Solution Biases and Pheromone Representation Selection in Ant Colony Optimisation.

Abstract

Combinatorial optimisation problems (COPs) pervade human society: scheduling, design,layout, distribution, timetabling, resource allocation and project management all feature problems where the solution is some combination of elements, the overall value of which needs to be either maximised or minimised (i.e., optimised), typically subject to a number of constraints. Thus, techniques to efficiently solve such problems are an important area of research. A popular group of optimisation algorithms are the metaheuristics, approaches that specify how to search the space of solutions in a problem independent way so that high quality solutions are likely to result in a reasonable amount of computational time.Although metaheuristic algorithms are specified in a problem independent manner, they must be tailored to suit each particular problem to which they are applied. This thesis investigates a number of aspects of the application of the relatively new Ant Colony Optimisation (ACO) metaheuristic to different COPs. The standard ACO metaheuristic is a constructive algorithm loosely based on the foraging behaviour of ant colonies, which are able to find the shortest path to a food source by indirect communication through pheromones. ACO’s artificial pheromone represents a model of the solution components that its artificial ants use to construct solutions. Developing an appropriate pheromone representation is a key aspect of the application of ACO to a problem. Since its inception in the early 1990s, ACO has been applied to an increasing range of problems, leading to the development of a range of pheromone representations (Dorigo and St¨utzle, 2002). However, pheromone representations have typically been chosen in an ad hoc fashion, either by selecting a representation used previously for a similar problem or by developing a new representation that appears intuitively to suit the problem in question. The absence of a systematic approach to adapting ACO to different COPs has resulted in inconsistent performance across different problems.An examination of existing ACO applications and the constructive approach more generally reveals how the metaheuristic can be applied more systematically across a range of COPs. The two main issues addressed in this thesis are biases inherent in the constructive process and the systematic selection of pheromone representations.All constructive metaheuristics explore a tree of constructive decisions (a construction tree) the shape of which is determined by problem constraints and the chosen method of building solutions. The shape of this tree, combined with the mapping from paths in the tree to solutions, can bias a constructive search. This is particularly a problem in COPs where infeasible solutions cannot be avoided—such infeasible solutions have an elevated probability of being discovered by a constructive algorithm. This situation is common in COPs in which a number of entities (e.g., tasks, projects, or individuals) compete for limited resources. Alternative techniques for determining the order in which demands for resources are considered can improve the probability of reaching feasible solutions in these types of COP. A number of these techniques are investigated, revealing that commonly used static and dynamic heuristics for this task generally work well, although cannot guarantee a good probability of finding feasible solutions across all problem instances.The effectiveness of a given pheromone representation is related to how it maps on to the construction tree for a problem. Considering this finding, a systematic approach is developed for the selection of an appropriate pheromone representation based on characteristics of the COP being solved. The comparative performance of ACO using alternative pheromone representations—those used in the literature, suggested by the new system, or potentially applicable—is investigated for six problem types, including the travelling salesman,multiple knapsack, quadratic assignment, generalised assignment, shop scheduling and car sequencing problems. Results confirm that the algorithm’s suggested pheromone representations generally perform well, with two main exceptions. First, an intuitively inappropriate pheromone representation previously unused with the knapsack problem was found to perform best on that problem, a finding that will be the subject of further investigation.Second, results for the car sequencing problem suggest that using the simplest pheromone representation that models solution identity (rather than structure) may be better than attempting to model the full complexity of solution characteristics that contribute to solution cost.The systematisation of ACO should lead to more consistently high performance of the algorithm across different problems. Additionally, it supports the creation of a generalised ACO system, capable of adapting itself to suit many different combinatorial problems without the need for manual intervention