Summary
We address the Identical Parallel Machine Scheduling Problem, one of the most important basic problems in scheduling theory, and some generalizations of it arising from real world situations. We survey the current state of the art for the most performing meta-heuristic algorithms for this class of problems, with special emphasis on recent results obtained through Scatter Search. We present insights in the development of this heuristic technique, and discuss the combinatorial difficulties of the problems through the analysis of extensive computational results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
A.C.F. Alvim and C.C. Ribeiro. A hybrid bin-packing heuristic to multiprocessor scheduling. In C.C. Ribeiro and S.L. Martins, editors, Lecture Notes in Computer Science, volume 3059, pages 1–13. Springer-Verlag, Berlin, 2004.
L. Babel, H. Kellerer, and V. Kotov. The k-partitioning problem. Mathematical Methods of Operations Research, 47:59–82, 1998.
P. Brucker. Scheduling Algorithms. Springer-Verlag, New York, 2001.
S. Cahon, N. Melab, and E.-G. Talbi. Paradiseo: A framework for the reusable design of parallel and distributed meta-heuristics. Journal of Heuristics, 10(3):357–380, 2004.
B. Chen. Parallel scheduling for early completion. In J.Y.T. Leung, editor, Handbook of Scheduling: Algorithms, Models, and Performance Analysis, chapter 9, pages 175–184. CRC Press, Boca Raton, FL, 2004.
E.G. Coffman, M.R. Garey, and D.S. Johnson. An application of bin-packing to multiprocessor scheduling. SIAM Journal on Computing, 7:1–17, 1978.
E.G. Coffman, G.S. Lueker, and A.H.G. Rinnooy Kan. Asymptotic methods in the probabilistic analysis of sequencing and packing heuristics. Management Science, 34:266–290, 1988.
M. Dell’Amico, M. Iori, and S. Martello. Heuristic algorithms and scatter search for the cardinality constrained P||C max problem. Journal of Heuristics, 10: 169–204, 2004.
M. Dell’Amico, M. Iori, S. Martello, and M. Monaci. Lower bounds and heuristic algorithms for the k i -partitioning problem. European Journal of Operational Research, 171:725–742, 2006.
M. Dell’Amico, M. Iori, S. Martello, and M. Monaci. Heuristic and exact algorithms for the identical parallel machine scheduling problem. INFORMS Journal on Computing, 2007 (to appear).
M. Dell’Amico and S. Martello. Optimal scheduling of tasks on identical parallel processors. ORSA Journal on Computing, 7:191–200, 1995.
M. Dell’Amico and S. Martello. Bounds for the cardinality constrained P||C max problem. Journal of Scheduling, 4:123–138, 2001.
M. Dell’Amico and S. Martello. A note on exact algorithms for the identical parallel machine scheduling problem. European Journal of Operational Research, 160:576–578, 2005.
R. Martí (ed.). Feature Cluster on Scatter Search Methods for Optimization. EuropeanJournalofOperationalResearch, 169, 2, 2006.
G. Felinskas. An investigation of heuristic methods and application to optimization of resource constrained project schedules. PhD thesis, Vytautas Magnus University, Vilnius, Lithuania, 2007.
P.M. França, M. Gendreau, G. Laporte, and F.M. Müller. A composite heuristic for the identical parallel machine scheduling problem with minimum makespan objective. Computers & Operations Research, 21:205–210, 1994.
A. Frangioni, E. Necciari, and M. G. Scutellà. A multi-exchange neighborhood for minimum makespan machine scheduling problems. Journal of Combinatorial Optimization, 8:195–220, 2004.
F. Glover. Heuristic for integer programming using surrogate constraints. Decision Sciences, 8:156–166, 1977.
F. Glover. A template for scatter search and path relinking. In J. K. Hao, E. Lutton, E. Ronald, M. Schoenauer, and D. Snyers, editors, Lecture Notes in Computer Science, volume 1363, pages 1–45. Springer-Verlag, 1998.
F. Glover, M. Laguna, and R. Martí. Scatter search and path relinking: Foundations and advanced designs. In G. C. Onwubolu and B. V. Babu, editors, New Optimization Techniques in Engineering. Springer-Verlag, Heidelberg, 2004.
R.L. Graham. Bounds for certain multiprocessing anomalies. Bell System Technical Journal, 45:1563–1581, 1966.
R.L. Graham. Bounds on multiprocessing timing anomalies. SIAM Journal on Applied Mathematics, 17:416–429, 1969.
R.L. Graham, E.L. Lawler, J.K. Lenstra, and A.H.G. Rinnooy Kan. Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics, 5:287–326, 1979.
M. Haouari, A. Gharbi, and M. Jemmali. Tight bounds for the identical parallel machine scheduling problem. International Transactions in Operational Research, 13:529–548, 2006.
M. S. Hillier and M. L. Brandeau. Optimal component assignment and board grouping in printed circuit board manufacturing. Operations Research, 46(5):675–689, 1998.
D. S. Hochbaum and D. B. Shmoys. Using dual approximation algorithms for scheduling problems: practical and theoretical results. Journal of ACM, 34: 144–162, 1987.
J.Y.T. Leung (ed.). Handbook of Scheduling: Algorithms, Models, and Performance Analysis. CRC Press, Boca Raton, FL, 2004.
R. Martí, M. Laguna, and F. Glover. Principles of scatter search. European Journal of Operational Research, 169:359–372, 2006.
E. Mokotoff. Parallel machine scheduling problems: a survey. Asia-Pacific Journal of Operational Research, 18:193–242, 2001.
E. Mokotoff. An exact algorithm for the identical parallel machine scheduling problem. European Journal of Operational Research, 152:758–769, 2004.
E. Mokotoff, J. J. Jimeno, and I. Gutiérrez. List scheduling algorithms to minimize the makespan on identical parallel machines. TOP, 9:243–269, 2001.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Iori, M., Martello, S. (2008). Scatter Search Algorithms for Identical Parallel Machine Scheduling Problems. In: Xhafa, F., Abraham, A. (eds) Metaheuristics for Scheduling in Industrial and Manufacturing Applications. Studies in Computational Intelligence, vol 128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78985-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-540-78985-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78984-0
Online ISBN: 978-3-540-78985-7
eBook Packages: EngineeringEngineering (R0)