Annals of Operations Research

, Volume 180, Issue 1, pp 197–211 | Cite as

Generating artificial chromosomes with probability control in genetic algorithm for machine scheduling problems

  • Pei-Chann Chang
  • Shih-Hsin Chen
  • Chin-Yuan Fan
  • V. Mani
Article

Abstract

In this paper, a novel genetic algorithm is developed by generating artificial chromosomes with probability control to solve the machine scheduling problems. Generating artificial chromosomes for Genetic Algorithm (ACGA) is closely related to Evolutionary Algorithms Based on Probabilistic Models (EAPM). The artificial chromosomes are generated by a probability model that extracts the gene information from current population. ACGA is considered as a hybrid algorithm because both the conventional genetic operators and a probability model are integrated. The ACGA proposed in this paper, further employs the “evaporation concept” applied in Ant Colony Optimization (ACO) to solve the permutation flowshop problem. The “evaporation concept” is used to reduce the effect of past experience and to explore new alternative solutions. In this paper, we propose three different methods for the probability of evaporation. This probability of evaporation is applied as soon as a job is assigned to a position in the permutation flowshop problem. Experimental results show that our ACGA with the evaporation concept gives better performance than some algorithms in the literature.

Keywords

Evolutionary algorithm with probabilistic models Single machine scheduling Total deviations Flowshop machine scheduling Artificial chromosomes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdul-Razaq, T., & Potts, C. (1988). Dynamic programming state-space relaxation for single-machine scheduling. The Journal of the Operational Research Society, 39(2), 141–152. Google Scholar
  2. Ackley, D. H. (1987). A connectionist machine for genetic hillclimbing. Dordrecht: Kluwer Academic. Google Scholar
  3. Akturk, M. S., & Ozdemir, D. (2001). A new dominance rule to minimize total weighted tardiness with unequal release dates. European Journal of Operational Research, 135(2), 394–412. CrossRefGoogle Scholar
  4. Alves, M. J., & Almeida, M. (2007). MOTGA: A multiobjective Tchebycheff based genetic algorithm for the multidimensional knapsack problem. Computers and Operations Research, 34(11), 3458–3470. CrossRefGoogle Scholar
  5. Baker, K. R. (1974). Introduction to sequencing and scheduling. New York: Wiley. Google Scholar
  6. Baluja, S. (1995). An empirical comparison of seven iterative and evolutionary function optimization heuristics. Google Scholar
  7. Baluja, S., & Davies, S. (1998). Fast probabilistic modeling for combinatorial optimization. In Proceedings of the fifteenth national/tenth conference on artificial intelligence/innovative applications of artificial intelligence table of contents (pp. 469–476). Google Scholar
  8. Baraglia, R., Hidalgo, J., Perego, R., NUCE I, & CNR P (2001). A hybrid heuristic for the traveling salesman problem. IEEE Transactions on Evolutionary Computation, 5(6), 613–622. CrossRefGoogle Scholar
  9. Belouadah, H., Posner, M., & Potts, C. (1992). Scheduling with release dates on a single machine to minimize total weighted completion time. Discrete Applied Mathematics, 36(3), 213–231. CrossRefGoogle Scholar
  10. Birbil, Ş., & Fang, S. C. (2003). An electromagnetism-like mechanism for global optimization. Journal of Global Optimization, 25(3), 263–282. CrossRefGoogle Scholar
  11. Chang, P. C. (1999). A branch and bound approach for single machine scheduling with earliness and tardiness penalties. Computers and Mathematics with Applications, 37(10), 133–144. CrossRefGoogle Scholar
  12. Chang, P. C., & Lee, H. C. (1992a). A greedy heuristic for bicriterion single machine scheduling problems. Computers and Industrial Engineering, 22(2), 121–131. CrossRefGoogle Scholar
  13. Chang, P. C., & Lee, H. C. (1992b). A two phase approach for single machine scheduling: minimizing the total absolute deviation. Journal of the Chinese Institute of Engineers, 15(6), 735–742. Google Scholar
  14. Chang, P. C., Chen, S. H., & Fan, C. Y. (2008a). A novel electromagnetism-like algorithm in single machine scheduling problem with distinct due dates. Expert Systems with Applications 39(3). Google Scholar
  15. Chang, P. C., Chen, S. H., & Fan, C. Y. (2008b). Mining gene structures to inject artificial chromosomes for genetic algorithm in single machine scheduling problems. Applied Soft Computing Journal, 8(1), 767–777. CrossRefGoogle Scholar
  16. Chang, P. C., Chen, S. H., & Mani, V. (2009). A hybrid genetic algorithm with dominance properties for single machine scheduling with dependent penalties. Applied Mathematical Modeling, 33(1), 579–596. CrossRefGoogle Scholar
  17. Corne, D., Dorigo, M., Glover, F., Dasgupta, D., Moscato, P., Poli, R., & Price, K. (1999). New ideas in optimization. New York: McGraw-Hill. Google Scholar
  18. Dimopoulos, C., & Zalzala, A. (2000). Recent developments in evolutionary computation for manufacturing optimization: problems, solutions, and comparisons. IEEE Transactions on Evolutionary Computation, 4(2), 93–113. CrossRefGoogle Scholar
  19. Framinan, J. M., Gupta, J. N. D., & Leisten, R. (2004). A review and classification of heuristics for permutation flow-shop scheduling with makespan objective. Journal of the Operational Research Society, 55(12), 1243–1255. CrossRefGoogle Scholar
  20. Glover, F., & Kochenberger, G. (1996). Critical event tabu search for multidimensional knapsack problems. In Meta-heuristics: theory & applications. Dordrecht: Kluwer Academic. Google Scholar
  21. Harik, G. (1999). Linkage learning via probabilistic modeling in the ECGA. Urbana, 51, 61, 801. Google Scholar
  22. Harik, G., Lobo, F., & Goldberg, D. (1999). The compact genetic algorithm. IEEE Transactions on Evolutionary Computation, 3(4), 287–297. CrossRefGoogle Scholar
  23. Hejazi, S., & Saghafian, S. (2005). Flowshop-scheduling problems with makespan criterion: a review. International Journal of Production Research, 43(14), 2895–2929. CrossRefGoogle Scholar
  24. Jouglet, A., Savourey, D., Carlier, J., & Baptiste, P. (2008). Dominance-based heuristics for one-machine total cost scheduling problems. European Journal of Operational Research, 184(3), 879–899. CrossRefGoogle Scholar
  25. Larrañaga, P., & Lozano, J. A. (2002). Estimation of distribution algorithms: a new tool for evolutionary computation. Dordrecht: Kluwer Academic. Google Scholar
  26. Lee, C. Y., Lei, L., & Pinedo, M. (1997). Current trends in deterministic scheduling. Annals of Operations Research, 70, 1–41. CrossRefGoogle Scholar
  27. Lenstra, J., Kan, A., & Brucker, P. (1975). Complexity of machine scheduling problems. Stud. integer Program, Proc. Workshop Bonn. Google Scholar
  28. Li, G. (1997). Single machine earliness and tardiness scheduling. European Journal of Operational Research, 96(3), 546–558. CrossRefGoogle Scholar
  29. Liaw, C. F. (1999). A branch-and-bound algorithm for the single machine earliness and tardiness scheduling problem. Computers and Operations Research, 26(7), 679–693. CrossRefGoogle Scholar
  30. Lin, S., & Kernighan, B. (1973). An effective heuristic algorithm for the traveling-salesman problem. Operations Research, 21(2), 498–516. CrossRefGoogle Scholar
  31. Lozano, J. A. (2006). Towards a new evolutionary computation: advances in the estimation of distribution algorithms. Berlin: Springer. Google Scholar
  32. Michalewicz, Z., Dasgupta, D., Le Riche, R., & Schoenauer, M. (1996). Evolutionary algorithms for constrained engineering problems. Computers & Industrial Engineering, 30(4), 851–870. CrossRefGoogle Scholar
  33. Montgomery, D. C. (2001). Design and analysis of experiments. Google Scholar
  34. Muhlenbein, H., & Paaß, G. (1996). From recombination of genes to the estimation of distributions I. Binary parameters. Lecture Notes in Computer Science (Vol. 1141, pp. 178–187). Berlin: Springer. Google Scholar
  35. Murata, T., Ishibuchi, H., & Tanaka, H. (1996). Genetic algorithms for flowshop scheduling problems. Computers & Industrial Engineering, 30(4), 1061–1071. CrossRefGoogle Scholar
  36. Ow, P. S., & Morton, T. E. (1989). The single machine early/tardy problem. Management Science, 35(2), 177–191. CrossRefGoogle Scholar
  37. Pelikan, M., Goldberg, D. E., & Cantu-Paz, E. (1999). BOA: The Bayesian optimization algorithm. In Proceedings of the genetic and evolutionary computation conference GECCO-99 (Vol. 1, pp. 525–532). Google Scholar
  38. Pelikan, M., Goldberg, D. E., & Lobo, F. G. (2002). A survey of optimization by building and using probabilistic models. Computational Optimization and Applications, 21(1), 5–20. CrossRefGoogle Scholar
  39. Rastegar, R., & Hariri, A. (2006). A step forward in studying the compact genetic algorithm. Evolutionary Computation, 14(3), 277–289. CrossRefGoogle Scholar
  40. Reeves, C. R. (1995). A genetic algorithm for flowshop sequencing. Computers and Operations Research, 22(1), 5–13. CrossRefGoogle Scholar
  41. Ruiz, R., & Maroto, C. (2005). A comprehensive review and evaluation of permutation flowshop heuristics. European Journal of Operational Research, 165(2), 479–494. CrossRefGoogle Scholar
  42. Schoonderwoerd, R., Holland, O. E., Bruten, J. L., & Rothkrantz, L. J. M. (1997). Ant-based load balancing in telecommunications networks. Adaptive Behavior, 5(2), 169. CrossRefGoogle Scholar
  43. Sim, K. M., & Sun, W. H. (2003). Ant colony optimization for routing and load-balancing: survey and new directions. IEEE Transactions on Systems, Man and Cybernetics, Part A, 33(5), 560–572. CrossRefGoogle Scholar
  44. Sourd, F., & Kedad-Sidhoum, S. (2003). The one-machine problem with earliness and tardiness penalties. Journal of Scheduling, 6(6), 533–549. CrossRefGoogle Scholar
  45. Sourd, F., & Kedad-Sidhoum, S. (2007). A faster branch-and-bound algorithm for the earliness-tardiness scheduling problem. Journal of Scheduling (pp. 1–10). Google Scholar
  46. Stutzle, T., Hoos, H. H. et al. (2000). MAX-MIN ant system. Future Generation Computer Systems, 16(8), 889–914. CrossRefGoogle Scholar
  47. Syswerda, G. (1993). Simulated crossover in genetic algorithms. Foundations of Genetic Algorithms, 2, 239–255. Google Scholar
  48. Valente, J. M. S., & Alves, R. A. F. S. (2005). Improved heuristics for the early/tardy scheduling problem with no idle time. Computers and Operations Research, 32(3), 557–569. CrossRefGoogle Scholar
  49. Valente, J. M. S., & Alves, R. A. F. S. (2007). Heuristics for the early/tardy scheduling problem with release dates. International Journal of Production Economics, 106(1), 261–274. CrossRefGoogle Scholar
  50. Wu, S. D., Storer, R. H., & Chang, P. C. (1993). One-machine rescheduling heuristics with efficiency and stability as criteria. Computers and Operations Research, 20(1), 1–14. CrossRefGoogle Scholar
  51. Zhang, Q., & Muhlenbein, H. (2004). On the convergence of a class of estimation of distribution algorithms. IEEE Transactions on Evolutionary Computation, 8(2), 127–136. CrossRefGoogle Scholar
  52. Zhang, Q., Sun, J., & Tsang, E. (2005). An evolutionary algorithm with guided mutation for the maximum clique problem. IEEE Transactions on Evolutionary Computation, 9(2), 192–200. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Pei-Chann Chang
    • 1
  • Shih-Hsin Chen
    • 2
  • Chin-Yuan Fan
    • 3
  • V. Mani
    • 4
  1. 1.Department of Information ManagementYuan-Ze UniversityChung-LiROC
  2. 2.Department of Electronic Commerce ManagementNanhua UniversityChiayiROC
  3. 3.Department of Industrial Engineering and ManagementYuan-Ze UniversityChung-LiROC
  4. 4.Department of Aerospace EngineeringIndian Institute of ScienceBangaloreIndia

Personalised recommendations