Greedy Randomized Adaptative Search Procedure for set packing problems

The principles of the Greedy Randomized Adaptative Search Procedure (GRASP) metaheuristic are instantiated for the set packing problem. We investigated several construction phases, and evaluated improvements based on advanced strategies. These improvements include a self-tuning procedure (using reactive GRASP), an intensification procedure (using path relinking) and a procedure involving the diversification of the selection (using a learning process). Two sets of various numerical instances were used to perform the computational experiments. The first set contains randomly generated instances, while the second includes instances relating to real problems in railway planning. No metaheuristic has previously been applied to this combinatorial problem. Consequently, we have discussed GRASP's performances both in relation to lower/upper bounds and to the results obtained with Cplex when such results are available. Our analysis, based on the average performances observed, shows the impact of the suggested strategies, and indicates the configuration that produces the best results.