Several variants of the classical Constrained Shortest Path Problem have been presented in the literature so far. One of the most recent is the k-Color Shortest Path Problem (\(k\)-CSPP), that arises in the field of transmission networks design. The problem is formulated on a weighted edge-colored graph and the use of the colors as edge labels allows to take into account the matter of path reliability while optimizing its cost. In this work, we propose a dynamic programming algorithm and compare its performances with two solution approaches: a Branch and Bound technique proposed by the authors in their previous paper and the solution of the mathematical model obtained with CPLEX solver. The results gathered in the numerical validation evidenced how the dynamic programming algorithm vastly outperformed previous approaches.

迄今为止，经典约束最短路径问题的几种变体已在文献中提出。最近的一种是k颜色最短路径问题（\（k \）-CSPP），这是在传输网络设计领域出现的。该问题在加权的边缘彩色图形上表示，并且使用颜色作为边缘标签可以在优化成本的同时考虑路径可靠性问题。在这项工作中，我们提出了一种动态规划算法，并将其性能与两种解决方案方法进行了比较：作者在前一篇论文中提出的Branch and Bound技术以及使用CPLEX求解器获得的数学模型的解决方案。数值验证中收集的结果证明了动态规划算法在很大程度上优于以前的方法。