Given an undirected weighted graph, in which each vertex is assigned to a color and one of them is identified as source, in the all-colors shortest path problem we look for a minimum cost shortest path that starts from the source and spans all different colors. The problem is known to be NP-Hard and hard to approximate. In this work we propose a variant of the problem in which the source is unspecified and show the two problems to be computationally equivalent. Furthermore, we propose a mathematical formulation, a compact representation for feasible solutions and a VNS metaheuristic that is based on it. Computational results show the effectiveness of the proposed approach for the two problems.

A two-level metaheuristic for the all colors shortest path problem

Carrabs, F.;Cerulli, R.;Raiconi, A.
2018-01-01

Abstract

Given an undirected weighted graph, in which each vertex is assigned to a color and one of them is identified as source, in the all-colors shortest path problem we look for a minimum cost shortest path that starts from the source and spans all different colors. The problem is known to be NP-Hard and hard to approximate. In this work we propose a variant of the problem in which the source is unspecified and show the two problems to be computationally equivalent. Furthermore, we propose a mathematical formulation, a compact representation for feasible solutions and a VNS metaheuristic that is based on it. Computational results show the effectiveness of the proposed approach for the two problems.
2018
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4713408
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