Solving Hop-constrained MST problems with ACO

The Hop-constrained Minimum cost Flow Spanning Tree (HMFST) problem is an extension of the Hop-Constrained Minimum Spanning Tree problem since it considers flow requirements other than unit flows. Given that we consider the total costs to be nonlinearly flow dependent with a fixed-charge component and given the combinatorial nature of this class of problems, we propose a heuristic approach to address them. The proposed approach is a hybrid metaheuristic based on Ant Colony Optimization (ACO) and on Local Search (LS). In order to test the performance of our algorithm we have solved a set of benchmark problems and compared the results obtained with the ones reported in the literature for a Multi-Population Genetic Algorithm (MPGA). We have also compared our results, regarding computational time, with those of CPLEX. Our algorithm proved to be able to find an optimum solution in more than 75% of the runs, for each problem instance solved, and was also able to improve on many results reported for the MPGA. Furthermore, for every single problem instance we were able to find a feasible solution, which was not the case for the MPGA nor for CPLEX. Regarding running times, our algorithm improves upon the computational time used by CPLEX and was always lower than that of the MPGA. ∗This work is funded by the ERDF through the Programme COMPETE and by the Portuguese Government through FCT Foundation for Science and Technology, projects PTDC/EGE-GES/099741/2008 and PTDC/EEACRO/116014/2009. †Corresponding author.