Multistart Solution-Based Tabu Search For The Set-Union Knapsack Problem

The NP-hard Set-Union Knapsack Problem is a general model able to formulate a number of practical problems. As a variant of the popular knapsack problem, SUKP is to find a subset of candidate items (an item is composed of several distinct weighted elements) such that a profit function is maximized while a knapsack capacity constraint is satisfied. We investigate for the first time a multistart solution-based tabu search algorithm for solving the problem. The proposed algorithm combines a solution-based tabu search procedure with a multistart strategy to ensure an effective examination of candidate solutions. We report computational results on 60 benchmark instances from the literature, including new best results (improved lower bounds) for 7 large instances. We show additional experiments to shed lights on the roles of the key composing ingredients of the algorithm. The code of the algorithm will be publicly available. (C) 2021 Elsevier B.V. All rights reserved.