Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
An enumerative procedure for identifying maximal covers
PDF (Español (España))

Keywords

Maximal covers
tighter formulations
knapsack constraints
dominated inequalities
Cubrimientos maximales
formulaciones más fuertes
restricciones de tipo mochila
desigualdades dominadas

How to Cite

Muñoz, S. (2003). An enumerative procedure for identifying maximal covers. Revista De Matemática: Teoría Y Aplicaciones, 10(1-2), 173–186. https://doi.org/10.15517/rmta.v10i1-2.233

Abstract

In this paper we present an enumerative procedure for identifying all maximal covers from the set of covers implied by a 0-1 knapsack constraint. The inequalities induced by these maximal covers are not dominated by the inequality induced by any other cover implied by the knapsack constraint. Thus, their identification can help to tighten 0-1 models. On the other hand, we present an improvement on a procedure taken from the literature for identifying certain maximal covers. Some comparative computational experiments where both procedures have been applied to randomly generated knapsack constraints are also reported.

https://doi.org/10.15517/rmta.v10i1-2.233
PDF (Español (España))

References

Dietrich, B.L.; Escudero, L.F.; Garín, A.; Pérez, G. (1993) “O(n) procedures for identifying maximal cliques and non-dominated extensions of consecutive minimal covers and alternates”, Top 1(1): 139–160.

Escudero, L.F.; Martello, S.; Toth, P. (1998) “On tightening 0-1 programs based on extensions of pure 0-1 knapsack and subset-sum problems”, Annals of Operations Research 81: 379–404.

Escudero, L.F.; Muñoz, S. (1998) “On characterizing tighter formulations for 0-1 programs”, European Journal of Operational Research 106(1): 172–176.

Escudero, L.F.; Muñoz, S. (2002) “On characterizing maximal covers”, Investigación Operacional (to appear).

Hoffman, K.L.; Padberg, M. (1991) “Improving LP-representations of zero-one linear programs for branch-and-cut”, ORSA Journal on Computing 3(2): 121–134.

Johnson, E.L.; Nemhauser, G.L.; Savelsbergh, M.W.P. (2000) “Progress in linear programming-based algorithms for integer programming: An exposition”, INFORMS Journal on Computing 12(1): 2–23.

Muñoz, S. (1995) “A correction of the justification of the Dietrich-Escudero- Garín -Pérez O(n) procedures for identifying maximal cliques and non-dominated extensions of consecutive minimal covers and alternates”, Top 3(1): 161–165.

Muñoz, S. (1999) Reforzamiento de Modelos en Programación Lineal 0-1. Tesis Doctoral, Universidad Complutense de Madrid, Madrid.

Nemhauser, G.L.; Wolsey, L.A. (1998) Integer and Combinatorial Optimization. John Wiley, New York.

Press, W.H.; Teukolsky, S.A.; Vetterling, W.T.; Flannery, B.P. (1992) Numerical Recipes in FORTRAN. The Art of Scientific Computing. Cambridge University Press.

Savelsbergh, M.W.P. (1994) “Preprocessing and probing techniques for mixed integer programming problems”, ORSA Journal on Computing 6(4): 445–454.

Comments

Downloads

Download data is not yet available.