Robust Transportation Network Design Under Demand Uncertainty

Abstract: This article addresses the problem of a traffic network design problem (NDP) under demand uncertainty. The origin–destination trip matrices are taken as random variables with known probability distributions. Instead of finding optimal network design solutions for a given future scenario, we are concerned with solutions that are in some sense “good” for a variety of demand realizations. We introduce a definition of robustness accounting for the planner's required degree of robustness. We propose a formulation of the robust network design problem (RNDP) and develop a methodology based on genetic algorithm (GA) to solve the RNDP. The proposed model generates globally near-optimal network design solutions, f, based on the planner's input for robustness. The study makes two important contributions to the network design literature. First, robust network design solutions are significantly different from the deterministic NDPs and not accounting for them could potentially underestimate the network-wide impacts. Second, systematic evaluation of the performance of the model and solution algorithm is conducted on different test networks and budget levels to explore the efficacy of this approach. The results highlight the importance of accounting for robustness in transportation planning and the proposed approach is capable of producing high-quality solutions.

[1]  D.A. Van Veldhuizen,et al.  On measuring multiobjective evolutionary algorithm performance , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[2]  Larry J. LeBlanc,et al.  CONTINUOUS EQUILIBRIUM NETWORK DESIGN MODELS , 1979 .

[3]  H. Poorzahedy,et al.  Application of Ant System to network design problem , 2005 .

[4]  Terry L. Friesz,et al.  A Simulated Annealing Approach to the Network Design Problem with Variational Inequality Constraints , 1992, Transp. Sci..

[5]  Dean A. Jones,et al.  Robust optimization for fleet planning under uncertainty , 2003 .

[6]  Larry J. LeBlanc,et al.  An Algorithm for the Discrete Network Design Problem , 1975 .

[7]  Clermont Dupuis,et al.  An Efficient Method for Computing Traffic Equilibria in Networks with Asymmetric Transportation Costs , 1984, Transp. Sci..

[8]  Hai Yang,et al.  Models and algorithms for road network design: a review and some new developments , 1998 .

[9]  Gary A. Davis,et al.  Exact local solution of the continuous network design problem via stochastic user equilibrium assignment , 1994 .

[10]  Genaro J. Gutierrez,et al.  A robustness approach to international sourcing , 1995, Ann. Oper. Res..

[11]  Hoang Hai Hoc,et al.  Topological optimization of networks: A nonlinear mixed integer model employing generalized benders , 1980 .

[12]  Athanasios K. Ziliaskopoulos,et al.  Stochastic Dynamic Network Design Problem , 2001 .

[13]  B. Rustem,et al.  Robust capacity planning under uncertainty , 1991 .

[14]  Zvi Drezner,et al.  Using hybrid metaheuristics for the one‐way and two‐way network design problem , 2002 .

[15]  Scott A. Malcolm,et al.  Robust Optimization for Power Systems Capacity Expansion under Uncertainty , 1994 .

[16]  Alper Atamtürk Strong Formulations of Robust Mixed 0–1 Programming , 2006, Math. Program..

[17]  T. Friesz,et al.  The multiobjective equilibrium network design problem revisited: A simulated annealing approach , 1993 .

[18]  Terry L. Friesz,et al.  Equilibrium Decomposed Optimization: A Heuristic for the Continuous Equilibrium Network Design Problem , 1987, Transp. Sci..

[19]  Larry J. LeBlanc,et al.  A comparison of user-optimum versus system-optimum traffic assignment in transportation network design , 1984 .

[20]  Marc Goetschalckx,et al.  A stochastic programming approach for supply chain network design under uncertainty , 2004, Eur. J. Oper. Res..

[21]  George B. Dantzig,et al.  Formulating and solving the network design problem by decomposition , 1979 .

[22]  Satish V. Ukkusuri,et al.  Single-Point Approximations for Traffic Equilibrium Problem under Uncertain Demand , 2006 .

[23]  T L Friesz,et al.  BOUNDING THE SOLUTION OF THE CONTINUOUS EQUILIBRIUM NETWORK DESIGN PROBLEM , 1984 .

[24]  Jerry B. Schneider,et al.  Processing of Constraints in Transportation Network Design Problem , 1995 .