The multi-objective network design problem using minimizing externalities as objectives: comparison of a genetic algorithm and simulated annealing framework

Abstract

Incorporation of externalities in the Multi-Objective Network Design Problem (MO NDP) as objectives is an important step in designing sustainable networks. In this research the problem is defined as a bi-level optimization problem in which minimizing externalities are the objectives and link types which are associated with certain link characteristics are the discrete decision variables. Two distinct solution approaches for this multi-objective optimization problem are compared. The first heuristic is the non-dominated sorting genetic algorithm II (NSGA-II) and the second heuristic is the dominance based multi objective simulated annealing (DBMO-SA). Both heuristics have been applied on a small hypothetical test network as well as a realistic case of the city of Almelo in the Netherlands. The results show that both heuristics are capable of solving the MO NDP. However, the NSGA-II outperforms DBMO-SA, because it is more efficient in finding more non-dominated optimal solutions within the same computation time and maximum number of assessed solutions.

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References

  1. Abdulaal, M., LeBlanc, L.J.: Continuous equilibrium network design models. Transp. Res. B 13B, 19–32 (1979)

    Article  Google Scholar 

  2. Boyce, D.E., Janson, B.N.: A discrete transportation network design problem with combined trip distribution and assignment. Transp. Res. B 14B, 147–154 (1980)

    Article  Google Scholar 

  3. Bureau of Public Roads: Traffic assignment manual, Urban Planning Division. US Department of Commerce, Washington DC (1964)

    Google Scholar 

  4. Burke, E.K., Kendall, G.: Search methodologies: introductory tutorials in optimization and decision support techniques. In: Sastry, K., Goldberg, D., Kendall, G. (eds.) Chapter 4: genetic algorithms. Springer Science + Business Media, Inc, Berlin (2005)

    Google Scholar 

  5. Cantarella, G.E., Pavone, G., Vitetta, A.: Heuristics for urban road network design: lane layout and signal settings. Euro. J. Oper. Res. 175, 1682–1695 (2006)

    Article  Google Scholar 

  6. Chiou, S.: Bi-level programming for the continuous transport network design problem. Transp. Res. Part B 39, 361–383 (2005)

    Article  Google Scholar 

  7. CROW (2004). Richtlijn essentiële herkenbaarheidkenmerken van weginfrastructuur: wegwijzer voor implementatie. Publicatie 203. CROW kenniscentrum voor verkeer, vervoer en infrastructuur, Ede

  8. Dantzig, G.B., Harvey, R.P., Lansdowne, Z.F., Robinson, D.W., Maier, S.F.: Formulating and solving the network design problem by decomposition. Transp. Res. B 13B, 5–17 (1978)

    Google Scholar 

  9. Drezner, Z., Wesolowsky, G.O.: Network design: selection and design of links and facility location. Transp. Res. Part A 37, 241–256 (2003)

    Google Scholar 

  10. Deb, K.: Multi-objective optimization using evolutionary algorithms. Wiley, New York (2001)

    Google Scholar 

  11. Deb K, Agrawal S, Pratap A and Meyarivan T.: A Fast elitist no dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Proceedings of sixth international conference on parallel problem solving from nature (PPSN VI), Paris, France, September 2000, pp. 849–858. Springer, Berlin (2000)

  12. Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.A.: A fast elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  13. Frank, M., Wolfe, P.: An algorithm for quadratic programming. Naval Res. Logist. Quart. 3, 95–110 (1956)

    Article  Google Scholar 

  14. Friesz, T.L., Cho, H.J., Mehta, N.J., Tobin, R.L., Anandalingham, G.: A simulated annealing approach to the network design problem with variational inequality constraints. Transp. Sci. 26, 18–26 (1992)

    Article  Google Scholar 

  15. Friesz, T.L., Anandalingam, G., Mehta, N.J., Nam, K., Shah, S.J., Tobin, R.L.: The multi-objective equilibrium network design problem revisited —A simulated annealing approach. Eur. J. Oper. Res. 65, 44–57 (1993)

    Article  Google Scholar 

  16. Gao, Z., Wu, J., Sun, H.: Solution algorithm for the bi-level discrete network design problem. Transp. Res. Part B 39, 479–495 (2005)

    Article  Google Scholar 

  17. Johnson, D.S., Lenstra, J.K., Rinooy Kan, A.H.G.: The complexity of the network design problem. Networks 8, 279–285 (1978)

    Article  Google Scholar 

  18. Karoonsoontawong, A. and Waller, S.T.: Dynamic continuous network design problem—Linear bi-level programming and meta-heuristic approaches. Network Modeling 2006, Transp. Res. Rec., 104–117 (2006)

  19. Konak, A., Coit, D.W., Smith, A.E.: Multi-objective optimization using genetic algorithms: a tutorial. Reliab. Eng. Syst. Saf. 91, 992–1007 (2006)

    Article  Google Scholar 

  20. LeBlanc, L.J.: An algorithm for the discrete network design problem. Transp. Sci. 9, 183–199 (1975)

    Article  Google Scholar 

  21. LeBlanc, L.J., Abdulaal, M.: An efficient dual approach to the urban network design problem. Comput. & Math. Appl. 5, 11–19 (1978)

    Article  Google Scholar 

  22. Loon Van, A.A.P.M., Wismans, L.J.J.: Gebiedsgericht Benutten plus Duurzaam Veilig met RBV. Verkeerskunde DVM-congres 2007 (2007)

  23. Mathew, T. V., S. Sharma.: Continuous network design with emission pricing as a bi-level optimization problem. Applications of advanced technology in transportation. In: Proceedings of the Ninth international conference on applications of advanced technology in transportation, Chicago, IL (2006)

  24. Mathew, T.V., Sharma, S.: Capacity Expansion Problem for Large Urban Transportation Networks. J. Transp. Eng. ASCE 135(7), 406–415 (2009)

    Article  Google Scholar 

  25. Mathew, T.V., Sharma, S.: Multiobjective network design for emission and travel-time trade-off for a sustainable large urban transportation network. Environ. Plan. B Plan. Des. 38, 520–538 (2011)

    Article  Google Scholar 

  26. Memon, G.Q., Bullen, A.G.R.: Multivariant optimization strategies for real-time traffic control signals. Transp. Res. Rec. 1554, 36–42 (1997)

    Article  Google Scholar 

  27. 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. Part B 35, 83–105 (2001)

    Article  Google Scholar 

  28. Ministerie van Volkshuisvesting, Ruimtelijke Ordening en Milieubeheer (VROM): Meet- en rekenvoorschriften voor luchtkwaliteit, www.vrom.nl (2006) (last visit: 14-08-2009)

  29. Poorzahedy, H., Turnquist, M.A.: Approximate algorithms for the discrete network design problem. Transp. Res. B 16B, 45–55 (1982)

    Article  Google Scholar 

  30. Poorzahedy, H., Rouhani, O.M.: Hybrid meta-heuristic algorithms for solving network design problem. Eur. J. Oper. Res. 182, 578–596 (2007)

    Article  Google Scholar 

  31. Sharma, S., Ukkusuri, S.V., Mathew, T.V.: Pareto optimal multi-objective optimization for robust transportation network design problem. Transp. Res. Rec. 2090, 95–104 (2009)

    Article  Google Scholar 

  32. Sharma, S., Mathew, T.V.: Multi-objective network design for emission and travel-time trade-off for a sustainable large urban transportation network. Environ. Plann. B 38, 520–538 (2011)

    Article  Google Scholar 

  33. Smith, K.I.: A study of simulated annealing techniques for multi-objective optimization. Thesis for the degree of Doctor of Philosophy in Computer Science at the University of Exeter, Exeter (2006)

    Google Scholar 

  34. Steenbrink, P.A.: Optimization of transport network. John Wiley, New York (1974)

    Google Scholar 

  35. Tan, K.C., Khor, E.F., Lee, T.H.: Multiobjective evolutionary algorithms and applications. Springer, London (2005)

    Google Scholar 

  36. Tzeng, G.H., Tsaur, S.H.: Application of multiple criteria decision making for network improvement. J. Adv. Transp. 31(1), 49–74 (1997)

    Article  Google Scholar 

  37. Wismans, L.J.J., van Berkum, E.C., Bliemer, M.C.J.: Comparison of multiobjective evolutionary algorithms for optimization of externalities using dynamic traffic management measures. Transp. Res. Rec. 2263, 163–173 (2011)

    Article  Google Scholar 

  38. Wismans, L.J.J., Brands, T., Van Berkum, E.C., Bliemer, M.C.J.: Pruning and ranking the Pareto optimal set, application for the dynamic multi-objective network design problem. J. Adv. Transp. 48(6), 588–607 (2014)

    Article  Google Scholar 

  39. Xu, T., Wei, H., Wang, Z.: Study on continuous network design problem using simulated annealing and genetic algorithm. Exp. Syst. Appl. 36, 2735–2741 (2009)

    Article  Google Scholar 

  40. Yang, H., Bell, M.G.H.: Models and algorithms for road network design: a review and some new developments. Transp. Rev. 18(3), 257–278 (1998)

    Article  Google Scholar 

  41. Yin, Y.: Multiobjective bilevel optimization for transport planning and management problems. J. Adv. Transp. 36(1), 93–105 (2002)

    Article  Google Scholar 

  42. Zhang, G., Lu, J.: Genetic algorithm for continuous network design problem. J. Transp. Syst. Eng. Inform. Technol. 7, 101–105 (2007)

    Google Scholar 

  43. Zhao, F., Zeng, X.: Simulated annealing-genetic algorithm for transit network optimization. J. Comput. Civil Eng. 20, 57–68 (2006)

    Article  Google Scholar 

Download references

Acknowledgments

The authors are grateful for the financial contributions of Goudappel Coffeng and the ATMA (Advanced Traffic MAnagement) and Pay-as-you-drive projects of the TRANSUMO program. TRANSUMO (TRANsition SUstainable MObility) is a Dutch platform for companies, governments and knowledge institutes that cooperate in the development of knowledge with regard to sustainable mobility.

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Correspondence to Bastiaan Possel.

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Possel, B., Wismans, L.J.J., Van Berkum, E.C. et al. The multi-objective network design problem using minimizing externalities as objectives: comparison of a genetic algorithm and simulated annealing framework. Transportation 45, 545–572 (2018). https://doi.org/10.1007/s11116-016-9738-y

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Keywords

  • Multi-objective network design problem
  • Externalities
  • Genetic algorithm
  • Simulated annealing
  • Accessibility
  • Traffic safety
  • Emission