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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 718015, 11 pages
Determining Optimal Link Capacity Expansions in Road Networks Using Cuckoo Search Algorithm with Lévy Flights
Department of Civil Engineering, Faculty of Engineering, Pamukkale University, 20070 Denizli, Turkey
Received 28 June 2013; Accepted 31 July 2013
Academic Editor: Xin-She Yang
Copyright © 2013 Ozgur Baskan. 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.
- J. G. Wardrop, “Some theoretical aspects of road traffic research,” Proceedings of the Institution of Civil Engineers Part II, vol. 1, pp. 325–378, 1952.
- O. Baskan, “Harmony search algorithm for continuous network design problem with link capacity expansions,” KSCE Journal of Civil Engineering, pp. 1–11, 2013.
- M. Abdulaal and L. J. LeBlanc, “Continuous equilibrium network design models,” Transportation Research B, vol. 13, no. 1, pp. 19–32, 1979.
- C. Suwansirikul, T. L. Friesz, and R. L. Tobin, “Equilibrium decomposed optimisation: a heuristic for the continuous equilibrium network design problem,” Transportation Science, vol. 21, no. 4, pp. 254–263, 1987.
- P. Marcotte, “Network optimization with continuous control parameters,” Transportation Science, vol. 17, no. 2, pp. 181–197, 1983.
- P. Marcotte and G. Marquis, “Efficient implementation of heuristics for the continuous network design problem,” Annals of Operations Research, vol. 34, no. 1, pp. 163–176, 1992.
- T. L. Friesz, R. L. Tobin, H.-J. Cho, and N. J. Mehta, “Sensitivity analysis based heuristic algorithms for mathematical programs with variational inequality constraints,” Mathematical Programming, vol. 48, no. 2, pp. 265–284, 1990.
- H. J. Cho, analysis of equilibrium network flows and its application to the development of solution methods for equilibrium network design problems [Ph.D. thesis], University of Pennsylvania, Philadelphia, Pa, USA, 1988.
- Y. Hai, “Sensitivity analysis for queuing equilibrium network flow and its application to traffic control,” Mathematical and Computer Modelling, vol. 22, no. 4–7, pp. 247–258, 1995.
- H. Yang, “Sensitivity analysis for the elastic-demand network equilibrium problem with applications,” Transportation Research B, vol. 31, no. 1, pp. 55–70, 1997.
- T. L. Friesz, H.-J. Cho, N. J. Mehta, R. L. Tobin, and G. Anandalingam, “Simulated annealing approach to the network design problem with variational inequality constraints,” Transportation Science, vol. 26, no. 1, pp. 18–26, 1992.
- T. L. Friesz, G. Anandalingam, N. J. Mehta, K. Nam, S. J. Shah, and R. L. Tobin, “The multiobjective equilibrium network design problem revisited: a simulated annealing approach,” European Journal of Operational Research, vol. 65, no. 1, pp. 44–57, 1993.
- G. A. Davis, “Exact local solution of the continuous network design problem via stochastic user equilibrium assignment,” Transportation Research B, vol. 28, no. 1, pp. 61–75, 1994.
- Q. Meng, H. Yang, and M. G. H. Bell, “An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem,” Transportation Research B, vol. 35, no. 1, pp. 83–105, 2001.
- S.-W. Chiou, “Bilevel programming for the continuous transport network design problem,” Transportation Research B, vol. 39, no. 4, pp. 361–383, 2005.
- X. Ban, H. X. Liu, J. Lu, and M. C. Ferris, “Decomposition scheme for continuous network design problem with asymmetric user equilibria,” Transportation Research Record, no. 1964, pp. 185–192, 2006.
- A. Karoonsoontawong and S. T. Waller, “Dynamic continuous network design problem: linear bilevel programming and metaheuristic approaches,” Transportation Research Record, no. 1964, pp. 104–117, 2006.
- Z. Gao, H. Sun, and H. Zhang, “A globally convergent algorithm for transportation continuous network design problem,” Optimization and Engineering, vol. 8, no. 3, pp. 241–257, 2007.
- T. Xu, H. Wei, and G. Hu, “Study on continuous network design problem using simulated annealing and genetic algorithm,” Expert Systems with Applications, vol. 36, no. 2, pp. 1322–1328, 2009.
- T. V. Mathew and S. Sharma, “Capacity expansion problem for large urban transportation networks,” Journal of Transportation Engineering, vol. 135, no. 7, pp. 406–415, 2009.
- D. Z. W. Wang and H. K. Lo, “Global optimum of the linearized network design problem with equilibrium flows,” Transportation Research B, vol. 44, no. 4, pp. 482–492, 2010.
- C. Li, H. Yang, D. Zhu, and Q. Meng, “A global optimization method for continuous network design problems,” Transportation Research B, vol. 46, pp. 1144–1158, 2012.
- O. Baskan and M. Dell’Orco, “Artificial bee colony algorithm for continuous network design problem with link capacity expansions,” in Proceedings of the 10th International Congress on Advances in Civil Engineering, Middle East Technical University, Ankara, Turkey, October 2012.
- O. Baskan and H. Ceylan, “Modified differential evolution algorithm for the continuous network design problem,” in Proceedings of the 16th Euro Working Group on Transportation, Porto, Portugal, 2013.
- H. Yang and J. Y. T. Wang, “Travel time minimization versus reserve capacity maximization in the network design problem,” Transportation Research Record, no. 1783, pp. 17–26, 2002.
- G. Ziyou and S. Yifan, “A reserve capacity model of optimal signal control with user-equilibrium route choice,” Transportation Research B, vol. 36, no. 4, pp. 313–323, 2002.
- S.-W. Chiou, “A hybrid approach for optimal design of signalized road network,” Applied Mathematical Modelling, vol. 32, no. 2, pp. 195–207, 2008.
- C. S. Fisk, “Optimal signal controls on congested networks,” in Proceedings of the 9th International Symposium on Transportation and Traffic Theory, pp. 197–216, VNU Science Press, Utrecht, 1984.
- M. Frank and P. Wolfe, “An algorithm for quadratic programming,” Naval Research Logistics Quarterly, vol. 3, pp. 95–110, 1956.
- Y. Sheffi, Urban Transport Networks: Equilibrium Analysis With Mathematical Programming Methods, Prentice-Hall, New Jersey, NJ, USA, 1985.
- X. S. Yang and S. Deb, “Cuckoo search via Lévy flights,” in Proceedings of the world congress on nature and biologically inspired computing (NaBIC '09), pp. 210–214, IEEE Press, Piscataway, NJ, USA, December 2009.
- X.-S. Yang and S. Deb, “Engineering optimisation by cuckoo search,” International Journal of Mathematical Modelling and Numerical Optimisation, vol. 1, no. 4, pp. 330–343, 2010.
- X.-S. Yang and S. Deb, “Multiobjective cuckoo search for design optimization,” Computers & Operations Research, vol. 40, no. 6, pp. 1616–1624, 2013.
- R. B. Payne, M. D. Sorenson, and K. Klitz, The Cuckoos, Oxford University Press, 2005.
- E. Valian, S. Mohanna, and S. Tavakoli, “Improved Cuckoo search algorithm for global optimization,” International Journal of Communications and Information Technology, vol. 1, no. 1, pp. 31–44, 2011.
- X. S. Yang, Nature-Inspired Metaheuristic Algorithms, Luniver Press, 2nd edition, 2010.
- X. S. Yang and S. Deb, “Cuckoo search: recent advances and applications,” Neural Computing and Applications, 2013.
- E. Valian and E. Valian, “A cuckoo search algorithm by Lévy flights for solving reliability redundancy allocation problems,” Engineering Optimization, 2013.
- I. Pavlyukevich, “Lévy flights, non-local search and simulated annealing,” Journal of Computational Physics, vol. 226, no. 2, pp. 1830–1844, 2007.
- S. Walton, O. Hassan, K. Morgan, and M. R. Brown, “Modified cuckoo search: a new gradient free optimisation algorithm,” Chaos, Solitons and Fractals, vol. 44, no. 9, pp. 710–718, 2011.
- A. Kaveh and T. Bakhshpoori, “Optimum design of steel frames using Cuckoo Search algorithm with Lévy flights,” Structural Design of Tall and Special Buildings, vol. 22, no. 13, pp. 1023–1036, 2013.
- R. E. Allsop, “possibilities for using traffic control to influence trip distribution and route choice,” in Proceedings of the 6th International Symposium on Transportation and Traffic Theory, pp. 345–375, Elsevier, New York, NY, USA, 1974.
- H. Yang and S. Yagar, “Traffic assignment and signal control in saturated road networks,” Transportation Research A, vol. 29, no. 2, pp. 125–139, 1995.
- P. Luathep, A. Sumalee, W. H. K. Lam, Z.-C. Li, and H. K. Lo, “Global optimization method for mixed transportation network design problem: a mixed-integer linear programming approach,” Transportation Research B, vol. 45, no. 5, pp. 808–827, 2011.