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International audience; In this work we address the Hop-Constrained Minimum cost Flow Spanning Tree (HMFST) problem with nonlinear costs. The HMFST problem is an extension of the Hop-Constrained Minimum Spanning Tree problem since it considers flow requirements other than unit flows. We propose a hybrid heuristic, based on ant colony optimization and on local search, to solve this class of problems given its combinatorial nature and also that the total costs are nonlinearly flow dependent with a fixed-charge component. We solve a set of benchmark problems available online and compare the results obtained with the ones reported in the literature for a Multi-Population hybrid biased random key Genetic Algorithm (MPGA). 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. Regarding running times, our algorithm improves upon the computational time used by CPLEX and was always lower than that of the MPGA.

In this work we address the Single-Source Uncapacitated Minimum Cost Network Flow Problem with concave cost functions. This problem is NP-Hard, therefore we propose a hybrid heuristic to solve it. Our goal is not only to apply an ant colony optimization (ACO) algorithm to such a problem, but also to provide an insight on the behaviour of the parameters in the performance of the algorithm. The performance of the ACO algorithm is improved with the hybridization of a local search (LS) procedure. The core ACO procedure is used to mainly deal with the exploration of the search space, while the LS is incorporated to further cope with the exploitation of the best solutions found. The method we have developed has proven to be very efficient while solving both small and large size problem instances. The problems we have used to test the algorithm were previously solved by other authors using other population based heuristics. Our algorithm was able to improve upon some of their results in terms of solution quality, proving that the HACO algorithm is a very good alternative approach to solve these problems. In addition, our algorithm is substantially faster at achieving these improved solutions. Furthermore, the magnitude of the reduction of the computational requirements grows with problem size.

In this work we address the Singe-Source Uncapacitated Minimum Cost Network Flow Problem with concave cost functions. Given that this problem is of a combinatorial nature and also that the total costs are nonlinear, we propose a hybrid heuristic to solve it. In this type of algorithms one usually tries to manage two conflicting aspects of searching behaviour: exploration, the algorithm's ability to search broadly through the search space; and exploitation, the algorithm ability to search locally around good solutions that have been found previously. In our case, we use an Ant Colony Optimization algorithm to mainly deal with the exploration, and a Local Search algorithm to cope with the exploitation of the search space. Our method proves to be very efficient while solving both small and large size problem instances. The problems we have used to test the algorithm were previously solved by other authors using other population based heuristics and our algorithm was able to improve upon their results, both in terms of computing time and solution quality.