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

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