Abstract
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.
Highlights
In the past few decades, communication networks have swiftly become a key infrastructure in any modern society
The k-Color Shortest Path Problem (k-CSPP) has already been tackled by means of a Branch and Bound algorithm; on the other hand the dynamic programming framework has been widely used to deal with Resource Constrained Shortest Path Problems [4,5]
The main contribution of the present work is the design of a dynamic programming algorithm based on a path-labeling approach and an A∗-like exploration strategy
Summary
In the past few decades, communication networks have swiftly become a key infrastructure in any modern society. The k-CSPP has already been tackled by means of a Branch and Bound algorithm; on the other hand the dynamic programming framework has been widely used to deal with Resource Constrained Shortest Path Problems [4,5]. With this in mind, the main contribution of the present work is the design of a dynamic programming algorithm based on a path-labeling approach and an A∗-like exploration strategy.
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