Ant colony optimization for finding the global minimum M. Duran Toksari Erciyes University, Engineering Faculty, Industrial Engineering Department, 38039 Kayseri, Turkey Abstract The ant colony optimization (ACO) algorithms are multi-agent systems in which the behaviour of each ant is inspired by the foraging behaviour of real ants to solve optimization problem. This paper presents the ACO based algorithm to find global minimum. Algorithm is based on that each ant searches only around the best solution of the previous iteration. This algorithm was experimented on test problems, and successful results were obtained. The algorithm was compared with other methods which had been experimented on the same test problems, and observed to be better. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Ant colony optimization; Global minimum; Metaheuristics; Random optimization 1. Introduction Many heuristic methods such as random search technique (ARSET) [1], heuristic random optimization (HRO) [2] and David–Fletcher method were developed to find global minimum. In this paper, ACO based algorithm will be suggested to find global minimum. ACO belong to class of biologically inspired heuristics. The basic idea of ACO is to imitate the cooperative behaviour of ant colonies. The function should have many local minimum points, but only one of them is the global minimum. If F(x min ) 6 F(x) for all x values, x min value is defined as the point makes the function minimum. If F(x) is con- tinuous and differentiable, the minimum value can be found on the point dF dx . However, wherever the function is not differentiable, it could prove more advantageous to utilize stochastic methods instead of deterministic ones [1]. The paper is organized as follows. First, ACO will be explained shortly. The proposed ACO based algo- rithm to find global minimum will be detailed in Section 3. In Section 4, the algorithm will be solved on five benchmark problems. Finally, the proposed algorithm will be compared with other heuristic methods. 2. Ant colony optimization (ACO) The idea of imitating the behaviour of ants for finding good solutions to combinatorial optimization prob- lems was initiated by Dorigo [3]. The principle of these methods is based on the way ants search for food and 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.09.043 E-mail address: dtoksari@erciyes.edu.tr Applied Mathematics and Computation 176 (2006) 308–316 www.elsevier.com/locate/amc