Abstract
This paper addresses the non-preemptive scheduling problem of scheduling jobs on identical parallel machines to minimize the maximum completion time or makespan. The problem has been proved to be NP-hard in the strong sense. The NP-hardness of the problem motivates us to develop a new methodology to obtain near-optimal solutions. We formulate the problem as an integer programming and then propose a new iterated local search (ILS) algorithm based on a variable number of cyclic exchanges to solve it. The properties of the solutions are derived and the results are used to improve the computational efficiency of our algorithm. Computational experiments show that the cyclic exchange neighborhood embedded in an iterated local search framework is effective for solving the scheduling problems with up to 1000 jobs and 40 machines within a reasonable amount of computation time.
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R.K. Ahuja J.B. Orlin D. Sharma (2000) ArticleTitleVery large-scale neighborhood search International Transactions in Operational Research 7 301–317 Occurrence Handle10.1111/j.1475-3995.2000.tb00201.x
Besten, M., Stutzle, T., Dorigo, M. (2001). Design of iterated local search algorithms – An example application to the single machine total weighted tardiness problem. Applications of Evolutionary Computing, Proceedings Lecture Notes in Computer Science, 2037, 441–451.
Congram, R. K. (2000). Polynomially searchable exponential neighbourhood for sequencing problems in combinatorial optimization. Ph.D. Thesis, Faculty of Mathematical Studies, University of Southampton, U.K.
A. Frangioni E. Necciari M.G. Scutellá (2004) ArticleTitleA multi-exchange neighborhood for minimum makespan machine scheduling problem Journal of Combinatorial Optimization 8 IssueID2 195–220 Occurrence Handle10.1023/B:JOCO.0000031420.05971.29
C.A. Glass C.N. Potts P. Shade (1994) ArticleTitleUnrelated parallel machine scheduling using local search Mathematical and Computer Modeling 2 41–52 Occurrence Handle10.1016/0895-7177(94)90205-4
Lourenço, H.R., Martin, O., & Stützle, T. (2001). A beginner’s introduction to iterated local search. MIC’2001–4th Metaheuristics International Conference, Porto, Portugal, July 16–20.
P. Merz (2003) ArticleTitleAn iterated local search approach for minimum sum-of-squares clustering Advances in Intelligent Data Analysis Lecture Notes in Computer Science 2810 286–296
E. Mokotoff (2004) ArticleTitleAn exact algorithm for the identical parallel machine scheduling problem European Journal of Operational Research 152 758–769 Occurrence Handle10.1016/S0377-2217(02)00726-9
L. Paquete T. Stützle (2002) ArticleTitleAn experimental investigation of Iterated Local Search for coloring graphs Applications of Evolutionary Computing, Proceedings Lecture Notes in Computer Science 2279 122–131
Pinedo, M. (1995) Scheduling: theory, algorithm, and systems, Appendices, Prentice hall, Englewood cliffs, New Jersey.
P.M. Thompson J.B. Orlin (1989) The theory of cyclic transfers Working paper, Operations Research Center, MIT Cambridge, Mass
P.M. Thompson H.N. Psaraftis (1993) ArticleTitleCyclic transfer algorithms for multivehicle routing and scheduling problems Operations Research 5 935–946 Occurrence Handle10.1287/opre.41.5.935
S. L. Velde ParticleVan de (1993) ArticleTitleDuality-based algorithms for scheduling unrelated parallel machines ORSA Journal on Computing 5 192–205
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Received: April 2005 / Accepted: January 2006
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Tang, L., Luo, J. A new ILS algorithm for parallel machine scheduling problems. J Intell Manuf 17, 609–619 (2006). https://doi.org/10.1007/s10845-006-0032-2
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DOI: https://doi.org/10.1007/s10845-006-0032-2