Skip to main content
SpringerLink
Log in

Multi-objective Simulated Annealing for Permutation Flow Shop Problems

  • Chapter
Computational Intelligence in Flow Shop and Job Shop Scheduling

Part of the book series: Studies in Computational Intelligence ((SCI,volume 230))

Summary

In this chapter we present a Multi-Objective Simulated Annealing algorithm to deal with the Permutation Flow Shop Scheduling Problem in a real context. We have designed the models taking into account results obtained from a study conducted in the Spanish Ceramic Tile Sector. The proposed methods consist in obtaining a good approximation of the efficient frontier. Starting with a set of initial sequences, the algorithm samples a point in its neighbourhood. If this generated sequence is dominated, we still accept it with a certain probability. Different heuristics and constructive algorithms are used to compute initial good sequences and lower bounds for the different criteria. Makespan and flow time are considered. The procedure is good enough to give efficient solutions with little computational effort. A computational experiment has been carried out to check the performance of the proposed algorithms. Different metrics for comparing algorithms have been computed, and have been analyzed together with the CPU time. We have studied how the number of initial solutions, the neighbouring procedure, and other parameters, affect the results. For all the tested instances a net set of potentially efficient schedules has been obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agrawal, S., Dashora, Y., Tiwari, M.K., et al.: Interactive Particle Swarm: A Pareto-Adaptive Metaheuristic to Multiobjective Optimization. IEEE T. Syst. Man Cy. A. 38(2), 258–277 (2008)

    Article  Google Scholar 

  2. Aickelin, U.: Genetic Algorithms for Multiple-Choice Problems. PhD Thesis. University of Wales, Swansea (1999)

    Google Scholar 

  3. Akers, S.B.: A graphical approach to production scheduling problems. Oper. Res. 4, 244–245 (1956)

    Article  Google Scholar 

  4. Andrés, C.: Programación de la Producción en Talleres de Flujo Híbridos con Tiempos de Cambio de Partida Dependientes de la Secuencia: Modelos, Métodos y Algoritmos de Resolución: Aplicación a Empresas del Sector Cerámico. PhD Thesis. Universidad Politécnica de Valencia, Valencia (2001)

    Google Scholar 

  5. Arroyo, J., Armentano, V.: Genetic local search for multi-objective flowshop scheduling problems. Eur. J. Oper. Res. 167, 717–738 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bagchi, T.P.: Multiobjective Scheduling by Genetic Algorithms. Kluwer Academic Publishers, Dordrecht (1999)

    Google Scholar 

  7. Baker, K.R.: A comparative study of flow shop algorithms. Oper. Res. 23, 62–73 (1975)

    Article  MATH  Google Scholar 

  8. Blazewicz, J., Ecker, K., Pesch, E., et al.: Handbook on Scheduling. Springer, Berlin (2007)

    MATH  Google Scholar 

  9. Brucker, P.: An efficient algorithm for the job-shop problem with two jobs. Computing 40, 353–359 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  10. Brucker, P.: Scheduling Algorithms. Springer, Berlin (2004)

    Google Scholar 

  11. Bülbül, K., Kaminsky, P., Yano, C.: Flow shop scheduling with earliness, tardiness, and intermediate inventory holding costs. University of California, Berkeley (2003)

    Google Scholar 

  12. Burke, E.K., Landa-Silva, J.D., Soubeiga, E.: Hyperheuristic Approaches for Multiobjective Optimization. In: Proceedings of the 5th Metaheuristics International Conference, Kyoto (2003)

    Google Scholar 

  13. Campbell, H.G., Dudek, R.A., Smith, M.L.: A Heuristic Algorithm for the n-Job, m-Machine Sequencing Problem. Manag. Sci. 16(10), 630–637 (1970)

    Article  Google Scholar 

  14. Carlier, J., Rebaï, I.: Two branch and bound algorithms for the permutation flow shop problem. Eur. J. Oper. Res. 90, 238–251 (1996)

    Article  MATH  Google Scholar 

  15. Chang, P.C., Chen, S.H., Liu, C.H.: Sub-population genetic algorithm with mining gene structures for multiobjective flowshop scheduling problems. Expert. Syst. Appl. 33, 762–777 (2007)

    Article  Google Scholar 

  16. Chang, P.C., Hsieh, J.-C., Lin, S.G.: The development of gradual priority weighting approach for the multi-objective flowshop scheduling problem. Int. J. Prod. Econ. 79, 171–183 (2002)

    Article  Google Scholar 

  17. Chankong, V., Haimes, Y.Y.: Multiobjective Decision Making Theory and Methodology. Elsevier Science, New York (1983)

    MATH  Google Scholar 

  18. Charnes, A., Cooper, W.: Management Models and Industrial Applications of Linear Programming. John Wiley and Sons, Chichester (1961)

    MATH  Google Scholar 

  19. Coello, C., Mariano, C.: Algorithms and Multiple Objective. In: Ehrgott, M., Gandibleux, X. (eds.) Multiple Criteria Optimization. State of the Art Annotated Bibliographic Surveys. Kluwer Academic Publishers, Boston (2002)

    Google Scholar 

  20. Czyzak, P., Jaszkiewicz, A.: Pareto Simulated Annealing – a metaheuristic technique for multiple objective combinatorial optimization. J. Multicriteria. Dec. Anal. 7, 34–47 (1998)

    Article  MATH  Google Scholar 

  21. Daniels, R.L., Chambers, R.J.: Multiobjective flow-shop scheduling. Nav. Res. Log. 37, 981–995 (1990)

    Article  MATH  Google Scholar 

  22. Dorn, J., Girsch, M., Skele, G., et al.: Comparison of iterative improvement techniques for schedule optimization. Eur. J. Oper. Res. 94, 349–361 (1996)

    Article  MATH  Google Scholar 

  23. Dudek, R.A., Panwalkar, S.S., Smith, M.L.: The lessons of flowshop scheduling research. Oper. Res. 40, 7–13 (1992)

    Article  MATH  Google Scholar 

  24. Eck, B.T., Pinedo, M.: On the minimization of the makespan subject to flowtime optimality. Oper. Res. 41, 797–801 (1993)

    Article  MATH  Google Scholar 

  25. Ehrgott, M.: Approximation algorithms for combinatorial multicriteria optimization problems. Int. T. Oper. Res. 7, 5–31 (2000)

    Article  MathSciNet  Google Scholar 

  26. Ehrgott, M., Gandibleux, X.: Bounds and bound sets for biobjective Combinatorial Optimization problems. Lect. Notes Econ. Math., vol. 507, pp. 242–253 (2001)

    Google Scholar 

  27. Ehrgott, M., Gandibleux, X.: Multiobjective Combinatorial Optimization: Theory, Methodology, and Applications. In: Ehrgott, M., Gandibleux, X. (eds.) Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys. Kluwer Academic Publishers, Boston (2002)

    Google Scholar 

  28. Ehrgott, M., Wiecek, M.: Multiobjective Programming. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multiple Criteria Decision Analysis. Springer, New York (2005)

    Google Scholar 

  29. Emelichev, V.A., Perepelista, V.A.: On cardinality of the set of alternatives in discrete many-criterion problems. Discrete. Math. Appl. 2(5), 461–471 (1992)

    Article  MathSciNet  Google Scholar 

  30. Framinan, J.M., Leisten, R., Ruiz-Usano, R.: Efficient heuristics for flowshop sequencing with the objectives of makespan and flowtime minimisation. Eur. J. Oper. Res. 141, 559–569 (2002)

    Article  MATH  Google Scholar 

  31. French, S.: Sequencing and Scheduling: An Introduction to the Mathematics of the Job Shop. Ellis Horwood, Chichester (1982)

    MATH  Google Scholar 

  32. Gandibleux, X., Mezdaoui, N., Fréville, A.: A tabu search procedure to solve multiobjective combinatorial optimization problems. Lect. Notes Econ. Math., vol. 455, pp. 291–300 (1997)

    Google Scholar 

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

    MATH  Google Scholar 

  34. Geiger, M.: On operators and search space topology in multi-objective flow shop scheduling. Eur. J. Oper. Res. 181, 195–206 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  35. González, T., Johnson, D.B.: A new algorithm for preemptive scheduling of trees. J. Assoc. Comp. Mach. 27, 287–312 (1980)

    MATH  Google Scholar 

  36. Gordon, V., Proth, J.M., Chu, C.: A survey of the state of the art of common due date assignment and scheduling research. Eur. J. Oper. Res. 139, 1–25 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  37. Grabowski, J., Wodecki, M.: Some local search algorithms for no-wait flow-shop problem with makespan criterion. Comp. Oper. Res. 32, 2197–2212 (2004)

    Article  MathSciNet  Google Scholar 

  38. Graham, R.L., Lawler, E.L., Lenstra, J.K., et al.: Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann. Discrete Math. 5, 287–326 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  39. Gupta, J.N.D.: Heuristic Algorithms for Multistage Flowshop Scheduling Problem. AIIE T. 4(1), 11–18 (1972)

    Google Scholar 

  40. Gupta, J.N.D., Neppalli, V.R., Werner, F.: Minimizing total flow time in a two-machine flowshop problem with minimum makespan. Int. J. Prod. Econ. 69(3), 323–338 (2001)

    Article  Google Scholar 

  41. Hapke, M., Jaszkiewicz, A., Slowinski, R.: Interactive Analysis of multiple-criteria project scheduling problems. Eur. J. Oper. Res. 107(2), 315–324 (1998)

    Article  MATH  Google Scholar 

  42. Haupt, R.: A survey of priority rule-based scheduling. Oper. Res. Spektrum 11, 3–16 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  43. Ho, J.C., Chang, Y.-L.: A new heuristic for the n-job, m-machine flowshop problem. Eur. J. Oper. Res. 52, 194–202 (1991)

    Article  MATH  Google Scholar 

  44. Hoogeveen, H.: Multicriteria Scheduling. Eur. J. Oper. Res. 167, 592–623 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  45. Hoogeveen, J.A.: Single-Machine Bicriteria Scheduling. PhD Thesis. The Netherlands Technology, Amsterdam (1992)

    Google Scholar 

  46. Horsky, D., Rao, M.R.: Estimation of attribute weights from preference comparison. Manag. Sci. 30(7), 801–822 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  47. Huang, G., Lim, A.: Fragmental Optimization on the 2-Machine Bicriteria Flowshop Scheduling Problem. In: Proceedings of 15th IEEE International Conference on Tools with Artificial Intelligence (2003)

    Google Scholar 

  48. Ignall, E., Schrage, L.E.: Application of the branch-and-bound technique to some flow-shop scheduling problems. Oper. Res. 13, 400–412 (1965)

    Article  MathSciNet  Google Scholar 

  49. Isermann, H.: The enumeration of the set of all efficient solutions for a linear multiple objective program. Oper. Res. Quart. 28(3), 711–725 (1977)

    Article  MATH  Google Scholar 

  50. Ishibuchi, H., Misaki, S., Tanaka, H.: Modified simulated annealing algorithms for the flow shop sequencing problem. Eur. J. Oper. Res. 81, 388–398 (1995)

    Article  MATH  Google Scholar 

  51. Ishibuchi, H., Murata, T.: A multi-objective genetic local search algorithm and its application to flowshop scheduling. IEEE T. Syst. Man Cy. C. 28(3), 392–403 (1998)

    Article  Google Scholar 

  52. Jaszkiewicz, A.: A Comparative Study of Multiple-Objective Metaheuristics on the Bi-Objective Set Covering Problem and the Pareto Memetic Algorithm. Ann. Oper. Res. 131(1-4), 135–158 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  53. Jaszkiewicz, A., Ferhat, A.B.: Solving multiple criteria choice problems by interactive trichotomy segmentation. Eur. J. Oper. Res. 113(2), 271–280 (1999)

    Article  MATH  Google Scholar 

  54. Johnson, S.M.: Optimal two- and three-stage production schedules with setup times included. Nav. Res. Log. 1, 61–68 (1954)

    Article  Google Scholar 

  55. Jones, D.F., Mirrazavi, S.K., Tamiz, M.: Multi-objective meta-heuristics: An overview of the current state of the art. Eur. J. Oper. Res. 137, 1–9 (2002)

    Article  MATH  Google Scholar 

  56. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  57. Knowles, J., Corne, D.: On Metrics Comparing Nondominated Sets. In: Proceedings of the 2002 Congress on Evolutionary Computation Conference, pp. 711–716. IEEE Press, Los Alamitos (2002)

    Google Scholar 

  58. Koulamas, C.: A new constructive heuristic for the flowshop scheduling problem. Eur. J. Oper. Res. 105, 66–71 (1998)

    Article  MATH  Google Scholar 

  59. van Laarhoven, P.J.M., Aarts, E.H.L.: Simulated Annealing: Theory and Practice. Kluwer Academic Publishers, Dordrecht (1987)

    Google Scholar 

  60. Lageweg, B.J., Ixnstra, J.K., Rinnooy Kan, A.H.G.: A general bounding to minimize makespan/total flowtime of jobs. Eur. J. Oper. Res. 155, 426–438 (1978)

    Google Scholar 

  61. Laha, D., Chakraborty, U.K.: An efficient heuristic approach to flowtime minimization in permutation flowshop scheduling. Int. J. Adv. Manuf. Technol. (2007) (DOI: 10.1007/s00170-007-1156-z)

    Google Scholar 

  62. Laha, D., Chakraborty, U.K.: An efficient stochastic hybrid heuristic for flowshop scheduling. Engineering Applications of Artificial Intelligence 20, 851–856 (2007)

    Article  Google Scholar 

  63. Laha, D., Chakraborty, U.K.: A constructive heuristic for minimizing makespan in no-wait flowshop scheduling. Int. J. Adv. Manuf. Technol. (2008) (DOI: 10.1007/s00170-008-1454-0)

    Google Scholar 

  64. Landa-Silva, J.D., Burke, E.K., Petrovic, S.: An Introduction to Multiobjective Metaheuristics for Scheduling and Timetabling. Lect. Notes Econ. Math., vol. 535, pp. 91–129 (2004)

    Google Scholar 

  65. Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Sequencing and scheduling: Algorithms and complexity. In: Handbooks in Operations Research and Management Science, Logistics of Production and Inventory, vol. 4, pp. 445–524. North-Holland, Amsterdam (1993)

    Chapter  Google Scholar 

  66. Leung, J.Y.-T., Young, G.H.: Minimizing schedule length subject to minimum flow time. Siam. J.Comp. 18, 314–326 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  67. Liao, C.J., Yu, W.C., Joe, C.B.: Bicriterion scheduling in the two-machine flowshop. J. Oper. Res. Soc. 48, 929–935 (1997)

    Article  MATH  Google Scholar 

  68. Liu, J., Reeves, C.R.: Constructive and composite heuristic solutions to the P//∑C i scheduling problem. Eur. J. Oper. Res. 132, 439–452 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  69. Lomnicki, A.: Branch-and-bound algorithm for the exact solution of the three-machine scheduling problem. Oper. Res. Quart. 16, 89–100 (1965)

    Article  Google Scholar 

  70. Loukil, T., Teghem, J., Tuyttens, D.: Solving multi-objective production scheduling problems using metaheuristics. Eur. J. Oper. Res. 161, 42–61 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  71. McMahon, G.B.: Optimal Production Schedules for Flow Shop. Can. Oper. Res. Soc. J. 7, 141–151 (1969)

    MathSciNet  Google Scholar 

  72. Monma, C.L., Rinnooy Kan, A.H.G.: A concise survey of efficiently solvable special cases of the permutation flow-shop problem. RAIRO-Rech. Oper. 17, 105–119 (1983)

    MATH  MathSciNet  Google Scholar 

  73. Murata, T., Ishibuchi, H., Tanaka, H.: Multi-Objective Genetic Algorithm and its Applications to Flowshop Scheduling. Comp. Ind. Eng. 30(4), 957–968 (1996)

    Article  Google Scholar 

  74. Nagar, H.J., Heragu, S.S.: Multiple and bicriteria scheduling: A literature survey. Eur. J. Oper. Res. 81, 88–104 (1995)

    Article  MATH  Google Scholar 

  75. Nawaz, M., Enscore Jr., E.E., Ham, I.: A heuristic algorithm for the m-machine, n-job flowshop sequencing problem. OMEGA-Int. J. Manage. S. 11, 91–95 (1983)

    Article  Google Scholar 

  76. Neppalli, V.R., Chen, C.L., Gupta, J.N.D.: Genetic algorithms for the two-stage bicriteria flowshop problem. Eur. J. Oper. Res. 95, 356–373 (1996)

    Article  MATH  Google Scholar 

  77. Nowicki, E., Zdrzałka, S.: A survey of results for sequencing problems with controllable processing times. Discrete Appl. Math. 26, 271–287 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  78. Ogbu, F.A., Smith, D.K.: The Application of the Simulated Annealing Algorithm to the Solution of the n/m/Cmax Flowshop Problem. Comp. Oper. Res. 17(3), 243–253 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  79. Onwubolu, G., Davendra, D.: Scheduling flow shops using differential evolution algorithm. Eur. J. Oper. Res. 171, 674–692 (2006)

    Article  MATH  Google Scholar 

  80. Osman, I.H., Potts, C.N.: Simulated Annealing for Permutation Flowshop Scheduling. OMEGA-Int. J. Manage. S. 17(6), 551–557 (1989)

    Article  Google Scholar 

  81. Panwalkar, S.S., Iskander, W.: A survey of scheduling rules. Oper. Res. 25, 45–61 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  82. Parker, R.G.: Deterministic Scheduling Theory. Chapman & Hall, New York (1995)

    MATH  Google Scholar 

  83. Parthasarathy, S., Rajendran, C.: An experimental evaluation of heuristics for scheduling in a real-life flowshop with sequence-dependent setup times of jobs. Int. J. Prod. Econ. 49, 255–263 (1997)

    Article  Google Scholar 

  84. Pasupathy, T., Rajendran, C., Suresh, R.K.: A multi-objective genetic algorithm for scheduling in flow shops to minimize the makespan and total flow time of jobs. Int. J. Adv. Manuf. Technol. 27, 804–815 (2006)

    Article  Google Scholar 

  85. Pinedo, M.L.: Scheduling: Theory, Algorithms, and Systems. Prentice Hall, New Jersey (2002)

    MATH  Google Scholar 

  86. Potts, C.N.: An adaptive branching rule for the permutation flow-shop problem. Eur. J. Oper. Res. 5, 19–25 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  87. Potts, C.N., Shmoys, D.B., Williamson, D.P.: Permutation vs. non-permutation flow shop schedules. Oper. Res. Lett. 10, 281–284 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  88. Rajendran, C.: Two-stage flowshop scheduling problem with bicriteria. J. Oper. Res. Soc. 43(9), 879–884 (1992)

    Article  Google Scholar 

  89. Rajendran, C.: Heuristic algorithm for scheduling in a flowshop to minimize total flowtime. Int. J. Prod. Econ. 29, 65–73 (1993)

    Article  Google Scholar 

  90. Rajendran, C.: Heuristics for scheduling in flowshop with multiple objectives. Eur. J. Oper. Res. 82, 540–555 (1995)

    Article  MATH  Google Scholar 

  91. Rajendran, C., Ziegler, H.: An efficient heuristic for scheduling in a flowshop to minimize total weighted flowtime of jobs. Eur. J. Oper. Res. 103, 129–138 (1997)

    Article  MATH  Google Scholar 

  92. Rajendran, C., Ziegler, H.: Ant-colony algorithms for permutation: flowshop scheduling. Eur. J. Oper. Res. 155, 426–438 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  93. Reeves, C.R.: Improving the Efficiency of Tabu Search for Machine Scheduling Problems. J. Oper. Res. Soc. 44(4), 375–382 (1993)

    Article  MATH  Google Scholar 

  94. Reeves, C.R.: A Genetic Algorithm for Flowshop Sequencing. Comp. Oper. Res. 22, 5–13 (1995)

    Article  MATH  Google Scholar 

  95. Rinnooy Kan, A.H.G.: Machine Scheduling problems: Classification, Complexity and Computations, Martinus Nijhoff, The Hague (1976)

    Google Scholar 

  96. Ruiz, R: Técnicas Metaheurísticas para la Programación Flexible de la Producción. PhD Thesis. Universidad Politécnica de Valencia, Valencia (2003)

    Google Scholar 

  97. Ruiz, R., Maroto, C.: A comprehensive review and evaluation of permutation flowshop heuristics. Eur. J. Oper. Res. 165, 479–494 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  98. Ruiz-Díaz, F.S.: A survey of multi-objective combinatorial scheduling. In: French, S., Hartley, R., Thomas, L.C., et al. (eds.) Multi-Objective Decision Making. Academic Press, New York (1983)

    Google Scholar 

  99. Saaty, T.L.: The Analytic Hierarchy Process. McGrawHill, New York (1980)

    MATH  Google Scholar 

  100. Sayin, S., Karabati, S.: A bicriteria approach to the two-machine flow shop scheduling problem. Eur. J. Oper. Res. 113, 435–449 (1999)

    Article  MATH  Google Scholar 

  101. Schulz, A.: Scheduling and Polytopes. PhD Thesis. Technical University of Berlin, Berlin (1996)

    Google Scholar 

  102. Selen, W.J., Hott, D.D.: A mixed-integer goal-programming formulation of the standard flow-shop scheduling problem. J. Oper. Res. Soc. 12(37), 1121–1128 (1986)

    Article  Google Scholar 

  103. Serafini, P.: Simulated annealing for multiple objective optimization problems. In: Proceedings of the Tenth International Conference on Multiple Criteria Decision Making, Taipei (1992)

    Google Scholar 

  104. Shmoys, D.B., Tardos, É.: An approximation algorithm for the generalized assignment problem. Math. Program. 62, 461–474 (1993)

    Article  MathSciNet  Google Scholar 

  105. Sin, C.C.S.: Some topics of parallel-machine scheduling theory. Thesis. University of Manitoba (1989)

    Google Scholar 

  106. Sivrikaya-Serifoglu, F.S., Ulusoy, G.: A bicriteria two machine permutation flowshop problem. Eur. J. Oper. Res. 107, 414–430 (1998)

    Article  MATH  Google Scholar 

  107. Srinivas, N., Deb, K.: Multiobjective function optimization using nondominated sorting genetic algorithms. Evol. Comp. 2(3), 221–248 (1995)

    Article  Google Scholar 

  108. T’kindt, V., Billaut, J.-C.: Multicriteria scheduling problems: a survey. RAIRO-Oper. Res. 35, 143–163 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  109. T’kindt, V., Billaut, J.-C.: Multicriteria scheduling: Theory, Models and Algorithms, 2nd edn. Springer, Berlin (2006)

    MATH  Google Scholar 

  110. T’kindt, V., Gupta, J.N.D., Billaut, J.-C.: Two machine flowshop scheduling problem with a secondary criterion. Comp. Oper. Res. 30(4), 505–526 (2003)

    Article  MATH  Google Scholar 

  111. T’kindt, V., Monmarche, N., Tercinet, F., et al.: An ant colony optimization algorithm to solve a 2-machine bicriteria flowshop scheduling problem. Eur. J. Oper. Res. 142(2), 250–257 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  112. Taillard, E.: Some efficient heuristic methods for the flor shop sequencing problem. Eur. J. Oper. Res. 47, 67–74 (1990)

    Article  MathSciNet  Google Scholar 

  113. Taillard, E.: Benchmark for basic scheduling problems. Eur. J. Oper. Res. 64, 278–285 (1993)

    Article  MATH  Google Scholar 

  114. Ulungu, E.L.: Optimisation Combinatoire MultiCritère: Détermination de l’ensemble des solutions efficaces et méthodes interactives. PhD Thesis. Université de Mons-Hainaut, Mons (1993)

    Google Scholar 

  115. Ulungu, E.L., Teghem, J.: Multiobjective Combinatorial Optimization problems: A survey. J. Multicriteria Dec. Anal. 3, 83–104 (1994)

    Article  MATH  Google Scholar 

  116. Varadharajan, T.K., Rajendran, C.: A multi-objective simulated-annealing algorithm for scheduling in flowshops to minimize the makespan and total flowtime of jobs. Eur. J. Oper. Res. 167, 772–795 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  117. Wierzbicki, A.P.: A methodological guide to the multiobjective optimization. Lect. Notes Contr. Inf., vol. 1(23), pp. 99–123 (1980)

    Google Scholar 

  118. Wilson, J.M.: Alternative formulation of a flow shop scheduling problem. J. Oper. Res. Soc. 40(4), 395–399 (1989)

    Article  MATH  Google Scholar 

  119. Wodecki, M., Bozejko, W.: Solving the Flow Shop Problem by Parallel Simulated Annealing. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2001. LNCS, vol. 2328, pp. 236–244. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  120. Yagmahan, B., Yenisey, M.M.: Ant. colony optimization for multi-objective flow shop scheduling problem. Comp. Ind. Eng. 54, 411–420 (2008)

    Article  Google Scholar 

  121. Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. PhD Thesis. Swiss Federal Institute of Technology, Zurich (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, Universidad de Alcalá, Plaza Victoria 3, 28802, Alcalá de Henares, Spain

    E. Mokotoff

Authors
  1. E. Mokotoff
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Mathematics & Computer Science Department, University of Missouri, 63121, Saint Louis, MO, USA

    Uday K. Chakraborty

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Mokotoff, E. (2009). Multi-objective Simulated Annealing for Permutation Flow Shop Problems. In: Chakraborty, U.K. (eds) Computational Intelligence in Flow Shop and Job Shop Scheduling. Studies in Computational Intelligence, vol 230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02836-6_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02836-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02835-9

  • Online ISBN: 978-3-642-02836-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation