Multi-objective optimization for relevant sub-graph extraction Mohamed Elati, Cuong To, and R´ emy Nicolle Institute of Systems and Synthetic Biology, University of ´ Evry-Val-d’Essonne, 5 rue Henri Desbrures, 91030 Evry Cedex, France {mohamed.elati, remy.nicolle, cuong.to}@issb.genopole.fr Abstract. In recent years, graph clustering methods have rapidly emerged to mine latent knowledge and functions in networks. Most sub-graphs ex- tracting methods that have been introduced fall into graph clustering. In this paper, a novel trend of relevant sub-graphs extraction problem was considered as multi-objective optimization. Genetic Algorithms (GAs) and Simulated Annealing (SA) were then used to solve the problem ap- plied to biological networks. Comparisons between GAs, SA and Markov Cluster Algorithm (MCL) were carried out and the results showed that the proposed approach is superior. A biological case study shows that our method is able to discover additional protein complex members from an incomplete list of experimentally identified proteins and Pro-tein Protein Interaction (PPI) network. Keywords: graph clustering, genetic algorithms, simulated annealing, multi-objective optimization, protein-protein interaction network 1 Introduction Nowadays, there are many types of data that can be represented as graphs (net- works) such as web graphs, social networks, biological networks, communication networks, road networks, etc. Mining hidden knowledge in networks is a non- trivial task because networks are usually big (containing thousands of nodes and edges) and discrete (mathematics models are difficult to apply). A graph is a structure that consists of vertices (nodes) and edges. Vertices can be anything such as pages in web graphs, members in social networks, proteins or genes in biological networks, etc. Edges, which are links between two nodes, represent re- lationship between two nodes. There are many problems involving graphs such as the shortest paths, graph coloring, route, etc. In this work, we focus on graph clustering. Graph clustering is a problem where vertices are to be grouped into clusters satisfying some pre-defined criteria. Graph clustering methods have been applied in many fields, especially, in biological networks [1, 3, 2, 9]. Most of in- troduced sub-graph extraction methods are based on graph clustering such as the Markov Cluster Algorithm (MCL)[14], a scalable clustering algorithm for