An improved scatter search algorithm for the uncapacitated facility location problem

Abstract

The uncapacitated facility location (UFL) problem is a NP-hard and pure binary optimization problem. The main goal of UFL is that try to fmd an undetermined number of facilities to minimize the sum of constant setup and serving costs of customers. Nowadays, in solving many NP problems, optimization techniques are preferred instead of conventional ones due to their simple structure, ease of application and acceptable results in reasonable time. In this study, the scatter search algorithm (SS) was improved to solve the UFL problems. The SS method can be applied directly to problems with binary search space and supports random search mechanism with good solutions obtained from previous problem solving efforts as opposed to other evolutionary algorithms. In order to compromise between exploitation and exploration in the improved scatter search (ISS), the global search ability of the basic SS algorithm is enhanced by using different crossover techniques like an ensemble, while the local search ability is improved by mutation operations on the best solutions. To investigate effects of the improvements and to show its performance, the ISS is compared with the twelve different methods found in the literature for solving the 15 UFL problems in the OR-Lib dataset. The experimental results show that the proposed method obtained the optimum value for 13 of the 15 problems and had a superior performance compared to other techniques considering the solution quality and robustness. The ISS is also compared with a technique using the local search method on the OR-Lib and a different dataset named M*. When all experimental results are evaluated, it is seen that the proposed method is an effective, robust and successful tool for solving the UFL problems.