A direct local search mechanism for decomposition-based multi-objective evolutionary algorithms

In recent years, the development of multi-objective evolutionary algorithms (MOEAs) hybridized with mathematical programming techniques has significantly increased. However, most of these hybrid approaches are gradient-based, and tend to require a high number of extra objective function evaluations to estimate the gradient information required. The use of direct search methods-i.e., methods that do not require gradient information-has been, however, less popular in the specialized literature (although such approaches have been used with single-objective evolutionary algorithms). This paper precisely focuses on the design of a hybrid between the wellknownMOEA/ D and Nelder and Mead´s algorithm. Clearly, the mathematical programming technique adopted here, acts as a local search mechanism, whose goal is to improve the search performed by MOEA/D. Because of its nature, the proposed local search mechanism can be easily coupled to any other decomposition-based MOEA. Our preliminary results indicate that this sort of hybridization is quite promising for dealing with multi-objective optimization problems (MOPs) having high dimensionality (in decision variable space).