An ant colony optimisation algorithm for the set packing problem

Abstract

In this paper we consider the application of an Ant Colony Optimisation (ACO) metaheuristic on the Set Packing Problem (SPP) which is a NP-hard optimisation problem. For the proposed algorithm, two solution construction strategies based on exploration and exploitation of solution space are designed. The main difference between both strategies concerns the use of pheromones during the solution construction. The selection of one strategy is driven automatically by the search process. A territory disturbance strategy is integrated in the algorithm and is triggered when the convergence of the ACO stagnates. A set of randomly generated numerical instances, involving from 100 to 1000 variables and 100 to 5000 constraints, was used to perform computational experiments. To the best of our knowledge, only one other metaheuristic (Greedy Randomized Adaptative Search Procedure, GRASP) has been previously applied to the SPP. Consequently, we report and discuss the effectiveness of ACO when compared to the best known solutions and including those provided by GRASP. Optimal solutions obtained with Cplex on the smaller instances (up to 200 variables) are indicated with the calculation times. These experiments show that our ACO heuristic outperforms the GRASP heuristic. It is remarkable that the ACO heuristic is made up of simple search techniques whilst the considered GRASP heuristic is more evolved. © 2004 Springer-Verlag.