About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 505890, 24 pages
http://dx.doi.org/10.1155/2014/505890
Research Article

Retrofitting Transportation Network Using a Fuzzy Random Multiobjective Bilevel Model to Hedge against Seismic Risk

Lu Gan1,2 and Jiuping Xu2,3

1Urban and Rural Development College, Sichuan Agricultural University, Dujiangyan 611830, China
2Uncertainty Decision-Making Laboratory, Sichuan University, Chengdu 610064, China
3State Key laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610064, China

Received 28 August 2013; Revised 14 October 2013; Accepted 14 October 2013; Published 12 January 2014

Academic Editor: Mohamed Fathy El-Amin

Copyright © 2014 Lu Gan and Jiuping Xu. 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. Liu, Y. Fan, and F. Ordóñez, “A two-stage stochastic programming model for transportation network protection,” Computers and Operations Research, vol. 36, no. 5, pp. 1582–1590, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. S. D. Werner, C. E. Taylor, J. E. Moore, and J. S. Walton, Seismic Retrofitting Manuals for Highway Systems, Volume I, Seismic Risk Analysis of Highway Systems, and Technical Report for Volume I, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY, USA, 1999.
  3. J. Sohn, T. J. Kim, G. J. D. Hewings, J. S. Lee, and S.-G. Jang, “Retrofit priority of transport network links under an earthquake,” Journal of Urban Planning and Development, vol. 129, no. 4, pp. 195–210, 2003. View at Publisher · View at Google Scholar · View at Scopus
  4. M. J. N. Priestley, F. Seible, and G. F. Calvi, Seismic Design and Retrofit of Bridges, John Wiley & Sons, New York, NY, USA, 1996.
  5. M. Shinozuka, Y. Murachi, X. Dong, Y. Zhou, and M. J. Orlikowski, “Effect of seismic retrofit of bridges on transportation networks,” Earthquake Engineering and Engineering Vibration, vol. 2, no. 2, pp. 169–179, 2003. View at Scopus
  6. Y. Zhou, S. Banerjee, and M. Shinozuka, “Socio-economic effect of seismic retrofit of bridges for highway transportation networks: a pilot study,” Structure and Infrastructure Engineering, vol. 6, no. 1-2, pp. 145–157, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. H. Kwakernaak, “Fuzzy random variables-I. Definitions and theorems,” Information Sciences, vol. 15, no. 1, pp. 1–29, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. R. Zhao, W. Tang, and C. Wang, “Fuzzy random renewal process and renewal reward process,” Fuzzy Optimization and Decision Making, vol. 6, no. 3, pp. 279–295, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. W. Fei, “A generalization of bihari's inequality and fuzzy random differential equations with non-Lipschitz coefficients,” International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems, vol. 15, no. 4, pp. 425–439, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. A. F. Shapiro, “Fuzzy random variables,” Insurance, vol. 44, no. 2, pp. 307–314, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. Y. K. Liu and J. Gao, “The independence of fuzzy variables with applications to fuzzy random optimization,” International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems, vol. 15, supplement 2, pp. 1–20, 2007. View at Scopus
  12. J. P. Xu and Y. G. Liu, “Multi-objective decision making model under fuzzy random environment and its application to inventory problems,” Information Sciences, vol. 178, no. 14, pp. 2899–2914, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. J. Xu and Z. Zhang, “A fuzzy random resource-constrained scheduling model with multiple projects and its application to a working procedure in a large-scale water conservancy and hydropower construction project,” Journal of Scheduling, vol. 15, no. 2, pp. 253–272, 2012. View at Publisher · View at Google Scholar · View at Scopus
  14. M. L. Puri and D. A. Ralescu, “Fuzzy random variables,” Journal of Mathematical Analysis and Applications, vol. 114, no. 2, pp. 409–422, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. E. P. Klement, M. L. Puri, and D. A. Ralescu, “Limit theorems for fuzzy random variables,” Proceedings of The Royal Society of London A, vol. 407, no. 1832, pp. 171–182, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. M. Á. Gil, M. López-Díaz, and D. A. Ralescu, “Overview on the development of fuzzy random variables,” Fuzzy Sets and Systems, vol. 157, no. 19, pp. 2546–2557, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. R. Kruse and K. D. Meyer, Statistics with Vague Data, D. Reidel Publishing, Dordrecht, The Netherlands, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  18. J. Xu, F. Yan, and S. Li, “Vehicle routing optimization with soft time windows in a fuzzy random environment,” Transportation Research E, vol. 47, no. 6, pp. 1075–1091, 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. G. Zhang, J. Lu, and T. Dillon, “Decentralized multi-objective bilevel decision making with fuzzy demands,” Knowledge-Based Systems, vol. 20, no. 5, pp. 495–507, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. 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
  21. T. J. Ai, Particle Swarm Optimization for Generalized Vehicle Routing Problem [Doctoral Dissertation], Asian Institute of Technology, Thailand, 2008.
  22. G. Ueno, K. Yasuda, and N. Iwasaki, “Robust adaptive particle swarm optimization,” in Proceedings of the IEEE International Conference on Systems, Man, Cybernetics, pp. 3915–3920, October 2005. View at Scopus
  23. T. J. Ai and V. Kachitvichyanukul, “A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery,” Computers and Operations Research, vol. 36, no. 5, pp. 1693–1702, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  24. C. A. C. Coello and M. S. Lechunga, “MOPSO: a proposal for multiple objective particle swarm optimization,” in Proceedings of the IEEE Word Congress on Computational Intelligence, 2002. View at Publisher · View at Google Scholar
  25. C. Jasch, “The use of environmental management accounting (EMA) for identifying environmental costs,” Journal of Cleaner Production, vol. 11, no. 6, pp. 667–676, 2003. View at Publisher · View at Google Scholar · View at Scopus
  26. X. Xiao, Theory of Environment Cost, China Financial & Economic Publishing House, Beijing, China, 2002.
  27. R. Cooper, “The rise of activity-based costing part one: what is an activity-based cost system?” Journal of Cost Management, vol. 2, pp. 45–54, 1988.
  28. R. Cooper, “The rise of activity-based costing part two: when do I need an activity-based cost system?” Journal of Cost Management, vol. 2, pp. 41–48, 1988.
  29. R. Cooper, “The rise of activity-based costing part three: how many cost drivers do you need, and how do you select them?” Journal of Cost Management, vol. 2, pp. 34–46, 1989.
  30. R. Cooper, “The rise of activity-based costing part four: what do activity-based cost systems look like?” Journal of Cost Management, vol. 3, pp. 34–46, 1989.
  31. R. S. Kaplan, “Measuring manufacturing performance: a new challenge for managerial accounting research,” The Accounting Review, vol. 58, pp. 686–705, 1983.
  32. R. S. Kaplan, “Yesterday’s accounting undermines production,” Harvard Business Review, pp. 95–101, 1984.
  33. L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  34. V. Krätschmer, “A unified approach to fuzzy random variables,” Fuzzy Sets and Systems, vol. 123, no. 1, pp. 1–9, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  35. J. Li, J. Xu, and M. Gen, “A class of multiobjective linear programming model with fuzzy random coefficients,” Mathematical and Computer Modelling, vol. 44, no. 11-12, pp. 1097–1113, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  36. Y.-K. Liu and B. Liu, “Fuzzy random variables: a scalar expected value operator,” Fuzzy Optimization and Decision Making, vol. 2, no. 2, pp. 143–160, 2003. View at Publisher · View at Google Scholar · View at Scopus
  37. M. López-Díaz and M. A. Gil, “The λ-average value and the fuzzy expectation of a fuzzy random variable,” Fuzzy Sets and Systems, vol. 99, no. 3, pp. 347–352, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  38. L. Özdamar and O. Demir, “A hierarchical clustering and routing procedure for large scale disaster relief logistics planning,” Transportation Research E, vol. 48, no. 3, pp. 591–602, 2012. View at Publisher · View at Google Scholar · View at Scopus
  39. D. Dubois and H. Prade, Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum Press, New York, NY, USA, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  40. S. Nahmias, “Fuzzy variables,” Fuzzy Sets and Systems, vol. 1, no. 2, pp. 97–110, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  41. G. Zhang, J. Lu, and Y. Gao, “An algorithm for fuzzy multi-objective multi-follower partial cooperative bilevel programming,” Journal of Intelligent and Fuzzy Systems, vol. 19, no. 4-5, pp. 303–319, 2008. View at Zentralblatt MATH · View at Scopus
  42. J. F. Bard, “Some properties of the bilevel programming problem,” Journal of Optimization Theory and Applications, vol. 68, no. 2, pp. 371–378, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  43. L. Yao and J. Xu, “A class of expected value bilevel programming problems with random coefficients based on rough approximation and its application to a production-inventory system,” Abstract and Applied Analysis, vol. 2013, Article ID 312527, 12 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  44. J. F. Bard and J. E. Falk, “An explicit solution to the multi-level programming problem,” Computers and Operations Research, vol. 9, no. 1, pp. 77–100, 1982. View at Publisher · View at Google Scholar · View at Scopus
  45. J. Fortuny-Amat and B. McCarl, “A representation and economic interpretation of a two-level programming problem,” Journal of the Operational Research Society, vol. 32, no. 9, pp. 783–792, 1981. View at Zentralblatt MATH · View at Scopus
  46. L. Vicente, G. Savard, and J. Júdice, “Descent approaches for quadratic bilevel programming,” Journal of Optimization Theory and Applications, vol. 81, no. 2, pp. 379–399, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  47. L. M. Case, An l1 Penalty Function Approach to the Nonlinear Bilevel Programming Problem [Ph.D. thesis], University of Waterloo, Ottawa, Canada, 1999.
  48. B. Lucio, C. Massimiliano, and G. Stefano, “A bilevel flow model for hazmat transportation network design,” Transportation Research C, vol. 17, no. 2, pp. 175–196, 2009. View at Publisher · View at Google Scholar · View at Scopus
  49. Y. Gao, G. Zhang, J. Lu, and H.-M. Wee, “Particle swarm optimization for bi-level pricing problems in supply chains,” Journal of Global Optimization, vol. 51, no. 2, pp. 245–254, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  50. L. Cagnina, S. Esquivel, and C. A. C. Coello, “A particle swarm optimizer for multi-objective optimization,” Journal of Computer Science and Technology, vol. 5, no. 4, pp. 204–210, 2005.
  51. 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