A note on the use of a fuzzy approach in adaptive partitioning algorithms for global optimization

In global optimization, adaptive partitioning algorithms (APA) operate on the basis of partitioning the feasible region into subregions, sampling and evaluating each subregion, and selecting one or more subregions for repartitioning. The purpose of the repartitioning process is to locate a narrow neighborhood around the global optimum. In this correspondence, we propose to use a fuzzy approach in the assessment of subregions using random samples taken from these subregions. We discuss different types of uncertainties involved in APA and we conclude that the use of a fuzzy approach in the assessment of subregions is in concurrence with APA's convergence property. We provide numerical results for the fuzzy approach on 13 test functions from the literature.