Exactness as Heuristic Structure for Guiding Ant Colony System Stephen Gilmour and Mark Dras Department of Computing, Macquarie University, North Ryde, NSW, Australia 2109 {gilmour, madras}@ics.mq.edu.au Abstract. For solving combinatorial optimisation problems, exact meth- ods accurately exploit the structure of the problem but are tractable only up to a certain size; approximation or heuristic methods are tractable for very large problems but may possibly be led into a bad solution. A ques- tion that arises is, From where can we obtain knowledge of the problem structure via exact methods that can be used on large-scale problems by heuristic methods? We present a framework that allows the exploitation of existing techniques and resources to integrate such structural knowl- edge into the Ant Colony System metaheuristic, where the structure is determined through the notion of kernelization from the field of param- eterized complexity. We give experimental results using vertex cover as the problem instance, and show that knowledge of this type of structure improves performance beyond previously defined ACS algorithms. 1 Introduction For solving combinatorial optimisation problems, exact methods accurately ex- ploit the structure of the problem but are tractable only up to a certain size; approximation or heuristic methods are tractable for very large problems but may possibly be led into a bad solution. A third approach could be to combine heuristics and exact methods, which would hopefully still run quickly but the quality of solution would be improved over just regular heuristics. Some exam- ples of combining heuristics with exact methods are discussed in [2]. In the work discussed in this paper, we investigate the use of an already well established body of techniques from the field of parameterized complexity [6] for identifying problem structure as part of an exact solution, and the extent to which these techniques can be integrated into heuristics. There are a number of ways such an integration could be defined. For example, we could just use search trees on the problem until a certain point, or we could incorporate the techniques more centrally into the heuristic. In this paper we compare a number of different approaches to combining the notion of ‘kernelization’ from parameterized complexity with Ant Colony System (ACS) [5, 3]. The paper builds on the work of two papers before it: the first paper [7] is a proposal for our framework, and discusses a part of the framework which is now complete in this paper and gives some preliminary results for our research; the second paper [8] gives an ACS algorithm for the vertex cover problem that is a