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The Set-Union Knapsack Problem (SUKP) and Budgeted Maximum Coverage Problem(BMCP) are two closely related variant problems of the popular knapsackproblem. Given a set of weighted elements and a set of items with nonnegativevalues, where each item covers several distinct elements, these two problemsboth aim to find a subset of items that maximizes an objective function whilesatisfying a knapsack capacity (budget) constraint. We propose an efficient andeffective local search algorithm called E2LS for these two problems. To ourknowledge, this is the first time that an algorithm has been proposed for bothof them. E2LS trade-offs the search region and search efficiency by applying aproposed novel operator ADD$^*$ to traverse the refined search region. Such atrade-off mechanism allows E2LS to explore the solution space widely andquickly. The tabu search method is also applied in E2LS to help the algorithmescape from local optima. Extensive experiments on a total of 168 publicinstances with various scales demonstrate the excellent performance of theproposed algorithm for both the SUKP and BMCP.

Efficient and Effective Local Search for the Set-Union Knapsack Problem and Budgeted Maximum Coverage Problem