A genetic and iterative local search algorithm for solving subgraph isomorphism problem

Finding the subgraph of a graph that is isomorphic to a given graph has practical applications in several fields, from cheminformatics to image understanding. Since subgraph isomorphism problem is NP-Hard, meta-heuristics are of especial use and importance in solving it. In this paper a hybrid metaheuristic algorithm for subgraph isomorphism is proposed. The main idea of the new algorithm is to use the iterative local search (ILS) to improve the genetic operations and to better guide the search process in the genetic algorithm. The concept of the permutation matrix was used for the matching process. By applying permutation matrix, we could also define an efficient fitness function for the optimization version of the Subgraph Isomorphism problem which made possible the generation of instance problems of subgraph isomorphism for the first time. A landscape analysis was also conducted to justify the application of a population-based algorithm (namely GA) for this problem. The results of the hybrid GA and ILS are computed for four groups of instance problems and are compared to the solutions of the genetic algorithm which show the improvement in performance of the GA, both in value and time.