MOEA/D assisted by RBF networks for expensive multi-objective optimization problems

Abstract

The development of multi-objective evolutionary algorithms assisted by surrogate models has increased in the last few years. However, in real-world applications, the high modality and dimensionality that functions have, often causes problems to such models. In fact, 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. Because of this, a considerable amount of research has focused on improving the prediction of the surrogate models by adding the new solutions to the training set and retraining the model. However, when the size of the training set increases, the training complexity can significantly increase. In this paper, we present a surrogate model which maintains the size of the training set, and in which the prediction of the function is improved by using radial basis function networks in a cooperative way. Preliminary results indicate that our proposed approach can produce good quality results when it is restricted to performing only 200, 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.