates toward the feasible regions. The evolutionary search leveraging the surrogate broadly explores potential feasible regions, while the local search refines promising infeasible solutions into feasible ones. Experimental results highlight the capability and effectiveness of our proposed surrogate-assisted methodology for expensive optimization with equality constraints.