Multi-Colony Ant Algorithm

Abstract

The first ant colony optimization (ACO) called ant system was inspired through studying of the behavior of ants in 1991 by Macro Dorigo and co-workers [1]. An ant colony is highly organized, in which one interacting with others through pheromone in perfect harmony. Optimization problems can be solved through simulating ant’s behaviors. Since the first ant system algorithm was proposed, there is a lot of development in ACO. In ant colony system algorithm, local pheromone is used for ants to search optimum result. However, high magnitude of computing is its deficiency and sometimes it is inefficient. Thomas Stutzle et al. introduced MAX-MIN Ant System (MMAS) [2] in 2000. It is one of the best algorithms of ACO. It limits total pheromone in every trip or sub-union to avoid local convergence. However, the limitation of pheromone slows down convergence rate in MMAS. In optimization algorithm, it is well known that when local optimum solution is searched out or ants arrive at stagnating state, algorithm may be no longer searching the global best optimum value. According to our limited knowledge, only Jun Ouyang et al [3] proposed an improved ant colony system algorithm for multi-colony ant systems. In their algorithms, when ants arrived at local optimum solution, pheromone will be decreased in order to make algorithm escaping from the local optimum solution. When ants arrived at local optimum solution, or at stagnating state, it would not converge at the global best optimum solution. In this paper, a modified algorithm, multi-colony ant system based on a pheromone arithmetic crossover and a repulsive operator, is proposed to avoid such stagnating state. In this algorithm, firstly several colonies of ant system are created, and then they perform iterating and updating their pheromone arrays respectively until one ant colony system reaches its local optimum solution. Every ant colony system owns its pheromone array and parameters and records its local optimum solution. Furthermore, once a ant colony system arrives at its local optimum solution, it updates its local optimum solution and sends this solution to global best-found center. Thirdly, when an old ant colony system is chosen according to elimination rules, it will be destroyed and reinitialized through application of the pheromone arithmetic crossover and the repulsive operator based on several global best-so-far optimum solutions. The whole algorithm implements iterations until global best optimum solution is searched out. The following sections will introduce some concepts and rules of this multi-colony ant system. This paper is organized as follows. Section II briefly explains the basic ACO algorithm and its main variant MMAS we use as a basis for multi-colony ant algorithm. In Section III we