Abstract
This chapter reviews some urban transport problems that are vital in developing countries. These problems are formulated as optimization programs. They are usually nonlinear, discrete, bi-level, and multi-objective. Finding an efficient solution method for each problem is still a challenge. Besides, the reformulation of existing mathematical models in a solvable form is also an open question.
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References
Almond, J., Lott, R.S.: The Glasgow experiment: implementation and assessment. Road Research Laboratory Report 142, Road Research Laboratory, Crowthorne (1968)
Avishai, C.: Urban transit scheduling: framework, review and examples. J. Urban Plann. Dev. 128(4), 225–243 (2002)
Bai, Z.J., He, G.G., Zhao, S.Z.: Design and implementation of Tabu search algorithm for optimizing BRT Vehicles dispatch. Comput. Eng. Appl. 43(23), 229–232 (2007)
Ben Ayed, O., Boyce, D.E., Blair, C.E. III: A general bi-level linear programming formulation of the network design problem. Transp. Res. B 22(4), 311–318 (1988)
Ceylan, H., Bell, M.G.H.: Traffic signal timing optimisation based on genetic algorithm approach, including drivers’ routing. Transp. Res. B 38(4), 329–342 (2004)
Costantin, I., Florian, M.: Optimizing frequency in transit network: a nonlinear bi-level programming approach. Int. Trans. Oper. Res. 2(2), 149–164 (1995)
Cree, N.D., Maher, M.J., Paechter, B.: The continuous equilibrium optimal network design problem: a genetic approach. In: Bell, M.G.H. (ed.) Transportation Networks: Recent Methodological Advances, pp.163–174. Pergamon, Oxford (1998)
Dai, L.G., Liu, Z.D.: Research on the multi-objective assembled optimal model of departing interval on bus dispatch. J. Transp. Syst. Eng. Inf. Technol. 7(4), 43–46 (2007)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6, 182–197 (2002)
Fan, Q.S., Pan, W.: Application research of genetic algorithm in intelligent transport systems scheduling of vehicle. Comput. Digit. Eng. 35(5), 34–35 (2007)
Fitsum, T., Agachai, S.: A genetic algorithm approach for optimizing traffic control signals considering routing. Comput. Aided Civ. Inf. Eng. 22, 31–43 (2007)
Friesz, T.L., Tobin, R.L., Cho, H.J., Mehta, N.J.: Sensitivity analysis based heuristic algorithms for mathematical programs with variational inequality constraints. Math. Program. 48, 265–284 (1990)
Friesz, T.L., Cho, H.J., Mehta, N.J., Tobin, R., Anandalingam, G.: A simulated annealing approach to the network design problem with variational inequality constraints. Transp. Sci. 26, 18–26 (1992)
Gao, Z., Sun, H., Shan, L.L.: A continuous equilibrium network design model and algorithm for transit systems. Transp. Res. B 38(3), 235–250 (2004)
Han, A.F., Wilson, N.M.: The allocation of buses in heavily utilized networks with overlapping routes. Transp. Res. B 13(3), 221–232 (1982)
Hector, M., Antonio, M., Maria, E.U.: Frequency optimization in public transportation systems: formulation and methaheuristic approach. Eur. J. Oper. Res. 236, 27–36 (2014)
Hector, M., Antonio, M., Maria, E.U.: Mathematical programming formulations for transit network design. Transp. Res. B: Methodol. 77, 17–37 (2015)
Hunt, P.B., Robertson, D.I., Bretherton, R.D., Winton, R.I.: SCOOT-A traffic responsive method of coordinating signals, TRRL Laboratory Report 1014, TRRL, Berkshire, England (1981)
Kurauchi F., Bell M.G.H, Schmoecker, J.-D.: Capacity constrained transit assignment with common lines. J. Math. Model. Algorithms 2, 309–327 (2003)
Lawphongpanich, S., Hearn, D.W.: An MPEC approach to second-best toll pricing. Math. Program. B 101(1), 33–55 (2004)
LeBlanc, L., Boyce, D.: A bi-level programming for exact solution of the network design problem with user-optimal flows. Transp. Res. B Methodol. 20, 259–265 (1986)
Le Thi, H.A.: Contribution à l’optimisation non-convex and l’optimisation globale: théorie, algorithmes et applications. Habilitation à Diriger des recherches, Université de Rouen (1997)
Le Thi, H.A., Pham Dinh, T.: A branch and bound method via d.c. optimization algorithms and ellipsoidal technique for box constrained nonconvex quadratic problems. J. Glob. Optim. 13, 171–206 (1998)
Le Thi, H.A., Pham Dinh, T.: A continuous approach for globally solving linearly constrained quadratic zero-one programming problem. Optimization 50(1–2) , 93–120 (2001)
Le Thi, H.A., Pham Dinh, T.: The DC(difference of convex functions) Programming and DCA revisited with DC models of real world non-convex optimization problems. Ann. Oper. Res. 133, 23–46 (2005)
Le Thi, H.A., Pham Dinh, T., Huynh, V.N.: Exact penalty and error bounds in DC programming. J. Glob. Optim. 52(3), 509–535 (2012)
Levinson, H., Zimmerman, S., Clinger, J., Rutherford, S., Smith, R.L., Cracknell, J., Soberman, R.: Bus rapid transit, volume 1: case studies in bus rapid transit, TCRP Report 90, Transportation Research Board, Washington (2003)
Liang, S., He, Z., Sha, Z.: Bus rapid transit scheduling optimal model based on genetic algorithm. In: 11th International Conference of Chinese Transportation Professionals (ICCTP), pp. 1296–1305 (2011)
Luenberger, D.G.: Linear and Nonlinear Programming, 2nd edn. Springer, Berlin (2004)
Luo, Z., Pang, J.S., Ralph, D.: Mathematical Programs with Equilibrium Constraints. Cambridge University Press, New York (1996)
Meng, Q., Yang, H., Bell, M.G.H.: An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem. Transp. Res. B 35(1), 83–105 (2001)
Miller, M.A., Yin, Y., Balvanyos, T., Avishai, C.: Framework for bus rapid transit development and deployment planning. Research report, California PATH, University of California Berkeley (2004)
Nguyen, S., Pallotino, S.: Equilibrium assignment for large scale transit network. Eur. J. Oper. Res. 37, 176–186 (1988)
Nguyen, Q.T., Phan, N.B.T.: Scheduling Problem for Bus Rapid Transit Routes. Advances in Intelligent Systems and Computing, vol. 358, pp. 69–79. Springer, Heidelberg (2015)
Nguyen, N.D., Nguyen, Q.T., Vu, T.H., Nguyen, T.H.: Optimizing the bus network configuration in Danang city. Adv. Ind. Appl. Math. ISBN 978-604-80-0608-2 (2014)
Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to d.c programming: theory, algorithms and applications. Acta Math. Vietnam. 22(1), 289–355 (1997), dedicated to Professor Hoang Tuy on the occasion of his 70th birthday
Pham Dinh, T., Le Thi, H.A.: DC optimization algorithms for solving the trust region subproblem. SIAM J. Optim. 8, 476–505 (1998)
Ren, C.X., Zhang, H., Fan, Y.Z.: Optimizing dispatching of public transit vehicles using genetic simulated annealing algorithm. J. Syst. Simul. 17(9), 2075–2077 (2005)
Rickert, T.: Technical and operational challenges to inclusive bus rapid transit: a guide for practitioners. World Bank, Washington (2010)
Robertson, D.I.: ‘TRANSYT’ method for area traffic control. Traffic Eng. Control 10, 276–281 (1969)
Schaefer, R.: Foundations of Global Genetic Optimization. Studies in Computational Intelligence, vol. 74. Springer, Berlin (2007)
Shepherd, S.P.: A Review of Traffic Signal Control, Monograph, Publisher University of Leeds, Institute for Transport Studies (1992)
Shimamoto, H., Schmöcker, J.-D., Kurauchi F., Optimisation of a bus network configuration and frequency considering the common lines problem. J. Transp. Technol. 2, 220–229 (2012)
Shrivastava, P., Dhingra, S.L.: Development of coordinated schedules using genetic algorithms. J. Transp. Eng. 128(1), 89–96 (2002)
Sun, C., Zhou, W., Wang, Y.: Scheduling combination and headway optimization of bus rapid transit. J. Transp. Syst. Eng. Inf. Technol. 8(5), 61–67 (2008)
Suwansirikul, C., Friesz, T.L., Tobin, R.L.: Equilibrium decomposed optimization: a heuristic for the continuous equilibrium network design problem. Transp. Sci. 21(4), 254–263 (1987)
Tong, G.: Application study of genetic algorithm on bus scheduling. Comput. Eng. 31(13), 29–31 (2005)
Tran, D.Q., Phan, N.B.T., Nguyen, Q.T.A.: New Approach for Optimizing Traffic Signals in Networks Considering Rerouting. Advances in Intelligent Systems and Computing, vol. 359, pp. 143–154. Springer, Heidelberg (2015)
Van Vliet, D.: SATURN-A modern assignment model. Traffic Eng. Control 23, 578–581 (1982)
Verhoef, E.T.: Second-best congestion pricing in general networks: heuristic algorithms for finding second-best optimal toll levels and toll points. Transp. Res. B 36(8), 707–729 (2002)
Wardrop, J.G.: Some theoretical aspects of road traffic research. Proc. Inst. Civil Eng. 1(2), 325–378 (1952)
Webster, F.V.: Traffic Signal Settings, Road Research Technical Paper No. 39, HMSO, London (1958)
Wu, X., Deng, S., Du, X.: Jing MaGreen-Wave traffic theory optimization and analysis. World J. Eng. Technol. 2, 14–19 (2014)
Yang, H.: Sensitivity analysis for the elastic-demand network equilibrium problem with applications. Transp. Res. B 31(1), 55–70 (1997)
Yu, B., Yang, Z., Yao, J.: Genetic algorithm for bus frequency optimization. J. Transp. Eng. 136(6), 576–583 (2010)
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This work is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2013.10.
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Quynh, T.D., Thuan, N.Q. (2018). On Optimization Problems in Urban Transport. In: Pardalos, P., Migdalas, A. (eds) Open Problems in Optimization and Data Analysis. Springer Optimization and Its Applications, vol 141. Springer, Cham. https://doi.org/10.1007/978-3-319-99142-9_9
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