×

zbMATH — the first resource for mathematics

Improved quantum-inspired evolutionary algorithm for engineering design optimization. (English) Zbl 1264.90206
Summary: An improved quantum-inspired evolutionary algorithm is proposed for solving mixed discrete-continuous nonlinear problems in engineering design. The proposed Latin square quantum-inspired evolutionary algorithm (LSQEA) combines Latin squares and quantum-inspired genetic algorithm (QGA). The novel contribution of the proposed LSQEA is the use of a QGA to explore the optimal feasible region in macrospace and the use of a systematic reasoning mechanism of the Latin square to exploit the better solution in microspace. By combining the advantages of exploration and exploitation, the LSQEA provides higher computational efficiency and robustness compared to QGA and real-coded GA when solving global numerical optimization problems with continuous variables. Additionally, the proposed LSQEA approach effectively solves mixed discrete-continuous nonlinear design optimization problems in which the design variables are integers, discrete values, and continuous values. The computational experiments show that the proposed LSQEA approach obtains better results compared to existing methods reported in the literature.

MSC:
90C90 Applications of mathematical programming
90C59 Approximation methods and heuristics in mathematical programming
Software:
SPSS; ANSYS; Genocop; APDL
PDF BibTeX XML Cite
Full Text: DOI
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. · Zbl 0711.73167
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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. · Zbl 1168.65353
[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.
[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.
[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.
[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. · Zbl 1204.93034
[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. · Zbl 1208.34069
[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. · Zbl 1168.90636
[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. · Zbl 0922.68044
[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.
[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.
[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.
[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. · Zbl 05451968
[29] K. H. Han and J. H. Kim, “Quantum-inspired evolutionary algorithms with a new termination criterion, H\epsilon gate, and two-phase scheme,” IEEE Transactions on Evolutionary Computation, vol. 8, no. 2, pp. 156-169, 2004. · Zbl 05451870
[30] A. Malossini, E. Blanzieri, and T. Calarco, “Quantum genetic optimization,” IEEE Transactions on Evolutionary Computation, vol. 12, no. 2, pp. 231-241, 2008. · Zbl 05516165
[31] I. Grigorenko and M. E. Garcia, “Calculation of the partition function using quantum genetic algorithms,” Physica A, vol. 291, pp. 463-470, 2001. · Zbl 0998.82003
[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.
[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.
[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.
[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. · Zbl 1090.65078
[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.
[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.
[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.
[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. · Zbl 1207.65078
[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. · Zbl 0747.62072
[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. · Zbl 0721.68056
[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. · Zbl 05452169
[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.
[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. · Zbl 0452.90038
[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. · Zbl 0818.68017
[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.
[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. · Zbl 05586575
[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. · Zbl 1191.68828
[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. · Zbl 0946.62002
[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. · Zbl 1027.68108
[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.
[62] ANSYS, APDL Programmer’s Guide: ANSYS Release 10.0, ANSYS, Canonsburg, Pa, USA, 2005.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.