Tesis "On the Use of Scalarizing Functions to Solve Many-Objective Optimization Problems"
Sustentante: Auraham Sinué Camacho García.
Directores: Dr. Gregorio Toscano Pulido y Dr. Ricardo Landa Becerra, investigadores Cinvestav Tamaulipas.
Sinodales: César Torres Huitzil, ITESM, Campus Puebla; Dr. Iván López Arévalo, Cinvestav Unidad Tamaulipas; Dr. Edwyn Javier Aldana Bobadilla, CINVESTAV Unidad Tamaulipas; Dr. Carlos Alberto Lara Álvarez, CINVESTAV Unidad Tamaulipas.
Resumen:
Multiobjective optimization problems (MOPs) arise in many disciplines and design areas. An MOP involves several objective functions that need to be optimized simultaneously. Generally, these objectives are in conflict with each other, meaning that a single solution cannot improve all the objectives simultaneously. Problems with more than three objective functions are known as many-objective optimization problems (MaOPs). The term evolutionary multiobjective optimization (EMO) refers to the use of evolutionary algorithms (EAs) for addressing problems with multiple optimization criteria. Several multiobjective evolutionary algorithms (MOEAs) have been proposed in the literature. Among them, decomposition-based MOEAs have shown to be computationally efficient for solving MaOPs. A decomposition-based algorithm transforms an MOP into several scalar subproblems that are then solved in a collaborative way. This transformation requires a scalarizing function and a set of evenly distributed reference vectors. These parameters play a crucial role when decomposing a problem. If they are not properly tuned, decomposition-based MOEAs may face two limitations, that is, poor search ability and diversity deterioration. In order to address these issues, we require a method for determining a suitable parameter setting throughout the search process. In this thesis, we propose two approaches to enhance decomposition in many-objective optimization. First, we introduce a method for enhancing the search ability of decomposition-based algorithms, called Multiple Survival Selection (MSS). This method evaluates several scalarizing functions and selects the best of them regarding a performance indicator. The performance of a scalarizing function depends on its ability to find a good solution set at survival selection. Since we are dealing with multiple scalarizing functions, the proposed method explores several solution sets for survival selection. In the proposed method, the performance assessment is conducted frequently, meaning that suitable scalarizing functions are promoted throughout the search process. Second, we introduce an indicator called Median of Dispersion of the Population (MDP) to assist weight adaptation methods. In the literature, these methods change the locations of the reference vectors to improve the diversity of the population when decomposing a problem. Such adaptation is performed frequently throughout the search. Although, performing early adaptations may be ineffective, leading to unnecessary computational burden. The proposed indicator is employed to determine whether the population is stagnant by measuring its progress toward the Pareto front. In the proposed method, the adaptation of reference vectors is performed only after reaching the stagnation point, meaning that early adaptation is avoided. This way, we can conduct a more effective adaptation. Finally, we integrate both methods into a single framework. Both proposed methods are aimed to address the two previously mentioned limitations of decomposition-based algorithms. Our experimental results show that MSS is a promising direction for improving the convergence of the population, whereas MDP is a suitable way for enhancing the adaptation of reference vectors.