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A Performance Analysis of Tabu Search for Discrete-Continuous Scheduling Problems

  • Joanna Józefowska
  • Grzegorz Waligóra
  • Jan Węglarz
Part of the Applied Optimization book series (APOP, volume 86)

Abstract

Problems of scheduling jobs on parallel, identical machines under an additional continuous resource are considered. Jobs are non-preemptable and independent, and all are available at the start of the process. The total amount of the continuous resource available at a time is limited, and the resource is a renewable one. Each job simultaneously requires for its processing a machine and an amount (unknown in advance) of the continuous resource. The processing rate of a job depends on the amount of the resource allotted to this job at a time. Three scheduling criteria are considered: the makespan, the mean flow time, and the maximum lateness. The problem is to find a sequence of jobs on machines and, simultaneously, a continuous resource allocation that minimize the given criterion. A tabu search metaheuristic is presented to solve the problem. A computational analysis of the tabu search algorithm for the considered discrete-continuous scheduling problems is presented and discussed. Three different tabu list management methods are tested: the tabu navigation method, the cancellation sequence method, and the reverse elimination method.

Keywords

Discrete-continuous scheduling problems Makespan Mean flow time Maximum lateness Tabu search Tabu navigation method Cancellation sequence method Reverse elimination method. 

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Bibliography

  1. E.H.L. Aarts and P.J.M. van Laarhoven. Simulated Annealing: Theory and Applications. Reidel, Dordrecht, 1987.zbMATHGoogle Scholar
  2. W.N. Burkow. Raspriedielenije riesursow kak zadacza optimalnogo bystrodiejstwia. Avtomat. I Tielemieh., 27 (7), 1966.Google Scholar
  3. F. Glover. Tabu search–Part 1. ORSA J. Computing, 1: 190–206, 1989.MathSciNetzbMATHCrossRefGoogle Scholar
  4. F. Glover. Future path for integer programming and links to artificial intelligence. Computers & Operations Research, 5: 533–549, 1986.MathSciNetCrossRefGoogle Scholar
  5. F. Glover. Tabu search–Part 2. ORSA J. Computing, 2: 4–32, 1990.zbMATHCrossRefGoogle Scholar
  6. F. Glover and M. Laguna. Tabu Search. Kluwer Academic Publishers, Norwell, 1997.zbMATHCrossRefGoogle Scholar
  7. J. J6zefowska, M. Mika, R. R6zycki, G. Walig6ra, and J. Wgglarz. Discrete-continuous scheduling to minimize maximum lateness. In Proc. of the Fourth International Symposium on Methods and Models in Automation and Robotics MMAR’97, Migdzyzdroje 26–29.08.1997, pages 947–952, 1997a.Google Scholar
  8. J. J6zefowska, M. Mika, R. R6zycki, G. Walig6ra, and J. Wgglarz. Discrete continuous scheduling to minimize the mean flow time–computational experiments. Computational Methods in Science and Technology, 3: 25–37, 1997b.Google Scholar
  9. J. Józefowska, M. Mika, R. Rózycki, G. Walig6ra, and J. Wgglarz. Discrete-continuous scheduling with identical processing rates of jobs. Foundations of Computing and Decision Sciences, 22 (4): 279–295, 1997c.zbMATHGoogle Scholar
  10. J. Józefowska, M. Mika, R. Rózycki, G. Waligóra, and J. Wgglarz. Local search metaheuristics for some discrete-continuous scheduling problems. European Journal of Operational Research, 107 (2): 354–370, 1998a.zbMATHCrossRefGoogle Scholar
  11. J. Józefowska, M. Mika, R. Rózycki, G. Waligóra, and J. Wgglarz. Discrete-continuous scheduling to minimize the makespan with power processing rates of jobs. Discrete Applied Mathematics, 94: 263–285, 1999.MathSciNetzbMATHCrossRefGoogle Scholar
  12. J. Józefowska, G. Waligóra, and J. Wgglarz. Tabu search algorithm for some discrete-continuous scheduling problems. In Modern Heuristic Search Methods, pages 169–182. V.J. Rayward-Smith (ed.), Wiley, Chichester, 1996.Google Scholar
  13. J. Józefowska, G. Waligóra, and J. Wgglarz. Tabu search with the cancellation sequence method for a class of discrete-continuous scheduling problems. In Proc. of the Fifth International Symposium on Methods and Models in Automation and Robotics MMAR’98, Migdzyzdroje 25–29.08.1998, pages 1047–1052, 1998b.Google Scholar
  14. J. Józefowska, G. Waligóra, and J. Wgglarz. Tabu list management methods for a discrete-continuous scheduling problem. European Journal of Operational Research, 137 (2): 288–302, 2002.MathSciNetzbMATHCrossRefGoogle Scholar
  15. J. Józefowska and J. Wgglarz. Discrete-continuous scheduling problems–mean completion time results. European Journal of Operational Research, 94 (2): 302–309, 1996.zbMATHCrossRefGoogle Scholar
  16. J. Józefowska and J. Wgglarz. On a methodology for discrete-continuous scheduling. European Journal of Operational Research, 107 (2): 338–353, 1998.zbMATHCrossRefGoogle Scholar
  17. C. Lawrence, J.L. Zhou, and A.L. Tits. Users guide for CFSQP Version 2.3 (Released August 1995), 1995.Google Scholar
  18. J. Skorin-Kapov. Tabu search applied to the quadratic assignment problem. ORSA J. Computing, 2: 33–45, 1990.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Joanna Józefowska
    • 1
  • Grzegorz Waligóra
    • 1
  • Jan Węglarz
    • 1
    • 2
  1. 1.Institute of Computing SciencePoznań University of TechnologyPoznańPoland
  2. 2.Poznań Supercomputing and Networking CenterPoznańPoland

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