Comparing Decomposition-Based Evolutionary Algorithms for Multi and Many-Objective Optimization Problems - Peito, Marcela C. C. (2023)
Many real-world problems can be mathematically modeled as Multiobjective Optimization Problems (MOPs), as they involve multiple conflicting objective functions that must be minimized simultaneously. MOPs with more than 3 objective functions are called Many-objective Optimization Problems (MaOPs). MOPs are typically solved through Multiobjective Evolutionary Algorithms (MOEAs), which can obtain a set of non-dominated optimal solutions, known as a Pareto front, in a single run. The MOEA Based on Decomposition (MOEA/D) is one of the most efficient, dividing a MOP into several single-objective subproblems and optimizing them simultaneously. This study evaluated the performance of MOEA/D and four variants representing the state of the art in the literature (MOEA/DD, MOEA/D-DE, MOEA/D-DU, and MOEA/D-AWA) in MOPs and MaOPs. Computational experiments were conducted using benchmark MOPs and MaOPs from the DTLZ suite considering 3 and 5 objective functions. Additionally, a statistical analysis, including the Wilcoxon test, was performed to evaluate the results obtained in the IGD+ performance indicator. The Hypervolume performance indicator was also considered in the combined Pareto front, formed by all solutions obtained by each MOEA. The experiments revealed that MOEA/DD performed best in IGD+, and MOEA/D-AWA achieved the highest Hypervolume in the combined Pareto front, while MOEA/D-DE registered the worst result in this set of problems.