Traditionally, in a multiobjective optimization problem, the aim is to find the set of optimal solutions, the Pareto front, which provides the decision‐maker with a better understanding of the problem. This results in a more knowledgeable decision. However, multimodal solutions and nearly optimal solutions are ignored, although their consideration may be useful for the decision‐maker. In particular, there are some of these solutions which we consider specially interesting, namely, the ones that have distinct characteristics from those which dominate them (i.e., the solutions that are not dominated in their neighborhood). We call these solutions potentially useful solutions. In this work, a new genetic algorithm called nevMOGA is presented, which provides not only the optimal solutions but also the multimodal and nearly optimal solutions nondominated in their neighborhood. This means that nevMOGA is able to supply additional and potentially useful solutions for the decision‐making stage. This is its main advantage. In order to assess its performance, nevMOGA is tested on two benchmarks and compared with two other optimization algorithms (random and exhaustive searches). Finally, as an example of application, nevMOGA is used in an engineering problem to optimally adjust the parameters of two PI controllers that operate a plant.

In this paper we present the adjustment of controller parameters using multiobjective optimization techniques. Unlike other works, where only the Pareto optimal solutions are considered, we also consider the set of nearly optimal solutions nondominated in their neighborhood. These solutions are potentially useful for two reasons: 1) they are similar to the optimal solutions for the optimized objectives; 2) they differ significantly in their parameters. This last point makes them interesting since they bring diversity and different characteristics to the set of solutions for analyzing in the decision stage. In problems of controller parameter adjustment, especially for multivariable processes, there are many conflicting objectives. To simplify the optimization problem and decision stage, it is common to aggregate some of the objectives, and so simplify the initial problem. In this scenario, some controllers that were optimal for the initial problem can become nearly optimal in the simplified case. When these controllers are nondominated in their neighborhood, they are especially interesting because they usually present a different trade-off for the initial objectives. For the calculation of nearly optimal solutions nondominated in their neighborhood, the evolutionary algorithm nevMOGA was used. In this paper, the usefulness of considering these solutions is revealed in two controller design problems: the Wood & Berry distillation column and the CIC2018 control benchmark.

In this work, the parametric identification of a cooling system in a PEM (proton exchange membrane) fuel cell is carried out. This system is multivariable and nonlinear. In this type of system there are different objectives and the unmodeled dynamics cause conflicting objectives (prediction errors in each output). For this reason, resolution is proposed using a multi-objective optimization approach. Nearly optimal alternatives can exist in any optimization problem. Among them, the nearly optimal solutions that are significantly different (that we call nearly optimal solutions nondominated in their neighborhood) are potentially useful solutions. In identification problems, two situations arise for consideration: 1) aggregation in the design objectives (when considering the prediction error throughout the identification test). When an aggregation occurs in the design objectives, interesting non-neighboring (significantly different) multimodal and nearly optimal alternatives appear. These alternatives have different tradeoffs in the aggregated objectives; 2) new objectives in decision making appear. Some models can, with similar performance in the design objectives, obtain a significant improvement in new objectives not included in the optimization phase. A typical case of additional objectives are the validation objectives. In these situations, nearly optimal solutions nondominated in their neighborhood play a key role. These alternatives allow the designer to make the final decision with more valuable information. Therefore, this work highlights, as a novelty, the relevance of considering nearly optimal models nondominated in their neighborhood in problems of parametric identification of multivariable nonlinear systems and shows an application in a complex problem.