- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 505890, 24 pages
Retrofitting Transportation Network Using a Fuzzy Random Multiobjective Bilevel Model to Hedge against Seismic Risk
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.
- 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.
- 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.
- 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.
- M. J. N. Priestley, F. Seible, and G. F. Calvi, Seismic Design and Retrofit of Bridges, John Wiley & Sons, New York, NY, USA, 1996.
- 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.
- 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.
- H. Kwakernaak, “Fuzzy random variables-I. Definitions and theorems,” Information Sciences, vol. 15, no. 1, pp. 1–29, 1978.
- 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.
- 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.
- A. F. Shapiro, “Fuzzy random variables,” Insurance, vol. 44, no. 2, pp. 307–314, 2009.
- 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.
- 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.
- 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.
- M. L. Puri and D. A. Ralescu, “Fuzzy random variables,” Journal of Mathematical Analysis and Applications, vol. 114, no. 2, pp. 409–422, 1986.
- 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.
- 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.
- R. Kruse and K. D. Meyer, Statistics with Vague Data, D. Reidel Publishing, Dordrecht, The Netherlands, 1987.
- 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.
- 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.
- 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.
- T. J. Ai, Particle Swarm Optimization for Generalized Vehicle Routing Problem [Doctoral Dissertation], Asian Institute of Technology, Thailand, 2008.
- 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.
- 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.
- 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.
- 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.
- X. Xiao, Theory of Environment Cost, China Financial & Economic Publishing House, Beijing, China, 2002.
- 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.
- 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.
- 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.
- 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.
- R. S. Kaplan, “Measuring manufacturing performance: a new challenge for managerial accounting research,” The Accounting Review, vol. 58, pp. 686–705, 1983.
- R. S. Kaplan, “Yesterday’s accounting undermines production,” Harvard Business Review, pp. 95–101, 1984.
- L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965.
- V. Krätschmer, “A unified approach to fuzzy random variables,” Fuzzy Sets and Systems, vol. 123, no. 1, pp. 1–9, 2001.
- 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.
- 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.
- 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.
- 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.
- D. Dubois and H. Prade, Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum Press, New York, NY, USA, 1988.
- S. Nahmias, “Fuzzy variables,” Fuzzy Sets and Systems, vol. 1, no. 2, pp. 97–110, 1978.
- 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.
- J. F. Bard, “Some properties of the bilevel programming problem,” Journal of Optimization Theory and Applications, vol. 68, no. 2, pp. 371–378, 1991.
- 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.
- 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.
- 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.
- 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.
- L. M. Case, An l1 Penalty Function Approach to the Nonlinear Bilevel Programming Problem [Ph.D. thesis], University of Waterloo, Ottawa, Canada, 1999.
- 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.
- 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.
- 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.
- E. Zitzler, K. Deb, and L. Thiele, “Comparison of multiobjective evolutionary algorithms: empirical results,” Evolutionary Computation, vol. 8, no. 2, pp. 173–195, 2000.