We study the Partition Coloring Problem (PCP), a generalization of the Vertex Coloring Problem where the vertex set is partitioned. The PCP asks to select one vertex for each subset of the partition in such a way that the chromatic number of the induced graph is minimum. We propose a new Integer Linear Programming formulation with an exponential number of variables. To solve this formulation to optimality, we design an effective Branch-and-Price algorithm. Good quality initial solutions are computed via a new metaheuristic algorithm based on adaptive large neighborhood search. Extensive computational experiments on a benchmark test of instances from the literature show that our Branch-and-Price algorithm, combined with the new metaheuristic algorithm, is able to solve for the first time to proven optimality several open instances, and compares favorably with the current state-of-the-art exact algorithm.

An exact algorithm for the Partition Coloring Problem

Furini, Fabio;Malaguti, Enrico
;
Santini, Alberto
2018

Abstract

We study the Partition Coloring Problem (PCP), a generalization of the Vertex Coloring Problem where the vertex set is partitioned. The PCP asks to select one vertex for each subset of the partition in such a way that the chromatic number of the induced graph is minimum. We propose a new Integer Linear Programming formulation with an exponential number of variables. To solve this formulation to optimality, we design an effective Branch-and-Price algorithm. Good quality initial solutions are computed via a new metaheuristic algorithm based on adaptive large neighborhood search. Extensive computational experiments on a benchmark test of instances from the literature show that our Branch-and-Price algorithm, combined with the new metaheuristic algorithm, is able to solve for the first time to proven optimality several open instances, and compares favorably with the current state-of-the-art exact algorithm.
2018
Furini, Fabio; Malaguti, Enrico*; Santini, Alberto
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/657025
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