Theoretical investigation of aggregation in pseudo-polynomial network-flow models

  • Authors:

  • Marie-Emilie Voge;François Clautiaux

  • Affiliations:

  • Université de Lille 1, LIFL UMR CNRS 8022, INRIA Lille Nord Europe, Villeneuve d'Ascq, France;Université de Lille 1, LIFL UMR CNRS 8022, INRIA Lille Nord Europe, Villeneuve d'Ascq, France

  • Venue:
  • ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
  • Year:
  • 2012

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Abstract

In this paper, we address a class of arc-flow mathematical programming models that use a pseudo-polynomial number of variables and constraints. In [7], the authors have shown that such models can be used in practice to solve a vehicle routing problem using an aggregation algorithm. The purpose of this paper is to study the theoretical quality of the solutions and relaxations obtained when an aggregation is applied to such pseudo-polynomial flow models. We show that the approximation ratio and worst-case performance obtained by the heuristics and the relaxations depend on the concept of conflict-difference cliques. We then give an algorithm to compute the best aggregation.