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A branch-and-cut algorithm for a resource-constrained scheduling problem

Published online by Cambridge University Press:  21 August 2007

Renaud Sirdey  and
Hervé L. M. Kerivin
Renaud Sirdey
Affiliation:
Service d'architecture BSC (PC 12A7), Nortel GSM Access R&D, Parc d'activités de Magny-Châteaufort, 78928 Yvelines Cedex 09, France; renauds@nortel.com UMR CNRS Heudiasyc (Université de Technologie de Compiègne), Centre de recherches de Royallieu, BP 20529, 60205 Compiègne Cedex, France.
Hervé L. M. Kerivin
Affiliation:
UMR CNRS Limos (Université de Clermont-Ferrand II), Complexe scientifique des Cézeaux, 63177 Aubière Cedex, France; kerivin@math.univ-bpclermont.fr
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Abstract

This paper is devoted to the exact resolution of a strongly NP-hard resource-constrained scheduling problem, the Process Move Programming problem, which arises in relation to the operability of certain high-availability real-time distributed systems. Based on the study of the polytope defined as the convex hull of the incidence vectors of the admissible process move programs, we present a branch-and-cut algorithm along with extensive computational results demonstrating its practical relevance, in terms of both exact and approximate resolution when the instance size increases.

Keywords

Polyhedral combinatoricsschedulingbranch-and-cutdistributed systems
Type
Research Article
Information
RAIRO - Operations Research , Volume 41 , Issue 3: Journées Polyèdres et Optimisation Combinatoire , July 2007 , pp. 235 - 251
Copyright
© EDP Sciences, ROADEF, SMAI, 2007

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References

Computational infrastructure for operations research (www.coin-or.org), last access on July the 18th (2006).
G. Aggarwal, R. Motwani and A. Zhu, The load rebalancing problem, in Proceedings of the Fifteenth Annual ACM Symposium on Parallel Algorithms and Architectures (2003) 258–265.
E. Anderson, J. Hall, J. Hartline, M. Hobbs, A.R. Karlin, J. Saia, R. Swaminathan and J. Wilkes, An experimental study of data migration algorithms. In Proceedings of the 5th International Workshop on Algorithm Engineering. Lect. Notes Comput. Sci. (2001) 145.
J. Carlier. Le problème de l'ordonnancement des paiements de dettes. RAIRO: Oper. Res. 18 février (1984).
T. Christof and G. Reinelt, Algorithmic aspects of using small instance relaxations in parallel branch-and-cut. Technical report, Heidelberg University (1998).
E.G. Coffman, M.R. Garey, D.S. Johnson and A.S. Lapaugh, Scheduling file transfers in distributed networks, in Proceedings of the 2nd Annual ACM Symposium on Principles of Distributed Computing (1983) 254–266.
E.G. Coffman, M.R. Garey, D.S. Johnson and A.S. Lapaugh, Scheduling file transfers. SIAM J. Comput. 14 (1985).
Demange, M. and Paschos, V.T., On an approximation measure founded on the links between optimization and polynomial approximation theory. Theor. Comput. Sci. 158 (1996) 117–141. CrossRef
Fishburn, P.C., Induced binary probabilities and the linear ordering polytope: a status report. Math. Social Sci. 23 (1992) 67–80. CrossRef
M.R. Garey and D.S. Johnson, Computers and intractability|A guide to the theory of NP-completeness. W. H. Freeman and Company (1979).
Grötschel, M., Jünger, M. and Reinelt, G., A cutting plane algorithm for the linear ordering problem. Oper. Res. 32 (1984) 1195–1220. CrossRef
Grötschel, M., Jünger, M. and Reinelt, G., Facets of the linear ordering polytope. Math. Program. 33 (1985) 43–60. CrossRef
Grötschel, M., Jünger, M. and Reinelt, G., On the acyclic subgraph polytope. Math. Program. 33 (1985) 28–42. CrossRef
M. Grötschel, L. Lovász and A. Schrijver, Geometric algorithms and combinatorial optimization, Vol. 2 Algorithms and Combinatorics. Springer (1988).
J. Hall, J. Hartline, A.R. Karlin, J. Saia and J. Wilkes, On algorithms for efficient data migration. In Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (2001) 620–629.
P. Jalote, Fault tolerance in distributed systems. Distributed Systems. Prentice Hall (1994).
H. Kellerer, U. Pferschy and D. Pisinger, Knapsack problems. Springer (2004).
H. Kerivin and R. Sirdey, Polyhedral combinatorics of a resource-constrained ordering problem part II: on the process move program polytope. Technical Report PE/BSC/INF/017913 V01/EN, service d'architecture BSC, Nortel GSM Access R&D, France (submitted to Math. Program. (2006).
J. E. Mitchell and B. Borchers, Solving linear ordering problems with a combined interior point/simplex cutting plane algorithm, in High performance optimization, 349–366. Kluwer, 2000.
M. Queyranne and A.S. Schulz, Polyhedral approaches to machine scheduling. Technical Report 408/1994, Berlin University of Technology (1994).
G. Reinelt, The linear ordering problem: algorithms and applications, volume 8 of Research and exposition in mathematics. Heldermann Verlag, Berlin (1985).
J.C. Saia, Data migration with edge capacities and machine speeds. Technical report, Washington University (2001).
R. Sirdey, J. Carlier, H. Kerivin and D. Nace, On a resource-constrained scheduling problem with application to distributed systems reconfiguration. Eur. J. Oper. Res. (to appear, DOI : 10.1016/j.ejor.2006.10.011) (2005).
R. Sirdey, J. Carlier and D. Nace, Approximate resolution of a resource-constrained scheduling problem. J. Heuristics (in press) (2006).
R. Sirdey, J. Carlier and D. Nace, A fast heuristic for a resource-constrained scheduling problem. Technical Report PE/BSC/INF/017254 V01/EN, service d'architecture BSC, Nortel GSM Access R&D, France (2005).
R. Sirdey and H. Kerivin, Polyhedral combinatorics of a resource-constrained ordering problem part I: on the partial linear ordering polytope. Technical Report PE/BSC/INF/017912 V01/EN, service d'architecture BSC, Nortel GSM Access R&D, France (submitted to Math. Program.) (2006).
R. Sirdey, D. Plainfossé and J.-P. Gauthier, A practical approach to combinatorial optimization problems encountered in the design of a high availability distributed system. in Proceedings of the International Network Optimization Conference (2003) 532–539.