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A composite algorithm for multiprocessor scheduling

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Abstract

A composite algorithm is developed for the classical problem of scheduling independent jobs on identical parallel machines with the objective of minimizing the makespan. The algorithm at first obtains a family of initial partial solutions and combines these partial solutions until a feasible solution is generated. Then local search procedures are used for improving the solution. The effectiveness of this approach is evaluated through extensive computational comparisons with recent improvement heuristics for different classes of benchmark instances.

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References

  • Alvim, A.C.F., Ribeiro, C.C.: A hybrid bin-packing heuristic to multiprocessor scheduling. In: Ribeiro, C.C., Martins, S.L. (eds.) Lecture Notes in Computer Science, vol. 3059, pp. 1–13. Springer, Berlin (2004a)

    Google Scholar 

  • Alvim, A.C.F., Ribeiro, C.C.: A hybrid bin-packing heuristic to multiprocessor scheduling: Detailed computational results. http://www.uniriotec.br/~adriana/files/detPCmaxIN.pdf (2004b)

  • Alvim, A.C.F., Ribeiro, C.C., Glover, F., Aloise, D.J.: A hybrid improvement heuristic for the one-dimensional bin packing problem. J. Heuristics 10, 205–229 (2004)

    Article  Google Scholar 

  • Anderson, E.J., Glass, C.A., Potts, C.N.: Machine scheduling. In: Aarts, E., Lenstra, J.K. (eds.) Local Search in Combinatorial Optimization, pp. 361–414. Wiley, Chichester (1997)

    Google Scholar 

  • Blazewicz, J.: Selected topics in scheduling theory. Ann. Discrete Math. 31, 1–60 (1987)

    MathSciNet  Google Scholar 

  • Cheng, T.C.E., Sin, C.C.S.: A state-of-the-art review of parallel-machine scheduling research. Eur. J. Oper. Res. 47, 271–292 (1990)

    Article  MATH  Google Scholar 

  • Coffman, E.G. Jr., Garey, M.R., Johnson, D.S.: An application of bin-paking to multiprocessor scheduling. SIAM J. Comput. 7, 1–17 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  • Dell’Amico, M., Iori, M., Martello, S., Monaci, M.: Heuristic and exact algorithms for the identical parallel machine scheduling problem. INFORMS J. Comput. 20, 333–344 (2008)

    Article  MathSciNet  Google Scholar 

  • Dell’Amico, M., Martello, S.: Optimal scheduling of tasks on identical parallel processors. ORSA J. Comput. 7, 191–200 (1995)

    MATH  Google Scholar 

  • Fatemi Ghomi, S.M.T., Jolai Ghazvini, F.: A pairwise interchange algorithm for parallel machine scheduling. Prod. Plan. Control 9, 685–689 (1998)

    Article  Google Scholar 

  • Finn, G., Horowitz, E.: A linear time approximation algorithm for multiprocessor scheduling. BIT 19, 312–320 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  • França, P.M., Gendreau, M., Laporte, G., Müller, F.M.: A composite heuristic for the identical parallel machine scheduling problem with minimum makespan objective. Comput. Oper. Res. 21, 205–210 (1994)

    Article  MATH  Google Scholar 

  • Frangioni, A., Necciari, E., Scutellà, M.G.: A multi-exchange neighborhood for minimum makespan machine scheduling problems. TR 00-17, Dip. di Informatica, Univ. di Pisa (2000)

  • Frangioni, A., Necciari, E., Scutellà, M.G.: A multi-exchange neighborhood for minimum makespan parallel machine scheduling problems. J. Comb. Optim. 8, 195–220 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)

    MATH  Google Scholar 

  • Gent, I.P.: Heuristic solution of open bin packing problems. J. Heuristics 3, 299–304 (1998)

    Article  MATH  Google Scholar 

  • Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell Syst. Tech. J. 45, 1563–1581 (1966)

    Google Scholar 

  • Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17, 416–429 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  • Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann. Discrete Math. 5, 287–326 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  • Hoogeveen, A., Lenstra, J.K., Van de Velde, S.L.: Sequencing and Scheduling. In: Dell’Amico, M., Maffioli, F., Martello, S. (eds.) Annotated Bibliographies in Combinatorial Optimization, pp. 181–197. Wiley, Chichester (1997)

    Google Scholar 

  • Hübscher, R., Glover, F.: Applying tabu search with influential diversification to multiprocessor scheduling. Comput. Oper. Res. 21, 877–884 (1994)

    Article  MATH  Google Scholar 

  • Langston, M.A.: Improved 0/1 interchange scheduling. BIT 22, 282–290 (1982)

    Article  MATH  Google Scholar 

  • Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: Sequencing and scheduling: algorithms and complexity. In: Graves, S.C., Rinnooy Kan, A.H.G., Zipkin, P.H. (eds.) Logistics of Production and Inventory. Handbooks in Operations Research and Management Science, vol. 4, pp. 445–522. Elsevier, Amsterdam (1993)

    Chapter  Google Scholar 

  • Mokotoff, E.: Parallel machine scheduling problems: A survey. Asia-Pac. J. Oper. Res. 18, 193–242 (2001)

    MathSciNet  MATH  Google Scholar 

  • Mokotoff, E.: An exact algorithm for the identical parallel machine scheduling problem. Eur. J. Oper. Res. 152, 758–769 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Paletta, G., Pietramala, P.: A new approximation algorithm for the nonpreemptive scheduling of independent jobs on identical parallel processors. SIAM J. Discrete Math. 21, 313–328 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Thesen, A.: Design and evaluation of tabu search algorithms for multiprocessor scheduling. J. Heuristics 4, 141–160 (1998)

    Article  MATH  Google Scholar 

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Correspondence to Giuseppe Paletta.

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Paletta, G., Vocaturo, F. A composite algorithm for multiprocessor scheduling. J Heuristics 17, 281–301 (2011). https://doi.org/10.1007/s10732-010-9135-1

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