Local search with quadratic approximation in Genetic Algorithms for expensive optimization problems

In this paper, we propose a local search methodology to be coupled with a Genetic Algorithm to solve optimization problems with non-linear constraints. This methodology uses quadratic approximations for both objective function and constraints. In the local search phase, these quadratic approximations define an associated problem that is solved using a linear matrix inequality (LMI) formulation. The number of function evaluations needed for finding the point of optimum is significantly reduced with this procedure, what makes the proposed methodology suitable for dealing with costly black-box optimization problems. A case study is presented: the well- known TEAM 22 benchmark problem, an expensive problem of electromagnetic design. The results show that the hybrid algorithm has a better performance when compared to the same Genetic Algorithm without the proposed local search operator.