Combining Surrogate Models and Local Search for Dealing with Expensive Multi-objective Optimization Problems

The development of multi-objective evolutionary algorithms (MOEAs) assisted by surrogate models has significantly increased in the last few years. However, in real-world applications, the high modality and dimensionality that functions normally have, often causes problems to such models. Therefore, if the Pareto optimal set of a multi-objective optimization problem is located in a search space in which the surrogate model is not able to shape the corresponding region, the search could be misinformed and thus converge to wrong regions. This has motivated the idea of incorporating refinement mechanisms to such approaches, in order to improve the search. In this paper, we present a local search mechanism which improves the search of a MOEA assisted by surrogate models. Our preliminary results indicate that our proposed approach can produce good quality results when it is restricted to performing only between 1,000 and 5,000 fitness function evaluations. Our proposed approach is validated using a set of standard test problems and an airfoil design problem.