In this work, a new version of the Harmony Search algorithm for solving multi-objective optimization problems is proposed, MOHSg, with pitch adjustment using genotype. The main contribution consists of adjusting the pitch using the crowding distance by genotype; that is, the distancing in the search space. This adjustment automatically regulates the exploration–exploitation balance of the algorithm, based on the distribution of the harmonies in the search space during the formation of Pareto fronts. Therefore, MOHSg only requires the presetting of the harmony memory accepting rate and pitch adjustment rate for its operation, avoiding the use of a static bandwidth or dynamic parameters. MOHSg was tested through the execution of diverse test functions, and it was able to produce results similar or better than those generated by algorithms that constitute search variants of harmonies, representative of the state-of-the-art in multi-objective optimization with HS.

This work presents a methodology to solve optimization problems with dynamic-size solution vectors containing continuous and integer variables. It is achieved by reformulating the original problem through a bilevel optimization approach and implementing metaheuristic techniques to solve it. In the selected case study, the optimization problem corresponds to tuning a neuro-fuzzy controller (NFC) that operates in a biodiesel production system for controlling temperature. The NFC performs well and is especially robust to disturbances, but due to its complexity, it is difficult to determine the best set of parameters for its use. This has led to biased searches based on criteria such as the experiences of designers. With the proposed method, it was possible to obtain a tuning that—when implemented in a simulation—led to results that surpassed those documented in the literature. Finally, the proposal offers flexibility for implementation with other controllers that have similar architectures and can be integrated into various other plants or processes.

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.

In a mixed-integer nonlinear programming problem, integer restrictions divide the feasible region into discontinuous feasible parts with different sizes. Evolutionary Algorithms (EAs) are usually vulnerable to being trapped in larger discontinuous feasible parts. In this work, an improved version of an Estimation of Distribution Algorithm (EDA) is developed, where two new op-erations are proposed. The first one establishes a link between the learning-based histogram model and the $\varepsilon$ -constrained method. Here, the constraint violation level of the $\varepsilon$ -constrained method is used to explore the smaller discontinuous parts and form a better statistical model. The second operation is the hybridization of the EDA with a mutation operator to generate offspring from both the global distribution information and the parent information. A benchmark is used to test the performance of the improved proposal. The results indicated that the proposed approach shows a better performance against other tested EAs. This new proposal solves to a great extent the influence of the larger discontinuous feasible parts, and improve the local refinement of the real variables.

Modelo para la optimización del costo de operación de un campo de pozos en acuíferos