Distribution Endpoint Estimation Assessment for the use in Metaheuristic Optimization Procedure

Abstract

Metaheuristic algorithms are often applied to numerous optimization problems, involving large-scale and mixed-integer instances, specifically. In this contribution we discuss some refinements from the extreme value theory to the lately proposed modification of partition-based random search. The partition-based approach performs iterative random sampling at given feasible subspaces in order to exclude the less favourable regions. The quality of particular regions is evaluated according to the promising index of a region. From statistical perspective, determining the promising index is equivalent to the endpoint estimation of a probability distribution induced by the objective function at the sampling subspace. In the following paper, we give a short review of the recent endpoint estimators derived on the basis of extreme value theory, and compare them by simulations. We discuss also the difficulties in their application and suitability of the estimators for various optimization instances.