Tri-Objective Differential Evolution with Gradient Information Reused for Constrained Optimization

Many real-world optimization problems are inherently constrained, presenting significant challenges to the application of evolutionary algorithms. Successfully managing these constraints while simultaneously optimizing the objective function requires a considerable degree of population diversity. To address this, we have developed a methodology that effectively combines an
$\varepsilon$
-constraint-handling method with a niching technique. The
$\varepsilon$
-constraint- handling method is specifically designed to manage constraints, while the niching technique aims to preserve pop-ulation diversity. In our approach, a constrained optimization problem is transformed into a tri-objective optimization challenge, introducing two additional objectives: the density objective and the overall constraint objective. The density objective is a particularly innovative aspect of our method, as it prolongs the survival of promising yet infeasible solutions. This prolongation aids the evolutionary search in converging towards the feasible region from various directions, thereby increasing the chances of identifying optimal solutions. Moreover, an improved gradient repair mutation strategy, based on a successful information reuse approach, is implemented to further refine promising solutions. To evaluate the effectiveness of our method, we tested it on 30 real-world constrained optimization problems from the CEC 2020 benchmark test suite. The results demonstrate that our approach either exceeds or is equivalent to the performance of current state-of-the-art constrained optimization algorithms.