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A genetic algorithm approach for the single machine scheduling problem with linear earliness and quadratic tardiness penalties

  • Jorge M. S. Valente

    ()

    (LIAAD, Faculdade de Economia, Universidade do Porto, Portugal)

  • José Fernando Gonçalves

    ()

    (LIAAD, Faculdade de Economia, Universidade do Porto, Portugal)

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    In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We propose a genetic approach based on a random key alphabet. Several genetic algorithms based on this approach are presented. These versions differ on the generation of the initial population, as well as on the use of local search. The proposed procedures are compared with the best existing heuristic, as well as with optimal solutions for the smaller instance sizes. The computational results show that the performance of the proposed genetic approach is improved by the addition of a local search procedure, as well as by the insertion of simple heuristic solutions in the initial population. Indeed, the genetic versions that include either or both of these features not only provide significantly better results, but are also much faster. The genetic versions that use local search are clearly superior to the best existing heuristic, and the improvement in performance increases with both the size and difficulty of the instances. These procedures are also quite close to the optimum, and provided an optimal solution for most of the test instances.

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    File URL: http://www.fep.up.pt/investigacao/workingpapers/08.01.29_wp264.pdf
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    Paper provided by Universidade do Porto, Faculdade de Economia do Porto in its series FEP Working Papers with number 264.

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    Length: 28 pages
    Date of creation: Jan 2008
    Date of revision:
    Handle: RePEc:por:fepwps:264
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    1. Su, Ling-Huey & Chang, Pei-Chann, 1998. "A heuristic to minimize a quadratic function of job lateness on a single machine," International Journal of Production Economics, Elsevier, vol. 55(2), pages 169-175, July.
    2. Schaller, Jeffrey, 2002. "Minimizing the sum of squares lateness on a single machine," European Journal of Operational Research, Elsevier, vol. 143(1), pages 64-79, November.
    3. Jorge M. S. Valente, 2007. "Beam search heuristics for the single machine scheduling problem with linear earliness and quadratic tardiness costs," FEP Working Papers 250, Universidade do Porto, Faculdade de Economia do Porto.
    4. Goncalves, Jose Fernando & de Magalhaes Mendes, Jorge Jose & Resende, Mauricio G. C., 2005. "A hybrid genetic algorithm for the job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 167(1), pages 77-95, November.
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