Multi-Colony Ant Algorithms for the Dynamic Travelling Salesman Problem Michalis Mavrovouniotis and Shengxiang Yang Centre for Computational Intelligence (CCI) School of Computer Science and Informatics De Montfort University The Gateway, Leicester, LE1 9BH, UK Email: {mmavrovouniotis, syang}@dmu.ac.uk Xin Yao CERCIA School of Computer Science University of Birmingham Birmingham B15 2TT, UK Email: x.yao@bham.cs.ac.uk Abstract—A multi-colony ant colony optimization (ACO) al- gorithm consists of several colonies of ants. Each colony uses a separate pheromone table in an attempt to maximize the search area explored. Over the years, multi-colony ACO algorithms have been successfully applied on different optimization problems with stationary environments. In this paper, we investigate their per- formance in dynamic environments. Two types of algorithms are proposed: homogeneous and heterogeneous approaches, where colonies share the same properties and colonies have their own (different) properties, respectively. Experimental results on the dynamic travelling salesman problem show that multi-colony ACO algorithms have promising performance in dynamic en- vironments when compared with single colony ACO algorithms. I. I NTRODUCTION Ant colony optimization (ACO) algorithms are inspired from nature, i.e., the foraging behaviour of real ant colonies [3], [7]. Most of the optimization problems addressed so far by ACO assume a stationary environment. However, the en- vironment in many real-world applications changes over time. The difference between stationary and dynamic optimization problems (DOPs) is that the aim for the former type of problems is to locate the static global optimum efficiently whereas the aim for the latter type of problems is to track the moving global optimum efficiently [12], [23], [30]. Addressing DOPs is challenging to ACO algorithms, and generally to all optimization algorithms. Once an ACO al- gorithm converges to an optimum, then it is difficult for the algorithm to escape from it in order to track the newly generated optimum when a dynamic change occurs. The pheromone trails, generated with ACO algorithms, of the previous environment may bias the colony 1 of ants towards the optimum of the previous environment. A direct way to address this issue is to consider every dynamic change as the arrival of a new problem instance that needs to be solved from scratch by re-initializing all the pheromone trails with an equal amount. However, such strategy may be computationally expensive and requires the detection of a dynamic change. In case the changing environments have similarities, the re-optimization time may be improved by transferring knowledge from previous environments [1], [12], [15], [23]. 1 A term used in ACO, which also denotes a population. Over the years, several strategies have been proposed to enhance the performance of ACO algorithms for DOPs, in- cluding increasing diversity after a change [8], [10], maintain- ing diversity during the execution [15], [16], memory-based schemes [11] and memetic algorithms [14]. Although multi- population approaches have shown promising performance for evolutionary algorithms [5] and particle swarm optimization [2] when addressing DOPs, they have attracted little (or no) attention for ACO. Hence, in this paper we attempt to apply multi-colony ACO algorithms in dynamic environments and investigate their performance. In this paper, the investigated multi-colony ACO algorithms consist of more than one colony, where each colony has its own pheromone table and exchange information occasionally. In this way, the search area explored is increased. If the colonies have the same searching behaviour, they are called homogeneous; otherwise, if the colonies have different search- ing behaviour, they are called heterogeneous. Based on the dynamic benchmark generator proposed in [17], a series of dynamic test cases are constructed from several stationary travelling salesman problem (TSP) benchmark instances and experiments are systematically carried out for single and multi- colony ACO algorithms. The rest of the paper is organized as follows. Section II de- scribes the dynamic TSP (DTSP) generated by the benchmark generator. Sections III and IV describe the traditional single colony ACO and proposed multi-colony ACO, respectively. Section V gives the experimental results of ACO algorithms regarding their overall performance in dynamic environments. Finally, Section VI concludes this paper and outlines several future works. II. DYNAMIC TRAVELLING SALESMAN PROBLEM The TSP can be described as follows: given a collection of cities, the objective is to find the Hamiltonian cycle that starts from one city and visits each of the other cities once before returning to the starting city. Typically, the problem is modelled by a fully connected weighted graph  =(,), where  = {0,...,} is a set of nodes and  = {(, ):  ∕=  } is a set of arcs. Each arc (, ) is associated with a non-negative value   which represents the distance between cities  and  . 978-1-4799-4515-3/14/$31.00 ©2014 IEEE