Assume that a connected undirected edge weighted graph G is given. The Degree Constrained Minimum Spanning Tree Problem (DCMSTP) asks for a minimum cost spanning tree of G where vertex degrees do not exceed given pre-defined upper bounds. In this paper, three exact solution algorithms are investigated for the problem. All of them are Branch-and-cut based and rely on the strongest formulation currently available for the problem. Additionally, to speed up the computation of dual bounds, they all use column generation, in one way or another. To test the algorithms, new hard to solve DCMSTP instances are proposed here. These instances, combined with additional ones taken from the literature, are then used in computational experiments. The experiments compare the new algorithms among themselves and also against the best algorithms currently available in the literature. As an outcome of them, one of the new algorithms stands out on top.
In this paper, we describe and show the results of a combination of two metaheuristics to solve an unrelated parallel machines scheduling problem in which the setup times depend not only on the machine and job sequence, but also on the amount of resource assigned. This problem has been proposed recently on the literature and since then a couple of metaheuristics have been used to address it. The one proposed here, called GTS, consists of two phases: initially, some solutions are generated by the GRASP metaheuristic; subsequently, the Tabu Search (TS) is applied in the best solution found by GRASP. The numerical experiments show that the GTS heuristic was able to improve the results in 70% (251 out of 360) of the larger instances available in the literature.
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