A hybrid local search operator for multiobjective optimization

In recent years, the development of hybrid approaches to solve multiobjective optimization problems has become an important trend in the evolutionary computation community. Despite hybrid approaches of mathematical programming techniques with multiobjective evolutionary algorithms are not very popular, when both fields are successfully coupled, results are impressive. However, the main objective of this sort of hybridization relays on the needing of several executions of the mathematical approach in order to obtain a sample of the Pareto front, raising with this, the number of fitness function evaluations. However, the use of surrogate models has become a recurrent approach to diminish the number of function evaluations. In this work, a hybrid operator that transforms the original multiobjective problem into a set of modified goal programming models is proposed. Furthermore, a local surrogate model is used instead of the real function in the hybrid operator. The goal programming model with the surrogate is optimized by a direct search method. Additionally, a standalone algorithm that uses the hybrid operator is here proposed. The new algorithm is validated using several test problems and performance measures commonly adopted in the specialized literature. Results indicate that the proposed operator gives rise to an effective algorithm, which produces results that are competitive with respect to those obtained by two well-known multiobjective evolutionary algorithms.