Bounds and Heuristics for the Shortest Capacitated Paths Problem

Authors:
Marie-Christine Costa;Alain Hertz;Michel Mittaz
Affiliations:
CEDRIC, CNAM, 292 rue Saint-Martin, 75003 Paris, France;Department of Mathematics, EPFL, 1015 Lausanne, Switzerland;Department of Mathematics, EPFL, 1015 Lausanne, Switzerland
Venue:
Journal of Heuristics
Year:
2002

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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.