Efficiently handling constraints in mixed-integer nonlinear programming problems using gradient-based repair differential evolution

Abstract

Mixed integer nonlinear programming (MINLP) addresses optimization problems that involve continuous and discrete/integer decision variables, as well as nonlinear functions. These problems often exhibit multiple discontinuous feasible parts due to the presence of integer variables. Discontinuous feasible parts can be analyzed as subproblems, some of which may be highly constrained. This significantly impacts the performance of evolutionary algorithms (EAs), whose operators are generally insensitive to constraints, leading to the generation of numerous infeasible solutions. In this article, a variant of the differential evolution algorithm (DE) with a gradient-based repair method for MINLP problems (G-DEmi) is proposed. The aim of the repair method is to fix promising infeasible solutions in different subproblems using the gradient information of the constraint set. Extensive experiments were conducted to evaluate the performance of G-DEmi on a set of MINLP benchmark problems and a real-world case. The results demonstrated that G-DEmi outperformed several state-of-the-art algorithms. Notably, G-DEmi did not require novel improvement strategies in the variation operators to promote diversity; instead, an effective exploration within each subproblem is under consideration. Furthermore, the gradient-based repair method was successfully extended to other DE variants, emphasizing its capacity in a more general context.