Probability learning based tabu search for the budgeted maximum coverage problem

•We are the first to address the NP-hard Budgeted Maximum Coverage Problem.•We propose an algorithm that combines reinforcement learning with local search.•We introduce the first set of benchmark instances for the problem.•The proposed algorithm outperforms the comparison algorithms and the CPLEX solver. The Budgeted Maximum Coverage Problem (BMCP) is a general model with a number of real-world applications. Given n elements with nonnegative profits, m subsets of elements with nonnegative weights and a total budget, the BMCP aims to select some subsets such that the total weight of the selected subsets does not exceed the budget, while the total profit of the associated elements is maximized. BMCP is NP-hard and thus computationally challenging. We investigate for the first time an effective practical algorithm for solving this problem, which combines reinforcement learning and local search. The algorithm iterates through two distinct phases, namely a tabu search phase and a probability learning based perturbation phase. To assess the effectiveness of the proposed algorithm, we show computational results on a set of 30 benchmark instances introduced in this paper and present comparative studies with respect to the approximation algorithm, the genetic algorithm and the CPLEX solver.