About this Journal Submit a Manuscript Table of Contents
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 836597, 27 pages
http://dx.doi.org/10.1155/2012/836597
Research Article

Improved Quantum-Inspired Evolutionary Algorithm for Engineering Design Optimization

1Department of Computer Science, National Pingtung University of Education, 4-18 Min-Sheng Road, Pingtung 900, Taiwan
2Institute of System Information and Control, National Kaohsiung First University of Science and Technology, 1 University Road, Yenchao, Kaohsiung 824, Taiwan
3Department of Electrical Engineering, National Kaohsiung University of Applied Sciences, 415 Chien-Kung Road, Kaohsiung 807, Taiwan
4Department of Healthcare Administration and Medical Informatics, Kaohsiung Medical University, 100 Shi-Chuan 1st Road, Kaohsiung 807, Taiwan

Received 31 August 2012; Revised 26 October 2012; Accepted 31 October 2012

Academic Editor: Jung-Fa Tsai

Copyright © 2012 Jinn-Tsong Tsai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. Hajela and C. J. Shih, “Optimal design of laminated composites using a modified mixed integer and discrete programming algorithm,” Computers and Structures, vol. 32, no. 1, pp. 213–221, 1989. View at Scopus
  2. E. Sandgren, “Nonlinear integer and discrete programming in mechnical design optimization,” ASME Journal of Mechanical Design, vol. 112, no. 2, pp. 223–229, 1990. View at Scopus
  3. J. S. Arora, M. W. Huang, and C. C. Hsieh, “Methods for optimization of nonlinear problems with discrete variables: a review,” Structural Optimization, vol. 8, no. 2-3, pp. 69–85, 1994. View at Publisher · View at Google Scholar · View at Scopus
  4. M. Bremicker, P. Y. Papalambros, and H. T. Loh, “Solution of mixed-discrete structural optimization problems with a new sequential linearization algorithm,” Computers and Structures, vol. 37, no. 4, pp. 451–461, 1990. View at Scopus
  5. H. T. Loh and P. Y. Papalambros, “Sequential linearization approach for solving mixed-discrete nonlinear design optimization problems,” ASME Journal of Mechanical Design, vol. 113, no. 3, pp. 325–334, 1991. View at Scopus
  6. D. K. Shin, Z. Gurdal, and O. H. Grin, “A penalty approach for nonlinear optimization with discrete design variables,” Engineering Optimization, vol. 16, pp. 29–42, 1990.
  7. J. F. Fu, R. G. Fenton, and W. L. Cleghorn, “A mixed integer-discrete continuous programming method and its application to engineering design optimization,” Engineering Optimization, vol. 17, pp. 263–280, 1991.
  8. J. Cai and G. Thieraut, “Discrete optimization of structures using an improved penalty function method,” Engineering Optimization, vol. 17, pp. 293–306, 1993.
  9. O. Jonsson and T. Larsson, “Lagrangean relaxation and sub-gradient optimization applied to optimal design with discrete sizing,” Engineering Optimization, vol. 16, pp. 221–233, 1990.
  10. S. S. Lin, C. Zhang, and H. P. Wang, “On mixed-discrete nonlinear optimization problems: a comparative study,” Engineering Optimization, vol. 23, pp. 287–300, 1995.
  11. S. J. Wu and P. T. Chow, “Applications of genetic algorithms to discrete optimization problems,” Journal of the Chinese Society of Mechanical Engineers, vol. 16, no. 6, pp. 587–598, 1995. View at Scopus
  12. S. S. Rao and Y. Xiong, “A hybrid genetic algorithm for mixed-discrete design optimization,” Journal of Mechanical Design, vol. 127, no. 6, pp. 1100–1112, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. W. Tang and Q. Yuan, “Improved genetic algorithm for shape optimization of truss structures,” Chinese Journal of Theoretical and Applied Mechanics, vol. 38, no. 6, pp. 843–849, 2006. View at Scopus
  14. R. L. Haupt, “Antenna design with a mixed integer genetic algorithm,” IEEE Transactions on Antennas and Propagation, vol. 55, no. 3, pp. 577–582, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. K. Deep, K. P. Singh, M. L. Kansal, and C. Mohan, “A real coded genetic algorithm for solving integer and mixed integer optimization problems,” Applied Mathematics and Computation, vol. 212, no. 2, pp. 505–518, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. K. M. Lee, J. T. Tsai, T. K. Liu, and J. H. Chou, “Improved genetic algorithm for mixed-discrete-continuous design optimization problems,” Engineering Optimization, vol. 42, no. 10, pp. 927–941, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. W. H. Ho and C. S. Chang, “Genetic-algorithm-based artificial neural network modeling for platelet transfusion requirements on acute myeloblastic leukemia patients,” Expert Systems with Applications, vol. 38, no. 5, pp. 6319–6323, 2011. View at Publisher · View at Google Scholar · View at Scopus
  18. W. H. Ho, J. X. Chen, I. N. Lee, and H. C. Su, “An ANFIS-based model for predicting adequacy of vancomycin regimen using improved genetic algorithm,” Expert Systems with Applications, vol. 38, no. 10, pp. 13050–13056, 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. C. Zhang and H. P. Wang, “Mixed-discrete nonlinear optimization with simulated annealing,” Engineering Optimization, vol. 21, pp. 277–291, 1993.
  20. W.-H. Ho, J.-H. Chou, and C.-Y. Guo, “Parameter identification of chaotic systems using improved differential evolution algorithm,” Nonlinear Dynamics, vol. 61, no. 1-2, pp. 29–41, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. W.-H. Ho and A. L.-F. Chan, “Hybrid Taguchi-differential evolution algorithm for parameter estimation of differential equation models with application to HIV dynamics,” Mathematical Problems in Engineering, vol. 2011, Article ID 514756, 14 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. Y. J. Cao, L. Jiang, and Q. H. Wu, “An evolutionary programming approach to mixed-variable optimization problems,” Applied Mathematical Modelling, vol. 24, no. 12, pp. 931–942, 2000. View at Publisher · View at Google Scholar · View at Scopus
  23. P. W. Shor, “Algorithms for quantum computation: discrete logarithms and factoring,” in Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 124–134, Santa Fe, NM, USA, 1994.
  24. L. K. Grover, “Fast quantum mechanical algorithm for database search,” in Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, pp. 212–219, New York, NY, USA, May 1996. View at Scopus
  25. L. K. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Physical Review Letters, vol. 79, no. 2, pp. 325–328, 1997. View at Scopus
  26. K. H. Han, K. H. Park, C. H. Lee, and J. H. Kim, “Parallel quantum-inspired genetic algorithm for combinatorial optimization problem,” in Proceedings of IEEE Conference on Evolutionary Computation, pp. 1422–1429, Seoul, Korea, May 2001. View at Scopus
  27. K. H. Han and J. H. Kim, “Genetic quantum algorithm and its application to combinatorial optimization problem,” in Proceedings of the Congress on Evolutionary Computation, pp. 1354–1360, San Diego, Calif, USA, July 2000. View at Scopus
  28. K. H. Han and J. H. Kim, “Quantum-inspired evolutionary algorithm for a class of combinatorial optimization,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 6, pp. 580–593, 2002. View at Publisher · View at Google Scholar · View at Scopus
  29. K. H. Han and J. H. Kim, “Quantum-inspired evolutionary algorithms with a new termination criterion, Hε gate, and two-phase scheme,” IEEE Transactions on Evolutionary Computation, vol. 8, no. 2, pp. 156–169, 2004. View at Publisher · View at Google Scholar · View at Scopus
  30. A. Malossini, E. Blanzieri, and T. Calarco, “Quantum genetic optimization,” IEEE Transactions on Evolutionary Computation, vol. 12, no. 2, pp. 231–241, 2008. View at Publisher · View at Google Scholar · View at Scopus
  31. I. Grigorenko and M. E. Garcia, “Calculation of the partition function using quantum genetic algorithms,” Physica A, vol. 291, pp. 463–470, 2001.
  32. J. A. Yang, B. Li, and Z. Zhuang, “Multi-universe parallel quantum genetic algorithm and its application to blind source separation,” in Proceedings of the International Conference on Neural Networks and Signal Processing (ICNNSP '03), pp. 393–398, Nanjing, China, December 2003. View at Publisher · View at Google Scholar · View at Scopus
  33. G. Zhang, W. Jin, and L. Hu, “A novel parallel quantum genetic algorithm,” in Proceedings of the 4th International Conference on Parallel and Distributed Computing, Applications and Technologies, pp. 693–697, Chengdu, China, August 2003. View at Publisher · View at Google Scholar · View at Scopus
  34. C. Hui, Z. Jiashu, and Z. Chao, “Chaos updating rotated gates quantum-inspired genetic algorithm,” in Proceedings of the International Conference on Communications, Circuits and Systems, pp. 1108–1112, Chengdu, China, June 2004. View at Scopus
  35. L. Wang, F. Tang, and H. Wu, “Hybrid genetic algorithm based on quantum computing for numerical optimization and parameter estimation,” Applied Mathematics and Computation, vol. 171, no. 2, pp. 1141–1156, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  36. Q. Yang and S. Ding, “Methodology and case study of hybrid quantum-inspired evolutionary algorithm for numerical optimization,” in Proceedings of the 3rd International Conference on Natural Computation (ICNC '07), pp. 608–612, Haikou, China, August 2007. View at Publisher · View at Google Scholar · View at Scopus
  37. N. Li, P. Du, and H. Zhao, “Independent component analysis based on improved quantum genetic algorithm: application in hyperspectral images,” in Proceedings of IEEE International Geoscience and Remote Sensing Symposium (IGARSS '05), pp. 4323–4326, Seoul, Korea, July 2005. View at Publisher · View at Google Scholar · View at Scopus
  38. L. Abdesslem, M. Soham, and B. Mohamed, “Multiple sequence alignment by quantum genetic algorithm,” in Proceedings of the 20th International Parallel and Distributed Processing Symposium, pp. 8–15, Rhodes Island, Greece, 2006.
  39. Z. Dong, Y. Huang, and P. Han, “Thermal process identification with radial basis function network based on quantum genetic algorithm,” Proceedings of the Chinese Society of Electrical Engineering, vol. 28, no. 17, pp. 99–104, 2008. View at Scopus
  40. J. Gao and J. Wang, “A hybrid quantum-inspired immune algorithm for multiobjective optimization,” Applied Mathematics and Computation, vol. 217, no. 9, pp. 4754–4770, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  41. M. S. Phadke, Quality Engineering Using Robust Design, Prentice-Hall, Upper Saddle River, NJ, USA, 1989.
  42. D. C. Montgomery, Design and Analysis of Experiments, John Wiley & Sons, New York, NY, USA, 1991.
  43. S. H. Park, Robust Design and Analysis for Quality Engineering, Chapman and Hall, London, UK, 1996.
  44. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Boston, Mass, USA, 1989.
  45. M. Gen and R. Cheng, Genetic Algorithms and Engineering Design, John Wiley and Sons, New York, NY, USA, 1997.
  46. J. T. Tsai, T. K. Liu, and J. H. Chou, “Hybrid Taguchi-genetic algorithm for global numerical optimization,” IEEE Transactions on Evolutionary Computation, vol. 8, no. 4, pp. 365–377, 2004. View at Publisher · View at Google Scholar · View at Scopus
  47. J. T. Tsai, J. H. Chou, and T. K. Liu, “Tuning the structure and parameters of a neural network by using hybrid Taguchi-genetic algorithm,” IEEE Transactions on Neural Networks, vol. 17, no. 1, pp. 69–80, 2006. View at Publisher · View at Google Scholar · View at Scopus
  48. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes, vol. 187 of Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, Germany, 1981. View at Publisher · View at Google Scholar
  49. C. A. Floudas and P. M. Pardalos, Recent Advances in Global Optimization, Princeton University Press, Princeton, NJ, USA, 1992.
  50. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer, Berlin, Germany, 1994.
  51. J. J. Grefenstette, “Optimization of control parameters for genetic algorithms,” IEEE Transactions on Systems, Man and Cybernetics, vol. 16, no. 1, pp. 122–128, 1986. View at Scopus
  52. L. Davis, “Adapting operator probabilities in genetic algorithms,” in Proceedings of the International Conference on Genetic Algorithms (ICGA '89), pp. 61–69, San Mateo, Calif, USA, 1989.
  53. J. H. Chou, W. H. Liao, and J. J. Li, “Application of Taguchi-genetic method to design optimal grey-fuzzy controller of a constant turning force system,” in Proceedings of the 15th CSME Annual Conference, pp. 31–38, Taiwan, 1998.
  54. S. García, A. Fernández, J. Luengo, and F. Herrera, “A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability,” Soft Computing, vol. 13, no. 10, pp. 959–977, 2009. View at Publisher · View at Google Scholar · View at Scopus
  55. S. García, D. Molina, M. Lozano, and F. Herrera, “A study on the use of non-parametric tests for analyzing the evolutionary algorithms' behaviour: a case study on the CEC'2005 Special Session on Real Parameter Optimization,” Journal of Heuristics, vol. 15, no. 6, pp. 617–644, 2009. View at Publisher · View at Google Scholar · View at Scopus
  56. F. Wilcoxon, “Individual comparisons by ranking method,” Biometrics, vol. 1, pp. 80–83, 1945.
  57. A. Field, Discovering Statistics Using SPSS, SAGE Publications, London, UK, 2006.
  58. J. Kennedy, R. C. Eberhart, and Y. Shi, Swarm Intelligence, Morgan Kaufmann, San Francisco, Calif, USA, 2001.
  59. L. N. de Castro and J. Timmis, Artificial Immune Systems: A New Computational Intelligence Approach, Springer, London, UK, 2002.
  60. C. J. Shih and T. K. Lai, “Mixed-discrete fuzzy programming for nonlinear engineering optimization,” Engineering Optimization, vol. 23, pp. 187–199, 1995.
  61. K. M. Ragsdell and D. T. Phillips, “Optimal design of a class of welded structure using geometric programming,” ASME Journal of Engineering for Industry-Transactions, vol. 98, no. 3, pp. 1021–1025, 1976. View at Scopus
  62. ANSYS, APDL Programmer’s Guide: ANSYS Release 10.0, ANSYS, Canonsburg, Pa, USA, 2005.