Learning driven three-phase search for the maximum independent union of cliques problem

Given a simple and undirected graph, the maximum independent union of cliques (IUC) problem aims to identify a subset of vertices with maximum cardinality, such that each connected component of the induced subgraph is a complete graph. As a generalization of the popular NP -hard maximum clique problem, the maximum IUC problem is of great practical importance for social network analysis and network -based data mining. In this work, we present the first learning driven three-phase search algorithm for this relevant problem. The proposed algorithm incorporates a constrained swap -based tabu search to effectively examine candidate solutions and a frequency -based perturbation to diversify the search. It additionally integrates a probability learning mechanism to learn useful information during the search, which helps to build promising new starting solutions. Computational results on 83 benchmark graphs from the well-known 2nd DIMACS Challenge indicate that the algorithm competes very favorably with the current best -performing algorithms. We also present a practical application of the algorithm to social network analysis. Key algorithmic components are analyzed to understand their influences on the algorithm.