Learning-based multi-start iterated local search for the profit maximization set covering problem

The profit maximization set covering problem is a general model able to formulate practical problems including in particular an application in the mining industry. As a variant of the partial set covering problem, the studied problem is to select some subsets of elements to maximize the difference of the total gain of the covered elements subtracting the costs of the chosen subsets and their associated groups. We investigate for the first time a learning-based multi-start iterated local search algorithm for solving the problem. The proposed algorithm combines a multi-restart mechanism to enhance robustness, an intensification-driven local search to perform intensive solution examination, a learning-driven initialization to obtain high-quality starting solutions and a learning-based strategy to select suitable perturbations. Experimental results on 30 benchmark instances show the competitiveness of the algorithm against the state-of-the-art methods, by reporting 18 new lower bounds and 12 equal results (including 7 known optimal results). We also perform additional experiments to validate the design of the algorithmic components.