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

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.

Two-Swim Operators in the Modified Bacterial Foraging Algorithm for the Optimal Synthesis of Four-Bar Mechanisms.

This paper presents two-swim operators to be added to the chemotaxis process of the modified bacterial foraging optimization algorithm to solve three instances of the synthesis of four-bar planar mechanisms. One swim favors exploration while the second one promotes fine movements in the neighborhood of each bacterium. The combined effect of the new operators looks to increase the production of better solutions during the search. As a consequence, the ability of the algorithm to escape from local optimum solutions is enhanced. The algorithm is tested through four experiments and its results are compared against two BFOA-based algorithms and also against a differential evolution algorithm designed for mechanical design problems. The overall results indicate that the proposed algorithm outperforms other BFOA-based approaches and finds highly competitive mechanisms, with a single set of parameter values and with less evaluations in the first synthesis problem, with respect to those mechanisms obtained by the differential evolution algorithm, which needed a parameter fine-tuning process for each optimization problem.