Advanced Tabu Search Algorithms for Bipartite Boolean Quadratic Programs Guided by Strategic Oscillation and Path Relinking

Abstract

The bipartite Boolean quadratic programming problem (BBQP) is a generalization of the well-studied NP-hard Boolean quadratic programming problem and can be regarded as a unified model for many graph theoretic optimization problems, including maximum weight-induced subgraph problems, maximum weight biclique problems, matrix factorization problems, and maximum cut problems on bipartite graphs. This paper introduces three main algorithms for solving the BBQP, based on three variants of tabu search, the first two consisting of strategic oscillation–tabu search (SO-TS) algorithms, which use destructive and constructive procedures to guide the search into unexplored and promising areas. The third algorithm, whichDoes also incorporates the SO-TS algorithms as solution improvement methods, uses a path relinking (PR) algorithm that is capable of further enhancing search performance. Experimental results demonstrate that all three algorithms perform very effectively compared with the best methods in the literature, and the PR algorithm joined with tabu search is able to discover new best solutions for two-thirds of the large problem instances and match the previous best known solutions for the other instances. Additional analysis discloses the contributions of the key ingredients of each of the proposed algorithms.