A surrogate-based optimization algorithm for network design problems

Article
  • 74 Downloads

Abstract

Network design problems (NDPs) have long been regarded as one of the most challenging problems in the field of transportation planning due to the intrinsic non-convexity of their bi-level programming form. Furthermore, a mixture of continuous/discrete decision variables makes the mixed network design problem (MNDP) more complicated and difficult to solve. We adopt a surrogate-based optimization (SBO) framework to solve three featured categories of NDPs (continuous, discrete, and mixed-integer). We prove that the method is asymptotically completely convergent when solving continuous NDPs, guaranteeing a global optimum with probability one through an indefinitely long run. To demonstrate the practical performance of the proposed framework, numerical examples are provided to compare SBO with some existing solving algorithms and other heuristics in the literature for NDP. The results show that SBO is one of the best algorithms in terms of both accuracy and efficiency, and it is efficient for solving large-scale problems with more than 20 decision variables. The SBO approach presented in this paper is a general algorithm of solving other optimization problems in the transportation field.

Key words

Network design problem Surrogate-based optimization Transportation planning Heuristics 

CLC number

U491 TP202 

References

  1. Abdulaal, M., LeBlanc, L.J., 1979. Continuous equilibrium network design models. Transp. Res. B, 13(1): 19–32. https://doi.org/10.1016/0191-2615(79)90004-3CrossRefGoogle Scholar
  2. Allsop, R.E., 1974. Some possibilities for using traffic control to influence trip distribution and route choice. Proc. 6th Int. Symp. on Transportation and Traffic Theory, p. 345–373.Google Scholar
  3. Cantarella, G.E., Vitetta, A., 2006. The multi-criteria road network design problem in an urban area. Transportation, 33(6): 567–588. https://doi.org/10.1007/s11116-006-7908-zCrossRefGoogle Scholar
  4. Chen, X.Q., Yin, M.G., Song, M.Z., et al., 2014a. Social welfare maximization of multimodal transportation. Transp. Res. Rec. J. Transp. Res. Board, 2451: 36–49. https://doi.org/10.3141/2451-05CrossRefGoogle Scholar
  5. Chen, X.Q., Zhang, L., He, X., et al., 2014b. Surrogate-based optimization of expensive-to-evaluate objective for optimal highway toll charges in transportation network. Comput.-Aid. Civil Infrastr. Eng., 29(5): 359–381. https://doi.org/10.1111/mice.12058CrossRefGoogle Scholar
  6. Chen, X.Q., Zhu, Z., Zhang, L., 2015a. Simulation-based optimization of mixed road pricing policies in a large realworld network. Transp. Res. Proc., 8: 215–226. https://doi.org/10.1016/j.trpro.2015.06.056CrossRefGoogle Scholar
  7. Chen, X.Q., Zhu, Z., He, X., et al., 2015b. Surrogate-based optimization for solving a mixed integer network design problem. Transp. Res. Rec. J. Transp. Res. Board, 2497: 124–134. https://doi.org/10.3141/2497-13CrossRefGoogle Scholar
  8. Chiou, S.W., 2005. Bilevel programming for the continuous transport network design problem. Transp. Res. B, 39(4): 361–383. https://doi.org/10.1016/j.trb.2004.05.001CrossRefGoogle Scholar
  9. Chow, J.Y.J., Regan, A.C., 2014. A surrogate-based multiobjective metaheuristic and network degradation simulation model for robust toll pricing. Optim. Eng., 15(1): 137–165. https://doi.org/10.1007/s11081-013-9227-5MathSciNetCrossRefGoogle Scholar
  10. Davis, G.A., 1994. Exact local solution of the continuous network design problem via stochastic user equilibrium assignment. Transp. Res. B, 28(1): 61–75. https://doi.org/10.1016/0191-2615(94)90031-0CrossRefGoogle Scholar
  11. Farvaresh, H., Sepehri, M.M., 2011. A single-level mixed integer linear formulation for a bi-level discrete network design problem. Transp. Res. E, 47(5): 623–640. https://doi.org/10.1016/j.tre.2011.02.001CrossRefGoogle Scholar
  12. Friesz, T.L., Cho, H.J., Mehta, N.J., et al., 1992. A simulated annealing approach to the network design problem with variational inequality constraints. Transp. Sci., 26(1): 18–26. https://doi.org/10.1287/trsc.26.1.18CrossRefGoogle Scholar
  13. Gallo, M., D’Acierno, L., Montella, B., 2010. A meta-heuristic approach for solving the urban network design problem. Eur. J. Oper. Res., 201(1): 144–157. https://doi.org/10.1016/j.ejor.2009.02.026CrossRefGoogle Scholar
  14. Gao, Z.Y., Wu, J.J., Sun, H.J., 2005. Solution algorithm for the bi-level discrete network design problem. Transp. Res. B, 39(6): 479–495. https://doi.org/10.1016/j.trb.2004.06.004CrossRefGoogle Scholar
  15. Harker, P.T., Pang, J.S., 1990. Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math. Program., 48(1–3): 161–220. https://doi.org/10.1007/BF01582255MathSciNetCrossRefGoogle Scholar
  16. Jones, D.R., Schonlau, M., Welch, W.J., 1998. Efficient global optimization of expensive black-box functions. J. Glob. Optim., 13(4): 455–492. https://doi.org/10.1023/A:1008306431147MathSciNetCrossRefGoogle Scholar
  17. LeBlanc, L.J., 1975. An algorithm for the discrete network design problem. Transp. Sci., 9(3): 183–199. https://doi.org/10.1287/trsc.9.3.183CrossRefGoogle Scholar
  18. Li, C.M., Yang, H., Zhu, D.L., et al., 2012. A global optimization method for continuous network design problems. Transp. Res. B, 46(9): 1144–1158. https://doi.org/10.1016/j.trb.2012.05.003CrossRefGoogle Scholar
  19. Liu, H.X., Wang, D.Z.W., 2015. Global optimization method for network design problem with stochastic user equilibrium. Transp. Res. B, 72: 20–39. https://doi.org/10.1016/j.trb.2014.10.009CrossRefGoogle Scholar
  20. Lo, H.K., Szeto, W.Y., 2009. Time-dependent transport network design under cost-recovery. Transp. Res. B, 43(1): 142–158. https://doi.org/10.1016/j.trb.2008.06.005CrossRefGoogle Scholar
  21. Luathep, P., Sumalee, A., Lam, W.H.K., et al., 2011. Global optimization method for mixed transportation network design problem: a mixed-integer linear programming approach. Transp. Res. B, 45(5): 808–827. https://doi.org/10.1016/j.trb.2011.02.002CrossRefGoogle Scholar
  22. Meng, Q., Yang, H., Bell, M.G.H., 2001. An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem. Transp. Res. B, 35(1): 83–105. https://doi.org/10.1016/S0191-2615(00)00016-3CrossRefGoogle Scholar
  23. Müller, J., Shoemaker, C.A., Piché, R., 2013. SO-MI: a surrogate model algorithm for computationally expensive nonlinear mixed-integer black-box global optimization problems. Comput. Oper. Res., 40(5): 1383–1400. https://doi.org/10.1016/j.cor.2012.08.022MathSciNetCrossRefGoogle Scholar
  24. Nielsen, H.B., Lophaven, S.N., Søndergaard, J., 2002. DACE—a MATLAB Kriging Toolbox. Technical University of Denmark. Available from http://www2.imm.dtu.dk/projects/dace [Accessed on July 8, 2016].Google Scholar
  25. Poorzahedy, H., Turnquist, M.A., 1982. Approximate algorithms for the discrete network design problem. Transp. Res. B, 16(1): 45–55. https://doi.org/10.1016/0191-2615(82)90040-6MathSciNetCrossRefGoogle Scholar
  26. Poorzahedy, H., Abulghasemi, F., 2005. Application of ant system to network design problem. Transportation, 32(3): 251–273. https://doi.org/10.1007/s11116-004-8246-7CrossRefGoogle Scholar
  27. Poorzahedy, H., Rouhani, O.M., 2007. Hybrid meta-heuristic algorithms for solving network design problem. Eur. J. Oper. Res., 182(2): 578–596. https://doi.org/10.1016/j.ejor.2006.07.038MathSciNetCrossRefGoogle Scholar
  28. Regis, R.G., Shoemaker, C.A., 2007. A stochastic radial basis function method for the global optimization of expensive functions. INFORMS J. Comput., 19(4): 497–509. https://doi.org/10.1287/ijoc.1060.0182MathSciNetCrossRefGoogle Scholar
  29. Suwansirikul, C., Friesz, T.L., Tobin, R.L., 1987. Equilibrium decomposed optimization: a heuristic for the continuous equilibrium network design problem. Transp. Sci., 21(4): 254–263. https://doi.org/10.1287/trsc.21.4.254CrossRefGoogle Scholar
  30. Wang, D.Z.W., Lo, H.K., 2010. Global optimum of the linearized network design problem with equilibrium flows. Transp. Res. B, 44(4): 482–492. https://doi.org/10.1016/j.trb.2009.10.003CrossRefGoogle Scholar
  31. Wang, D.Z.W., Liu, H.X., Szeto, W.Y., 2015. A novel discrete network design problem formulation and its global optimization solution algorithm. Transp. Res. E, 79: 213–230. https://doi.org/10.1016/j.tre.2015.04.005CrossRefGoogle Scholar
  32. Wang, S.A., Meng, Q., Yang, H., 2013. Global optimization methods for the discrete network design problem. Transp. Res. B, 50: 42–60. https://doi.org/10.1016/j.trb.2013.01.006CrossRefGoogle Scholar
  33. Wardrop, J.G., 1952. Road Paper. Some theoretical aspects of road traffic research. Proc. Inst. Civil Eng., 1(3): 325–362. https://doi.org/10.1680/ipeds.1952.11259Google Scholar
  34. Yang, H., Bell, M.G.H., 1998. Models and algorithms for road network design: a review and some new developments. Transp. Rev., 18(3): 257–278. https://doi.org/10.1080/01441649808717016CrossRefGoogle Scholar
  35. Yang, H., Yagar, S., 1995. Traffic assignment and signal control in saturated road networks. Transp. Res. A, 29(2): 125–139. https://doi.org/10.1016/0965-8564(94)E0007-VCrossRefGoogle Scholar
  36. Yin, Y.F., 2000. Genetic-algorithms-based approach for bilevel programming models. J. Transp. Eng., 126(2): 115–120.CrossRefGoogle Scholar
  37. Yin, Y.F., Madanat, S.M., Lu, X.Y., 2009. Robust improvement schemes for road networks under demand uncertainty. Eur. J. Oper. Res., 198(2): 470–479. https://doi.org/10.1016/j.ejor.2008.09.008MathSciNetCrossRefGoogle Scholar

Copyright information

© Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Civil EngineeringTsinghua UniversityBeijingChina
  2. 2.College of Civil Engineering and ArchitectureZhejiang UniversityHangzhouChina

Personalised recommendations