General swap-based multiple neighborhood adaptive search for the maximum balanced biclique problem

Abstract

The maximum balanced biclique problem (MBBP) is to find the largest complete bipartite subgraph induced by two equal-sized subsets of vertices in a bipartite graph. MBBP is an NP-hard problem with a number of relevant applications. In this work, we propose a general swap-based multiple neighborhood adaptive search (SBMNAS) for MBBP. This algorithm combines a general k-SWAP operator which is used in local searches for MBBP for the first time, an adaptive rule for neighborhood exploration and a frequency-based perturbation strategy to ensure a global diversification. SBMNAS is evaluated on 60 random dense instances and 25 real-life large sparse instances from the popular Koblenz Network Collection (KONECT). Computational results show that our proposed algorithm attains all but one best-known solutions, and finds improved best-known results for 19 instances (new lower bounds).