### Hybridizing an Evolutionary Algorithm with Mathematical Programming Techniques for Multi-Objective Optimization

Abstract

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 nonlinear optimization approaches taken from the mathematical programming literature has been, however, less popular (although such approaches have been used with single-objective evolutionary algorithms). This paper precisely focuses on the design of a hybrid between a well-known MOEA (the NSGA-II) and two direct search methods taken from the mathematical programming literature (Nelder and Mead.s method and the golden section algorithm). The idea is to combine the explorative power of the evolutionary algorithm with the exploitative power of the direct search methods previously indicated (one is used for unidimensional functions and the other for multidimensional functions). Clearly, these mathematical programming techniques act as local search engines, whose goal is to refine the search performed by the MOEA. Our preliminary results indicate that this sort of hybridization is quite promising.