Application of genetic algorithms in graph searching problem

Graph searching is a common approach to solving a problem of capturing a hostile intruder by a group of mobile agents. We assume that this task is performed in an environment which we are able to model as a graph G. The question asked is how many agents are needed to capture an arbitrary fast, invisible and smart intruder. This number is called the (edge) search number of G. The strategy which must be performed by agents is called the (edge) search strategy. Unfortunately calculating both the optimal search strategy and the search number is NP-hard for general graphs. Furthermore, due to the complexity of the pursuit rules, the application of heuristic solutions is not straightforward. In this paper we suggest a method of applying genetic algorithms to solve graph searching problem. The idea is based on LaPaugh´s result on graph searching monotonicity and utilizes representation of a search strategy as a permutation of edges.