Evolution inspired binary flower pollination for the uncapacitated facility location problem

Abstract

The present paper introduces a modified flower pollination algorithm (FPA) enhanced by evolutionary operators to solve the uncapacitated facility location problem (UFLP), which is one of the well-known location science problems. The aim in UFLP is to select some locations to open facilities among a certain number of candidate locations so as to minimize the total cost, which is the sum of facility opening costs and transportation costs. Since UFLP is a binary optimization problem, FPA, which is introduced to solve real-valued optimization problems, is redesigned to be able to conduct search in binary domains. This constitutes one of the contributions of the present study. In this context, some evolutionary operators such as crossover and mutation are adopted by the proposed FPA. Next, the mutation operator is further enhanced by making use of an adaptive procedure that introduces greater level of diversity at earlier iterations and encourages intensification toward the end of search. Thus, while premature convergence and local optima problems at earlier iterations are avoided, a more intensified search around the found promising regions is performed. Secondarily, as demonstrated in this study, by making use of the reported evolutionary procedures, FPA is able to run in binary spaces without employing any additional auxiliary procedures such as transfer functions. All available benchmarking instances are solved by the proposed approach. As demonstrated by the comprehensive experimental study that includes statistically verified results, the developed approach is found as a promising algorithm that can be extended to numerous binary optimization problems.