A memetic algorithm for solving two variants of the two-stage uncapacitated facility location problem

Abstract

This paper deals with a T wo-Stage Uncapacitated Facility Location Problem (TSUFLP), which has important applications in designing telecommunication systems. Given a set of demand points and a set of possible locations for the first and second level concentrators (switches, multiplexors), the goal of the TSUFLP is to define the structure of two-level concentrator access network, such that the total cost of establishing such a network is minimized. We consider two variants of the TSUFLP from the literature and propose an efficient memetic algorithm (MA), based on hybridization of an evolutionary approach and two local-search heuristics. A greedy heuristic is incorporated in the MA frame for efficient calculation of the fitness function, which additionally decreases the overall MA running time. The described MA approach is benchmarked on test instances of medium and large dimensions from the literature, which are adapted for the TSUFLP and involve from 50 to 500 user nodes. On these instances, the proposed MA method quickly reaches all known optimal solutions, previously obtained by a linear programming method from the literature or CPLEX solver. In order to test effectiveness of the MA, we further modify some largescale instances from the literature involving 1000 and 2000 demand points, which can not be solved to optimality. Exhaustive computational experiments show that the MA provides solutions for the newly generated data set in relatively short CPU times. Regarding both solution quality and running times, we conclude that the proposed MA represents a powerful metaheuristic method for solving the TSUFLP and other similar network design problems.