The challenge of optimizing expensive black boxes: a scatter search/rough set theory approach

There is renewed interest in the development of effective and efficient methods for optimizing models of which the optimizer has no structural knowledge. This is what in the literature is referred to as optimization of black boxes. In particular, we address the challenge of optimizing expensive black boxes, that is, those that require a significant computational effort to be evaluated. We describe the use of rough set theory within a scatter search framework, with the goal of identifying high-quality solutions with a limited number of objective function evaluations. The rough set strategies that we developed take advantage of the information provided by the best and diverse solutions found during the search, in order to define areas of the solution space that are promising for search intensification. We test our procedure on a set of 92 nonlinear multimodal functions of varied complexity and size and compare the results with a state-of-the-art procedure based on particle swarm optimization.