This paper addresses the Minimum Spanning Tree Problem with Conflicting Edge Pairs, a variant of the classical Minimum Spanning Tree where, given a list of conflicting edges, the goal is to find the cheapest spanning tree with no edges in conflict. We adopt a Lagrangian relaxation approach together with a dual ascent and a subgradient procedure to find tight lower bounds on the optimal solution. The algorithm is also equipped with a heuristics approach which provides an upper bound by removing the conflicts from possible infeasible solutions met during the calculation of the lower bounds. The computational results, carried out on benchmark instances, show that the proposed algorithm finds the optimal solutions on several instances. ∗fcarrabs@unisa.it (Corresponding author) †manlio.gaudioso@unical.it

中文翻译：

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具有冲突边对的最小生成树问题的拉格朗日方法

本文解决了具有冲突边对的最小生成树问题，这是经典最小生成树的一种变体，在给定冲突边列表的情况下，目标是找到没有冲突边的最便宜的生成树。我们采用拉格朗日松弛方法以及双重上升和次梯度程序来找到最优解的严格下界。该算法还配备了启发式方法，该方法通过从计算下限期间遇到的可能不可行解决方案中去除冲突来提供上限。在基准实例上进行的计算结果表明，所提出的算法在多个实例上找到了最优解。∗fcarrabs@unisa.it (通讯作者) †manlio.gaudioso@unical.it