RESUMEN
This article proposes a benchmark instance generator for the Hop-Constrained Minimum Spanning Tree problem, the Delay-Constrained Minimum Spanning Tree problem, and their bi-objective variants. The generator is developed in C++ and does not uses external libraries, being understandable, easy-to-read, and easy-to-use. Furthermore, the generator employs five parameters that makes possible to generate personalized benchmark instances for these problems. We also describe 640 benchmark instances that were previously used in computational experiments in the literature. Lastly, we include raw results obtained from computational experiments with the described benchmark instances. We hope that the data introduced in this article can foster the development and the evaluation of new algorithms for solving constrained minimum spanning tree problems.
RESUMEN
This article deals with two min-max regret covering problems: the min-max regret Weighted Set Covering Problem (min-max regret WSCP) and the min-max regret Maximum Benefit Set Covering Problem (min-max regret MSCP). These problems are the robust optimization counterparts, respectively, of the Weighted Set Covering Problem and of the Maximum Benefit Set Covering Problem. In both problems, uncertainty in data is modeled by using an interval of continuous values, representing all the infinite values every uncertain parameter can assume. This study has the following major contributions: (i) a proof that MSCP is Σ p 2 -Hard, (ii) a mathematical formulation for the min-max regret MSCP, (iii) exact and (iv) heuristic algorithms for the min-max regret WSCP and the min-max regret MSCP. We reproduce the main exact algorithms for the min-max regret WSCP found in the literature: a Logic-based Benders decomposition, an extended Benders decomposition and a branch-and-cut. In addition, such algorithms have been adapted for the min-max regret MSCP. Moreover, five heuristics are applied for both problems: two scenario-based heuristics, a path relinking, a pilot method and a linear programming-based heuristic. The goal is to analyze the impact of such methods on handling robust covering problems in terms of solution quality and performance.