Two bi-objective hybrid approaches for the frequent subgraph mining problem

This paper proposes two hybrid bi-objective evolutionary algorithms to solve the frequent subgraph mining problem. In this contribution, we propose to improve the search ability of the stochastic local search (SLS) and the variable neighborhood search (VNS) algorithms by adding genetic operators (crossover and mutation) and Pareto dominance concept. A mined subgraph is defined by a bi-objective function which uses two parameters, support and size. We combine GA and SLS in a hybrid method denoted GASLS and GA with VNS in a hybrid method denoted GAVNS to solve the considered problem. The two proposed methods are implemented and evaluated on two synthetic and five real-world datasets of various sizes and their performance were compared against a single-objective stochastic local search algorithm and the well-known NSGA-II algorithm. The proposed methods are able to discover efficiently diversified subgraphs in the search space by exploring new solutions. The numerical results show that in general the GASLS method provides competitive results and finds high quality solutions compared to the other considered algorithms.