Multistart solution-based tabu search for the Set-Union Knapsack Problem

Abstract

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.