The resource constrained clustered shortest path tree problem: Mathematical formulation and Branch&Price solution algorithm

Abstract

In this article, the Resource Constrained Clustered Shortest Path Tree Problem is defined. It generalizes the classic Resource Constrained Shortest Path Tree Problem since it is defined on an undirected, complete and weighted graph whose set of nodes is partitioned into clusters. The aim is then to find a shortest path tree respecting some resource consumption constraints and inducing a connected subgraph within each cluster. The main support and motivation for studying this problem are related, among the others, to the design of telecommunication networks, and to Disaster Operations Management. In this work, we present a path‐based formulation for the problem, addressing the case of local resource constraints, that is, resource constraints on single paths. For its resolution, a Branch&Price algorithm featuring a Column Generation approach with Multiple Pricing Scheme is devised. A comprehensive computational study is conducted, comparing the proposed method with the results achieved by the CPLEX solver, adopted to solve the mathematical model. The numerical results underline that the Branch&Price algorithm outperforms CPLEX, both in terms of solution cost and time.

Advanced Network Connectivity Features and Zonal Requirements in Covering Location Problems

“…2. The second data-set consists of a subset of the High-R instances of Type 1, 5 and 6 used byFerone et al (2022) for the Resource Constrained Clustered Shortest Path Tree Problem. They are complete graphs whose costs verify the triangular inequality, and for which the set of nodes is partitioned in subsets called clusters.…”