Multi-wave tabu search for the boolean quadratic programming problem with generalized upper bound constraints

The boolean quadratic programming problem with generalized upper bound constraints (BQP-GUB) is an NP-hard problem with many practical applications. In this study, we propose an effective multi-wave tabu search algorithm for solving BQP-GUB. The algorithm performs a sequence of search waves, where each wave alternates between the forward and reverse phases, and the transition between two adjacent waves depends on a hybrid perturbation phase. The forward phase employs tabu search to reach a critical solution and the reverse phase follows to reverse previously performed moves and perform an equal number of moves by referring to the search information gathered from the latest search process. The hybrid perturbation phase randomly chooses a directed strategy, a frequency guided strategy and a recency guided strategy to achieve search diversification. Experimental results on 78 standard instances indicate that the proposed algorithm is able to improve the lower bounds for 6 instances and match the best solutions in the literature for most instances within competitive time.