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Mathematical Problems in Engineering
Volume 2015, Article ID 349781, 17 pages
http://dx.doi.org/10.1155/2015/349781
Research Article

A Multiobjective Genetic Algorithm Based on a Discrete Selection Procedure

1School of Science, Southwest University of Science and Technology, Mianyang 621010, China
2Australasian Joint Research Centre for Building Information Modelling School of Built Environment, Curtin University, Perth, WA 6845, Australia
3Department of Housing and Interior Design, Kyung Hee University, Seoul 136701, Republic of Korea
4School of Mathematics, Anhui Normal University, Wuhu 430000, China
5School of Mathematics, Chongqing Normal University, Chongqing 404100, China

Received 12 November 2014; Revised 15 January 2015; Accepted 20 January 2015

Academic Editor: Jianxiong Ye

Copyright © 2015 Qiang Long 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. C. J. Li, C. D. Li, X. F. Liao, and T. W. Huang, “Impulsive effects on stability of high-order BAM neural networks with time delays,” Neurocomputing, vol. 74, no. 10, pp. 1541–1550, 2011. View at Publisher · View at Google Scholar · View at Scopus
  2. C. J. Li, W. W. Yu, and T. W. Huang, “Impulsive synchronization schemes of stochastic complex networks with switching topology: average time approach,” Neural Networks, vol. 54, pp. 85–94, 2014. View at Publisher · View at Google Scholar · View at Scopus
  3. C. J. Li, D. Y. Gao, C. Liu, and G. Chen, “Impulsive control for synchronizing delayed discrete complex networks with switching topology,” Neural Computing and Applications, vol. 24, no. 1, pp. 59–68, 2014. View at Publisher · View at Google Scholar · View at Scopus
  4. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182–197, 2002. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Ehrgott, J. Ide, and A. Schöbel, “Minmax robustness for multi-objective optimization problems,” European Journal of Operational Research, vol. 239, no. 1, pp. 17–31, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  6. Q. Long, “A constraint handling technique for constrained multi-objective genetic algorithm,” Swarm and Evolutionary Computation, vol. 15, pp. 66–79, 2014. View at Publisher · View at Google Scholar · View at Scopus
  7. G. Mavrotas, O. Pechak, E. Siskos, H. Doukas, and J. Psarras, “Robustness analysis in Multi-Objective Mathematical Programming using Monte Carlo simulation,” European Journal of Operational Research, vol. 240, no. 1, pp. 193–201, 2015. View at Publisher · View at Google Scholar
  8. Y. T. Qi, X. L. Ma, F. Liu, L. C. Jiao, J. Y. Sun, and J. S. Wu, “MOEA/D with adaptive weight adjustment,” Evolutionary Computation, vol. 22, no. 2, pp. 231–264, 2014. View at Publisher · View at Google Scholar
  9. P. C. Fishburn, “Utility theory for decision making,” DTIC Document, 1970. View at Google Scholar
  10. I. Y. Kim and O. L. De Weck, “Adaptive weighted-sum method for bi-objective optimization: pareto front generation,” Structural and Multidisciplinary Optimization, vol. 29, no. 2, pp. 149–158, 2005. View at Publisher · View at Google Scholar · View at Scopus
  11. R. T. Marler and J. S. Arora, “The weighted sum method for multi-objective optimization: new insights,” Structural and Multidisciplinary Optimization, vol. 41, no. 6, pp. 853–862, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. J. J. Liu, C. Z. Wu, G. Wu, and X. Y. Wang, “A novel differential search algorithm and applications for structure design,” Submitted.
  13. Q. Long and C. Z. Wu, “A hybrid method combining genetic algorithm and Hooke-Jeeves method for constrained global optimization,” Journal of Industrial and Management Optimization, vol. 10, no. 4, pp. 1279–1296, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. Q. Long, C. Z. Wu, T. W. Huang, and X. Y. Wang, “A genetic algorithm for unconstrained multi-objective optimization,” Swarm and Evolutionary Computation, 2015. View at Publisher · View at Google Scholar
  15. D. F. Jones, S. K. Mirrazavi, and M. Tamiz, “Multi-objective meta-heuristics: an overview of the current state-of-the-art,” European Journal of Operational Research, vol. 137, no. 1, pp. 1–9, 2002. View at Publisher · View at Google Scholar · View at Scopus
  16. P. Kumar, D. Gospodaric, and P. Bauer, “Improved genetic algorithm inspired by biological evolution,” Soft Computing, vol. 11, no. 10, pp. 923–941, 2007. View at Publisher · View at Google Scholar · View at Scopus
  17. K. Sindhya, S. Ruuska, T. Haanpää, and K. Miettinen, “A new hybrid mutation operator for multiobjective optimization with differential evolution,” Soft Computing, vol. 15, no. 10, pp. 2041–2055, 2011. View at Publisher · View at Google Scholar · View at Scopus
  18. J. D. Schaffer, “Multiple objective optimization with vector evaluated genetic algorithms,” in Proceedings of the 1st international Conference on Genetic Algorithms, pp. 93–100, L. Erlbaum Associates, 1985.
  19. C. M. Fonseca and P. J. Fleming, “Multiobjective genetic algorithms,” in Proceedings of the IEE Colloquium on Genetic Algorithms for Control Systems Engineering, pp. 6/1–6/5, IET, London, UK, May 1993.
  20. J. Horn, N. Nafpliotis, and D. E. Goldberg, “A niched Pareto genetic algorithm for multiobjective optimization,” in Proceedings of the 1st IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, vol. 1, pp. 82–87, IEEE, Orlando, Fla, USA, June 1994. View at Publisher · View at Google Scholar
  21. P. Hajela and C.-Y. Lin, “Genetic search strategies in multicriterion optimal design,” Structural Optimization, vol. 4, no. 2, pp. 99–107, 1992. View at Publisher · View at Google Scholar · View at Scopus
  22. T. Murata and H. Ishibuchi, “MOGA: multi-objective genetic algorithms,” in Proceedings of the IEEE International Conference on Evolutionary Computation, vol. 1, pp. 289–294, IEEE, December 1995. View at Scopus
  23. N. Srinivas and K. Deb, “Muiltiobjective optimization using nondominated sorting in genetic algorithms,” Evolutionary Computation, vol. 2, no. 3, pp. 221–248, 1994. View at Publisher · View at Google Scholar
  24. E. Zitzler and L. Thiele, “Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach,” IEEE Transactions on Evolutionary Computation, vol. 3, no. 4, pp. 257–271, 1999. View at Publisher · View at Google Scholar · View at Scopus
  25. E. Zitzler, M. Laumanns, and L. Thiele, “SPEA2: improving the strength Pareto evolutionary algorithm,” Tech. Rep., Eidgenössische Technische Hochschule Zurich (ETH) Institut fur Technische Informatik und Kommunikationsnetze (TIK), 2001. View at Publisher · View at Google Scholar
  26. J. D. Knowles and D. W. Corne, “Approximating the nondominated front using the pareto archived evolution strategy,” Evolutionary computation, vol. 8, no. 2, pp. 149–172, 2000. View at Publisher · View at Google Scholar · View at Scopus
  27. D. W. Corne, J. D. Knowles, and M. J. Oates, “The Pareto envelope-based selection algorithm for multiobjective optimization,” in Parallel Problem Solving from Nature PPSN VI, vol. 1917 of Lecture Notes in Computer Science, pp. 839–848, Springer, Berlin, Germany, 2000. View at Publisher · View at Google Scholar
  28. E. Zitzler, K. Deb, and L. Thiele, “Comparison of multiobjective evolutionary algorithms: empirical results,” Evolutionary computation, vol. 8, no. 2, pp. 173–195, 2000. View at Publisher · View at Google Scholar · View at Scopus
  29. T. C. Koopmans and S. Reiter, “A model of transportation,” in Activity Analysis of Production and Allocation, p. 222, John Wiley & Sons, New York, NY, USA, 1951. View at Google Scholar · View at MathSciNet
  30. J. H. Holland, Adaptation in Natural and Artificial Systems, vol. 53, University of Michigan Press, Ann Arbor, Mich, USA, 1975. View at MathSciNet
  31. D. E. Goldberg, “A note on Boltzmann tournament selection for genetic algorithms and population-oriented simulated annealing,” Complex Systems, vol. 4, no. 4, pp. 445–460, 1990. View at Google Scholar
  32. D. E. Goldberg, B. Korb, and K. Deb, “Messy genetic algorithms: motivation, analysis, and first results,” Complex Systems, vol. 3, no. 5, pp. 493–530, 1989. View at Google Scholar · View at MathSciNet
  33. 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 Publisher · View at Google Scholar · View at Scopus
  34. H. Kitano, “Neurogenetic learning: an integrated method of designing and training neural networks using genetic algorithms,” Physica D: Nonlinear Phenomena, vol. 75, no. 1–3, pp. 225–238, 1994. View at Publisher · View at Google Scholar · View at Scopus
  35. T. Murata, H. Ishibuchi, and H. Tanaka, “Multi-objective genetic algorithm and its applications to flowshop scheduling,” Computers and Industrial Engineering, vol. 30, no. 4, pp. 957–968, 1996. View at Publisher · View at Google Scholar · View at Scopus
  36. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, Reading, Mass, USA, 1989.
  37. C. M. Fonseca and P. J. Fleming, “Genetic algorithms for multiobjective optimization: formulation discussion and generalization,” in Proceedings of the 5th International Conference on Genetic Algorithms (ICGA '93), pp. 416–423, 1993.
  38. J. Knowles and D. Corne, “The pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation,” in Proceedings of the Congress on Evolutionary Computation (CEC '99), vol. 1, pp. 98–105, July 1999. View at Publisher · View at Google Scholar · View at Scopus
  39. D. E. Goldberg and J. Richardson, “Genetic algorithms with sharing for multimodal function optimization,” in Proceedings of the 2nd International Conference on Genetic Algorithms and Their Applications, pp. 41–49, Lawrence Erlbaum Associates, 1987.
  40. H. Lu and G. G. Yen, “Rank-density-based multiobjective genetic algorithm and benchmark test function study,” IEEE Transactions on Evolutionary Computation, vol. 7, no. 4, pp. 325–343, 2003. View at Publisher · View at Google Scholar · View at Scopus
  41. G. G. Yen and H. Lu, “Dynamic multiobjective evolutionary algorithm: adaptive cell-based rank and density estimation,” IEEE Transactions on Evolutionary Computation, vol. 7, no. 3, pp. 253–274, 2003. View at Publisher · View at Google Scholar · View at Scopus
  42. Q. F. Zhang, A. Zhou, S. Z. Zhao, P. N. Suganthan, W. D. Liu, and S. Tiwari, “Multiobjective optimization test instances for the CEC 2009 special session and competition,” Tech. Rep. CES-487, University of Essex and Nanyang Technological University, 2009. View at Google Scholar
  43. Q. F. Zhang, W. D. Liu, and H. Li, “The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '09), pp. 203–208, IEEE, May 2009. View at Publisher · View at Google Scholar · View at Scopus
  44. S. Kukkonen and J. Lampinen, “Performance assessment of Generalized Differential Evolution 3 (GDE3) with a given set of problems,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '07), pp. 3593–3600, IEEE, September 2007. View at Publisher · View at Google Scholar · View at Scopus
  45. C.-M. Chen, Y.-P. Chen, and Q. F. Zhang, “Enhancing MOEA/D with guided mutation and priority update for multi-objective optimization,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '09), pp. 209–216, May 2009. View at Publisher · View at Google Scholar · View at Scopus
  46. L.-Y. Tseng and C. Chen, “Multiple trajectory search for unconstrained/constrained multi-objective optimization,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '09), pp. 1951–1958, IEEE, May 2009. View at Publisher · View at Google Scholar · View at Scopus
  47. H.-L. Liu and X. Q. Li, “The multiobjective evolutionary algorithm based on determined weight and sub-regional search,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '09), pp. 1928–1934, IEEE, May 2009. View at Publisher · View at Google Scholar · View at Scopus
  48. M. H. Liu, X. F. Zou, C. Yu, and Z. J. Wu, “Performance assessment of DMOEA-DD with CEC 2009 MOEA competition test instances,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '09), pp. 2913–2918, IEEE, Trondheim, Norway, May 2009. View at Publisher · View at Google Scholar · View at Scopus
  49. K. Sindhya, A. Sinha, K. Deb, and K. Miettinen, “Optimization algorithm for constrained and unconstrained problems,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '09), pp. 2919–2926, May 2009. View at Publisher · View at Google Scholar · View at Scopus
  50. V. L. Huang, S. Z. Zhao, R. Mallipeddi, and P. N. Suganthan, “Multi-objective optimization using self-adaptive differential evolution algorithm,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '09), pp. 190–194, May 2009. View at Publisher · View at Google Scholar · View at Scopus
  51. Y. P. Wang, C. Y. Dang, H. C. Li, L. X. Han, and J. X. Wei, “A clustering multi-objective evolutionary algorithm based on orthogonal and uniform design,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '09), pp. 2927–2933, IEEE, Trondheim, Norway, May 2009. View at Publisher · View at Google Scholar · View at Scopus
  52. S. Tiwari, G. Fadel, P. Koch, and K. Deb, “Performance assessment of the hybrid archive-based micro genetic algorithm (AMGA) on the CEC09 test problems,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '09), pp. 1935–1942, IEEE, Trondheim, Norway, May 2009. View at Publisher · View at Google Scholar
  53. B. Y. Qu and P. N. Suganthan, “Multi-objective evolutionary programming without non-domination sorting is up to twenty times faster,” in Proceedings of the 11th Conference on Congress on Evolutionary Computation (CEC '09), pp. 2934–2939, IEEE, 2009.
  54. A. Zamuda, J. Brest, B. Bošković, and V. Žumer, “Differential evolution with self-adaptation and local search for Constrained multiobjective optimization,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '09), pp. 195–202, May 2009. View at Publisher · View at Google Scholar · View at Scopus
  55. S. Gao, S. Y. Zeng, B. Xiao et al., “An orthogonal multi-objective evolutionary algorithm with lower-dimensional crossover,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '09), pp. 1959–1964, IEEE, May 2009. View at Publisher · View at Google Scholar · View at Scopus
  56. Q. F. Zhang and P. N. Suganthan, “Final report on CEC'09 MOEA competition,” in IEEE Congress on Evolutionary Computation (CEC '09), Piscataway, NJ, USA, 2009.