Abstract
We propose new local search algorithms for minimum makespan parallel machine scheduling problems, which perform multiple exchanges of jobs among machines. Inspired by the work of Thompson and Orlin (1989) on cyclic transfer neighborhood structures, we model multiple exchanges of jobs as special disjoint cycles and paths in a suitably defined improvement graph, by extending definitions and properties introduced in the context of vehicle routing problems (Thompson and Psaraftis, 1993) and of the capacitated minimum spanning tree problem (Ahuja et al., 2001). Several algorithms for searching the neighborhood are suggested.
We report the results of a wide computational experimentation, on different families of benchmark instances, performed for the case of identical machines. This problem has been selected as a case study to perform a comparison among the alternative algorithms, and to discover families of instances for which the proposed neighborhood may be promising in practice. Based on the results of the experiments, we can suggest which among the many possible variants of the proposed approaches may be more promising for developing local search algorithms based on multi-exchange moves for related problems. Also, on some families of instances, which are very hard to solve exactly, the most promising multi-exchange algorithms were observed to dominate, in solution quality and in computational time, competitive benchmark heuristics.
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References
E.J. Anderson, C.A. Glass, and C.N. Potts, “Machine scheduling,” in Local Search in Combinatorial Optimization, Aarts and Lenstra (eds.), Wiley, 1997, pp. 361–414.
R.K. Ahuja, O. Ergun, J.B. Orlin, and A.P. Punnen, “A survey of very large-scale neighborhood search techniques,” Discrete Applied Mathematics, vol. 23, pp. 75–102, 2002.
R.K. Ahuja, T.L. Magnanti, and J.B. Orlin, Network Flows: Theory, Algorithms and Applications, Prentice Hall: New Jersey, 1993.
R.K. Ahuja, J.B. Orlin, and D. Sharma, “New neighborhood search structures for the capacitated minimum spanning tree problem,” Mathematical Programming, vol. 91, pp. 71–97, 2001.
B.V. Cherkassky and A.V. Goldberg “Negative cycle detection algorithms,” Mathematical Programming, vol. 85, pp. 277–311, 1999.
E.G. Coffman Jr., M.R. Garey, and D.S. Johnson, “An application of bin packing to multiprocessor scheduling,” SIAM Journal on Computing, vol. 7, pp. 1–17, 1978.
M. Dell'Amico and S. Martello, “Optimal scheduling of tasks on identical parallel processors,” ORSA Journal on Computing, vol. 7,no. 2, pp. 181–200, 1995.
S.M. Fatemi-Ghomi and F. Jolai-Ghazvini, “A pairwise interchange algorithm for parallel machine scheduling,” Production Planning and Control, vol. 9,no. 7, pp. 685–689, 1998.
G. Finn and E. Horowitz, “A linear time approximation algorithm for multiprocessor scheduling,” BIT, vol. 19, pp. 312–320, 1979.
P.M. França, M. Gendrau, G. Laporte and F.M. Muller, “A composite heuristic for the identical parallel machine scheduling problem with minimum makespan objective,” Computers Ops. Res., vol. 21,no. 2, pp. 205–210, 1994.
A. Frangioni, M.G. Scutellà, and E. Necciari, “A multi-exchange neighborhood for minimum makespan machine scheduling problems,” TR 00-17, Dip. di Informatica, Univ. di Pisa, 2000
M.R. Garey and D.S. Johnson, “Strong NP-completeness results: Motivation, examples and implications,” J. Ass. Comp. Mach., vol. 25, pp. 499–508, 1978.
M. Gendrau, F. Guertin, J. Potvin, and R. Seguin, “Neighborhood search heuristics for a dynamic vehicle dispatching problem with pick-ups and deliveries,” Publication CRT-98-10, Centre de Recherche sur les Transports, Université de Montreal, 1999.
C.A. Glass, C.N. Potts, and P. Shade, “Unrelated parallel machine scheduling using local search,” Mathematical and Computer Modelling, vol. 20, pp. 41–52, 1994.
F. Glover, “Ejection chains, reference structures and alternating path methods for traveling salesman problems,” Discrete Applied Mathematics, vol. 65, pp. 223–253, 1996.
R.L. Graham, “Bounds for certain multiprocessing anomalies,” Bell System Tech. J., vol. 45, pp. 1563–1581, 1966.
R.L. Graham, E.L. Lawler, J.K. Lenstra, and A.H.G. Rinnoy-Kan, “Optimization and approximation in deterministic sequencing and scheduling: A survey,” Annals of Dicrete Mathematics, vol. 5, pp. 287–326, 1979.
A.M.A. Hariri and C.N. Potts, “Heuristics for scheduling unrelated parallel machines,” Computers Ops. Res., vol. 18, pp. 323–331, 1991.
R. Hübscher and F. Glover, “Applying tabu search with influential diversification to multiprocessor scheduling,” Computers Ops. Res., vol. 21,no. 8, pp. 877–884, 1994.
M.A. Langston, “Improved 0/1 interchange scheduling,” BIT, vol. 22, pp. 282–290, 1982.
E.L. Lawler, J.K. Lenstra, A.H.G. Rinnoy-Kan, and D.B. Shmoys, “Sequencing and scheduling: Algorithms and complexity, in logistics of production and inventory,” Handbooks in Operations Research and Management Science, vol. 4, Graves, Rinnoy Kan and Zipkin (Eds.), Elsevier Science Publishers, 1993, pp. 445–522.
J.K. Lenstra, D.B. Shmoys and E. Tardos, “Approximation algorithms for scheduling unrelated parallel machines,” Mathematical Programming, vol. 46, pp. 259–271, 1990.
S. Martello, F. Soumis, and P. Toth, “An exact algorithm for makespan minimization on unrelated parallel machines,” Integer Programming and Combinatorial Optimization, (Proc. of the Second IPCO Conference), Carnegie-Mellon University, Pittsburgh, E. Balas, G. Cornuejols and R. Kannan (Eds.), 1992, pp. 181–200.
E. Necciari, “Algoritmi di ricerca locale basati su grafi di miglioramento per il problema di assegnamento di lavori a macchine,” Master Thesis, Dipartimento di Informatica, Università di Pisa, 1999.
C. Rego, “Relaxed tours and path ejections for the traveling salesman problem,” European Journal of Operational Research, vol. 106, pp. 522–538, 1998.
P.M. Thompson, “Local search algorithms for vehicle routing and other combinatorial problems,” Ph.D. Thesis, Operations Research Center, MIT, Cambridge, 1988.
P.M. Thompson and J.B. Orlin, “Theory of cyclic transfers,” Working paper, Operations Research Center, MIT, 1989.
P.M. Thompson and H.N. Psaraftis, “Cyclic transfer algorithms for multivehicle routing and scheduling problems,” Operations Research, vol. 41,no. 5, pp. 935–946, 1993.
S.L. Van De Velde, “Duality-based algorithms for schedling unrelated parallel machines,” Orsa Journal on Computing, vol. 5, pp. 192–205, 1993.
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Frangioni, A., Necciari, E. & Scutellà, M.G. A Multi-Exchange Neighborhood for Minimum Makespan Parallel Machine Scheduling Problems. Journal of Combinatorial Optimization 8, 195–220 (2004). https://doi.org/10.1023/B:JOCO.0000031420.05971.29
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DOI: https://doi.org/10.1023/B:JOCO.0000031420.05971.29