A hybridisation of linear programming and genetic algorithm to solve the capacitated facility location problem

This paper introduces a cooperative approach of a swarm intelligence algorithm and a linear programming solver to solve the capacitated facility location problem (CFLP). Given a set of potential locations to open facilities, the aim in CFLP is to find the minimum cost, which is the sum of facility opening costs and transportation costs. The developed solution strategy decomposes CFLP into two sub-problems. The former sub-problem has a binary domain. Although most of the swarm intelligence algorithms employ additional procedures such as sigmoid function to deal with binary domains, the proposed algorithm does not require for such methods. An adaptive mutation operator enhances this algorithm. The aim of the latter sub-problem is to generate a policy that optimally assigns customers to the opened facilities. In this regard, the generated binary vectors by the proposed algorithm are passed to a solver to optimise the generated linear model. Commonly used instances available in the literature are solved by the proposed strategy. Comprehensive experimental study includes comparisons with the sate-of-the-art. According to the statistically verified results, the proposed strategy is found as promising in solving CFLP.