An [formula omitted]-constrained multiobjective differential evolution with adaptive gradient-based repair method for real-world constrained optimization problems

Abstract

Over the past decade, incorporating information from the objective function into the constraint-handling process has garnered considerable attention in evolutionary algorithm research. Stemming from this, multiobjective optimization has emerged as a promising approach that simultaneously optimizes the objective function and constraints. However, the challenges associated with optimizing objective functions and satisfying constraints exhibit significant variability. Some constraints and/or objective functions can be exceptionally challenging, necessitating specific methods to identify the optimal solution within a limited feasible region. This study proposes an adaptive gradient descent-based repair method to enhance the search capability for both objective function optimization and constraint satisfaction. This method leverages objective function information to rectify infeasible solutions using gradient descent, thereby reducing the limitations of a purely constraint-based approach and automating the application of the repair method. Furthermore, an enhanced variant of the ɛ-constrained multiobjective differential evolution algorithm is developed for solving constrained optimization problems. The efficacy of the proposed approach is assessed using 57 benchmark test functions derived from real-world applications. Empirical results demonstrate that our approach is capable of locating high-quality solutions, outperforming several selected state-of-the-art algorithms.