Ant colony optimization algorithm for the Euclidean location-allocation problem with unknown number of facilities

This paper addresses the Euclidean location-allocation problem with an unknown number of facilities, and an objective of minimizing the fixed and transportation costs. This is a NP-hard problem and in this paper, a three-stage ant colony optimization (ACO) algorithm is introduced and its performance is evaluated by comparing its solutions to the solutions of genetic algorithms (GA). The results show that ACO outperformed GA and reached better solutions in a faster computational time. Furthermore, ACO was tested on the relaxed version of the problem where the number of facilities is known, and compared to existing methods in the literature. The results again confirmed the superiority of the proposed algorithm.