Approximate Algorithms

  • Jose M. FraminanEmail author
  • Rainer Leisten
  • Rubén Ruiz García


In this chapter we deal with approximate algorithms. In principle, one may think that approximate algorithms are not a good option if exact approaches exist and indeed we already discussed that their widespread use is basically justified by the computational complexity inherent for most manufacturing scheduling models. As mentioned in Sect.  7.5.2, approximate algorithms are usually divided into heuristics and metaheuristics, being the main difference among them that the first are specifically tailored for a particular model, while the second constitute more generic procedures. This difference—although not entirely unambiguous– is very important when it comes to describing both approaches, as we intend to do in this chapter: While it is clear that it is possible to discuss the templates of the different metaheuristics that can be employed for manufacturing scheduling models, such thing is not possible regarding heuristics, as they are heavily problem-dependent.


Schedule Problem Flow Shop Flow Shop Problem Metaheuristic Method Bottleneck Machine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Adams, J., Balas, E., and Zawack, D. (1988). The shifting bottleneck procedure for job shop scheduling. Management Science, 34(3):391–401.Google Scholar
  2. Biegel, J. E. and Davern, J. J. (1990). Genetic Algorithms and Job Shop Scheduling. Computers and Industrial Engineering, 19(1):81–91.Google Scholar
  3. Birattari, M. (2005). The Problem of Tuning Metaheuristics as seen from a machine learning perspective. Intelligence-Infix, Berlin.Google Scholar
  4. Campbell, H. G., Dudek, R. A., and Smith, M. L. (1970). A Heuristic Algorithm for the \(n\) Job, \(m\) Machine Sequencing Problem. Management Science, 16(10):B-630–B-637.Google Scholar
  5. Chen, C.-L., Vempati, V. S., and Aljaber, N. (1995). An application of genetic algorithms for flow shop problems. European Journal of Operational Research, 80(2):389–396.Google Scholar
  6. Clerc, M. (2006). Particle Swarm Optimization. Wiley-ISTE, New York.Google Scholar
  7. Dannenbring, D. G. (1977). An evaluation of flowshop sequencing heuristics. Management Science, 23:1174–1182.Google Scholar
  8. Dasgupta, D., editor (1998). Artificial Immune Systems and Their Applications. Springer, New York.Google Scholar
  9. Davis, L. (1985). Job Shop Scheduling with Genetic Algorithms. In Grefenstette, J. J., editor, Proceedings of the First International Conference on Genetic Algorithms and their Applications, pages 136–140, Hillsdale. Lawrence Erlbaum Associates.Google Scholar
  10. Davis, L., editor (1996). Handbook of Genetic Algorithms. International Thomson Computer Press, London.Google Scholar
  11. de Castro, L. N. and Timmis, J. (2002). Artificial Immune Systems: A New Computational Intelligence Approach. Springer, London.Google Scholar
  12. Doerner, K. F., Gendreau, M., Greistorfer, P., Gurjahr, W. J., Hartl, R. F., and Reinmann, M., editors (2007). Metaheuristics: progress in complex systems optimization. Operations Research/Computer Science Interfaces. Springer, New York.Google Scholar
  13. Dorigo, M. and Stützle, T. (2004). Ant Colony Optimization. Bradford Books, USA.Google Scholar
  14. Eberhart, R. C. and Shi, Y. (2007). Computational Intelligence: Concepts to Implementations. Morgan Kaufmann, San Francisco.Google Scholar
  15. Engelbrecht, A. P. (2006). Fundamentals of Computational Swarm Intelligence. John Wiley & Sons, New York.Google Scholar
  16. Engelbrecht, A. P. (2007). Computational Intelligence: An Introduction. John Wiley & Sons, New York, second edition.Google Scholar
  17. Feo, T. A. and Resende, M. G. C. (1989). A probabilistic heuristic for a computationally difficult set covering problem. Operations Research Letters, 8(2):67–71.Google Scholar
  18. Feo, T. A. and Resende, M. G. C. (1995). Greedy randomized adaptive search procedures. Journal of Global Optimization, 6:109–133.Google Scholar
  19. Feoktistov, V. (2006). Differential Evolution. In Search of Solutions. Springer, New York.Google Scholar
  20. Framinan, J. M., Leisten, R., and Rajendran, C. (2003). Different initial sequences for the heuristic of Nawaz, Enscore and Ham to minimize makespan, idletime or flowtime in the static permutation flowshop sequencing problem. International Journal of Production Research, 41(1):121–148.Google Scholar
  21. Geem, Z. W., Kim, J. H., and Loganathan, G. V. (2001). A new heuristic optimization algorithm: Harmony search. Simulation, 76(2):60–68.Google Scholar
  22. Glover, F. and Kochenberger, G. A., editors (2003). Handbook of Metaheuristics. Kluwer Academic Publishers, Dordrecht.Google Scholar
  23. Glover, F. and Laguna, M. (1997). Tabu Search. Kluwer Academic Publishers, Dordrecht.Google Scholar
  24. Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading.Google Scholar
  25. Grabowski, J. and Wodecki, M. (2004). A very fast tabu search algorithm for the permutation flow shop problem with makespan criterion. Computers & Operations Research, 31(11):1891–1909.Google Scholar
  26. Hansen, P. and Mladenovic, N. (2001). Variable neighborhood search: Principles and applications. European Journal of Operational Research, 130(3):449–467.Google Scholar
  27. Holland, J. H. (1975). Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor.Google Scholar
  28. Hoos, Holger, H. and Stützle, T. (2005). Stochastic Local Search: Foundations and Applications. Morgan Kaufmann, San Francisco.Google Scholar
  29. Ibaraki, T., Nonobe, K., and Yagiura, M., editors (2005). Metaheuristics: progress as real problem solvers. Operations Research/Computer Science Interfaces. Springer, New York.Google Scholar
  30. Kennedy, J., Eberhart, R. C., and Shi, Y. (2001). Swarm Intelligence. Academic Press, San Diego.Google Scholar
  31. Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598):671–680.Google Scholar
  32. Konar, A. (2005). Computational Intelligence: Principles, Techniques and Applications. Springer, New York.Google Scholar
  33. Laguna, M. and Martí, R. (2003). Scatter search: methodology and implementations in C. Operations Research/Computer Science Interfaces. Kluwer Academic Publishers, New York.Google Scholar
  34. Larrañaga, P. and Lozano, J. A., editors (2002). Estimation of distribution algorithms: A new tool for evolutionary computation. Kluwer Academic Publishers, Dordrecht.Google Scholar
  35. Lozano, J. A., Larrañaga, P., Inza, I. n., and Bengoetxea, E., editors (2006). Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms. Springer, New York.Google Scholar
  36. Mattfeld, D. C. (1996). Evolutionary Search and the Job Shop; Investigations on Genetic Algorithms for Production Scheduling. Production and Logistics. Springer/Physica Verlag, Berlin.Google Scholar
  37. Michalewicz, Z. (1996). Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, Berlin, tercera edition.Google Scholar
  38. Mladenovic, N. and Hansen, P. (1997). Variable neighborhood search. Computers & Operations Research, 24(11):1097–1100.Google Scholar
  39. Morton, T. E. and Pentico, D. W. (1993). Heuristic Scheduling Systems With Applications to Production Systems and Project Management. Wiley Series in Engineering & Technology Management. John Wiley & Sons, Hoboken.Google Scholar
  40. Nawaz, M., Enscore, Jr, E. E., and Ham, I. (1983). A Heuristic Algorithm for the \(m\)-Machine, \(n\)-Job Flow-shop Sequencing Problem. OMEGA, The International Journal of Management Science, 11(1):91–95.Google Scholar
  41. Nowicki, E. and Smutnicki, C. (1996). A fast tabu search algorithm for the permutation flow-shop problem. European Journal of Operational Research, 91(1):160–175.Google Scholar
  42. Nowicki, E. and Smutnicki, C. (1998). The flow shop with parallel machines: A tabu search approach. European Journal of Operational Research, 106(2–3):226–253.Google Scholar
  43. Ogbu, F. A. and Smith, D. K. (1990). The Application of the Simulated Annealing Algorithm to the Solution of the \(n/m/{C}_{\max }\) Flowshop Problem. Computers and Operations Research, 17(3):243–253.Google Scholar
  44. Osman, I. H. and Potts, C. N. (1989). Simulated Annealing for Permutation Flow-shop Scheduling. OMEGA, The International Journal of Management Science, 17(6):551–557.Google Scholar
  45. Park, Y. B., Pegden, C., and Enscore, E. (1984). A survey and evaluation of static flowshop scheduling heuristics. International Journal of Production Research, 22(1):127–141.Google Scholar
  46. Pinedo, M. L. (2012). Scheduling: Theory, Algorithms, and Systems. Springer, New York, fourth edition.Google Scholar
  47. Price, K., Storn, R. M., and Lampinen, J. A. (2005). Differential Evolution: A Practical Approach to Global Optimization. Springer, New York.Google Scholar
  48. Rajendran, C. and Ziegler, H. (2004). Ant-colony algorithms for permutation flowshopn scheduling to minimize makespan/total flowtime of jobs. European Journal of Operational Research, 155(2):426–438.Google Scholar
  49. Reeves, C. and Yamada, T. (1998). Genetic algorithms, path relinking, and the flowshop sequencing problem. Evolutionary Computation, 6(1):45–60.Google Scholar
  50. Reeves, C. R. (1995). A genetic algorithm for flowshop sequencing. Computers & Operations Research, 22(1):5–13.Google Scholar
  51. Resende, M. G. C., Pinho de Sousa, J., and Viana, A., editors (2004). Metaheuristics: computer decision-making. Kluwer Academic Publishers, Dordrecht.Google Scholar
  52. Ribas, I., Companys, R., and Tort-Martorell, X. (2010). Comparing three-step heuristics for the permutation flow shop problem. Computers & Operations Research, 37(12):2062–2070.Google Scholar
  53. Ruiz, R. and Maroto, C. (2005). A comprehensive review and evaluation of permutation flowshop heuristics. European Journal of Operational Research, 165(2):479–494.Google Scholar
  54. Ruiz, R., Maroto, C., and Alcaraz, J. (2006). Two new robust genetic algorithms for the flowshop scheduling problem. OMEGA, The International Journal of Management Science, 34(5):461–476.Google Scholar
  55. Ruiz, R. and Stützle, T. (2007). A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. European Journal of Operational Research, 177(3):2033–2049.Google Scholar
  56. Syswerda, G. (1996). Scheduling Optimization Using Genetic Algorithms. In Davis, L., editor, Handbook of Genetic Algorithms, pages 332–349, London. International Thomson Computer Press.Google Scholar
  57. Taillard, E. (1990). Some efficient heuristic methods for the flow shop sequencing problem. European Journal of Operational Research, 47(1):67–74.Google Scholar
  58. Turner, S. and Booth, D. (1987). Comparison of Heuristics for Flow Shop Sequencing. OMEGA, The International Journal of Management Science, 15(1):75–78.Google Scholar
  59. Černý, V. (1985). A thermodynamical approach to the travelling salesman problem: an efficient simulation algorithm. Journal of Optimization Theory and Applications, 45(1):41–51.Google Scholar
  60. Wang, L. and Zheng, D. Z. (2003). An effective hybrid heuristic for flow shop scheduling. The International Journal of Advanced Manufacturing Technology, 21(1):38–44.Google Scholar
  61. Widmer, M. and Hertz, A. (1989). A new heuristic method for the flow shop sequencing problem. European Journal of Operational Research, 41(2):186–193.Google Scholar
  62. Woo, H.-S. and Yim, D.-S. (1998). A heuristic algorithm for mean flowtime objective in flowshop scheduling. Computers & Operations Research, 25(3):175–182.Google Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Jose M. Framinan
    • 1
    Email author
  • Rainer Leisten
    • 2
  • Rubén Ruiz García
    • 3
  1. 1.Departamento Organización Industrial y Gestión de EmpresasUniversidad de Sevilla Escuela Superior de IngenierosIsla de la CartujaSpain
  2. 2.Fakultät für Ingenieurwissenschaften Allgemeine Betriebswirtschaftslehre und Operations ManagementUniversität Duisburg-EssenDuisburgGermany
  3. 3.Grupo de Sistemas de Optimización Aplicada, Instituto Tecnológico de InformáticaUniversitat Politècnica de ValènciaValenciaSpain

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