Surrogate modeling based on granular models and fuzzy aptitude functions

Genetic algorithms are part of a family of heuristic optimization techniques that are nature inspired, and unlike many optimization techniques, are derivative-free. The effectiveness of this sort of algorithms has been proved in several domains and applications. However, when using GA in complex optimization problems, e.g., like those arising in engineering, the high dimensional space of solutions and the expensiveness of fitness functions produce heavy computational loads. An alternative to this drawback is using estimation techniques, known as surrogates, that provide approximated, but cheap evaluations of solutions. Making optimization tractable even for complex problems. In this paper, we focus on the use of a fuzzy system as an agent to construct surrogate models in the form of granules to be used with genetic algorithms. The novelty of this work relies on the extraction of knowledge from the search process and on the representation of granule's behavior with the aid of fuzzy aptitude functions. These functions control the behavior of granules, allowing the optimization technique considerable savings in terms of resources. First, by avoiding unnecessary evaluations of solutions that are far away from the optimal one, with the use of a granular global-surrogate model. At the same time, the methodology allows us working with granular local-surrogate models when the process requires a more intensive search around a specific region of the search space. Experimental results on benchmark functions show the validity and usefulness of the proposed techniques.