Abstract
Given a graph G, the Shortest Capacitated Paths Problem (SCPP) consists of determining a set of paths of least total length, linking given pairs of vertices in G, and satisfying capacity constraints on the arcs of G.
We formulate the SCPP as a 0-1 linear program and study two Lagrangian relaxations for getting lower bounds on the optimal value. We then propose two heuristic methods. The first one is based on a greedy approach, while the second one is an adaptation of the tabu search meta-heuristic.
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Costa, MC., Hertz, A. & Mittaz, M. Bounds and Heuristics for the Shortest Capacitated Paths Problem. Journal of Heuristics 8, 449–465 (2002). https://doi.org/10.1023/A:1015492014030
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DOI: https://doi.org/10.1023/A:1015492014030