Solving maximum quasi-clique problem by a hybrid artificial bee colony approach

Abstract

Given a graph and a threshold (γ), the maximum quasi-clique (MQC) problem is to find a maximum cardinality subset of vertices in the graph such that the edge density of a corresponding induced subgraph is not less than γ. This problem istended version of the famous maximum clique problem, which arises in a various application domains and is known as NP-hard. In this study, we propose a heuristic method called the hybrid artificial bee colony (HABC) algorithm to address the MQC problem by incorporating several dedicated strategies into the artificial bee colony framework, which starts with an opposition-based initialization phase and then repeatedly alternates between an employed bees phase, an onlooker bees phase and a scout bees phase to perform the search. The employed bees phase and onlooker bees phase employ a decent local search and solution-based tabu search to locate the local optima and intensify the search,whereas the scout bees phase employs an opposition-based mechanism to reconstruct the best-found solutions to escape from the local optima and diversify the search. Experimental results indicate that our proposed HABC algorithm can improve the best-known solutions for 46 out of 112 problem instances and match the best-known solutions for 63 instances. Comparisons with the state-of-the-art heuristics and exact methods demonstrate the merits of the proposed algorithm.