In this work, we present a branch-and-price algorithm to solve the weighted version of the List Coloring Problem, based on a vertex cover formulation by stable sets. This problem is interesting for its applications and also for the many other problems that it generalizes, including the well-known Graph Coloring Problem. With the introduction of the concept of indistinguishable colors, some theoretical results are presented which are later incorporated into the algorithm. We propose two branching strategies based on others for the Graph Coloring Problem, the first is an adaptation of the one used by Mehrotra and Trick in their pioneering branch-and-price algorithm, and the other is inspired by the one used by M\'endez-D\'iaz and Zabala in their branch-and-cut algorithm. The rich structure of this problem makes both branching strategies robust. Extended computation experimentation on a wide variety of instances shows the effectiveness of this approach and evidences the different behaviors that the algorithm can have according to the structure of each type of instance.

翻译：本文提出了一种基于稳定集顶点覆盖公式的分支定价算法，用于求解加权版本的列表着色问题。该问题因其应用价值及其所泛化的诸多问题（包括著名的图着色问题）而具有重要研究意义。通过引入不可区分颜色的概念，本文给出了一些理论结果，随后将其融入算法之中。我们基于图着色问题的已有分支策略提出了两种分支方法：第一种是对Mehrotra与Trick在其开创性分支定价算法中所用策略的改进，第二种灵感来源于Méndez-Díaz与Zabala在其分支切割算法中使用的策略。该问题的丰富结构使得这两种分支策略均表现出稳健性。在多种实例上进行的广泛计算实验表明，该方法的有效性得以验证，并揭示了算法根据不同类型实例的结构可能呈现的不同行为特征。