Multi-Output Neural Network-Assisted Differential Evolution for Optimization Problems with Expensive Objective Function and Inequalities

Surrogate-assisted evolutionary algorithms have primarily concentrated on reducing computational expenses in the domain of costly constrained optimization. This research introduces a neural network-based surrogate that employs a multi-output regression framework, specifically crafted to address the complexities of approximating both the objective function and inequality constraints concurrently. The surrogate's multi-output functionality is utilized to optimize the objective while ensuring adherence to constraints. Additionally, a novel two-stage local search strategy is presented, aimed at refining solutions that are promising yet not feasible. This strategy integrates surrogate assistance with gradient-based mutation to progressively accelerate the evolutionary process. Empirical analyses conducted on 13 test functions confirm the efficacy of this approach, representing a substantial advancement in managing inequalities within costly optimization scenarios. The results also underscore the efficiency gains of this methodology in fitting both the objective function and inequalities simultaneously, surpassing five contemporary state-of-the-art surrogate-assisted evolutionary algorithms in terms of achieving feasible solutions.