An Analysis of Problem Difficulty for a Class of Optimisation Heuristics

Abstract. This paper investigates the effect of the cost matrix standard deviation of Travelling Salesman Problem (TSP) instances on the performance of a class of combinatorial optimisation heuristics. Ant Colony Optimisation (ACO) is the class of heuristic investigated. Results demonstrate that for a given instance size, an increase in the standard deviation of the cost matrix of instances results in an increase in the difficulty of the instances. This implies that for ACO, it is insufficient to report results on problems classified only by problem size, as has been commonly done in most ACO research to date. Some description of the cost matrix distribution is also required when attempting to explain and predict the performance of these algorithms on the TSP.

Higher order pheromone models in ant colony optimisation

Ant colony optimisation is a constructive metaheuristic that successively builds solutions from problem-specific components. A parameterised model known as pheromone—an analogue of the trail pheromones used by real ants—is used to learn which components should be combined to produce good solutions. In the majority of the algorithm’s applications a single parameter from the model is used to influence the selection of a single component to add to a solution. Such a model can be described as first order. Higher order models describe relationships between several components in a solution, and may arise either by contriving a model that describes subsets of components from a first order model or because the characteristics of solutions modelled naturally relate subsets of components. This paper introduces a simple framework to describe the application of higher order models as a tool to understanding common features of existing applications. The framework also serves as an introduction to those new to the use of such models. The utility of higher order models is discussed with reference to empirical results in the literature

Les grand télescopes du Max-Planck-Institut für Astronomie

In Xin Yao et al, editors, Parallel Problem Solving from Nature (PPSN-VIII). Springer Verlag Berlin, Germany.info:eu-repo/semantics/publishe