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