Adaptive tabu search with strategic oscillation for the bipartite boolean quadratic programming problem with partitioned variables

Abstract The bipartite boolean quadratic programming problem with partitioned variables (BQP-PV) is an NP-hard combinatorial optimization problem that accommodates a variety of real-life applications. We propose an adaptive tabu search with strategic oscillation (ATS-SO) approach for BQP-PV, which employs a multi-pass search framework where each pass consists of an initial constructive phase, an adaptive tabu search phase and a frequency-driven strategic oscillation phase. In particular, the adaptive tabu search phase combines different move operators to collectively conduct neighborhood exploration and an adaptive tabu tenure management mechanism that obviates the task of determining a proper tabu tenure. The frequency-driven strategic oscillation phase diversifies the search when the search reaches a critical solution, drawing on a destructive procedure to unassign some variables by reference to frequency memory and a constructive procedure to re-assign these variables utilizing both frequency memory and problem specific knowledge. Computational experiments on five classes of problem instances indicate that the proposed ATS-SO algorithm is able to find improved solutions for 14 instances and match the best known solutions for all remaining instances, whereas no previous method has succeeded in finding the previous best solutions for all instances. Statistical tests indicate that ATS-SO significantly outperforms the state-of-the-art algorithms in the literature.