The network design problem （NDP） is one of the most difficult and challenging problems in transportation. Traditional NDP models are often posed as a deterministic bilevel program assuming that all relevant inputs a...The network design problem （NDP） is one of the most difficult and challenging problems in transportation. Traditional NDP models are often posed as a deterministic bilevel program assuming that all relevant inputs are known with certainty. This paper presents three stochastic models for designing transportation networks with demand uncertainty. These three stochastic NDP models were formulated as the expected value model, chance-constrained model, and dependent-chance model in a bilevel programming framework using different criteria to hedge against demand uncertainty. Solution procedures based on the traffic assignment algorithm, genetic algorithm, and Monte-Carlo simulations were developed to solve these stochastic NDP models. The nonlinear and nonconvex nature of the bilevel program was handled by the genetic algorithm and traffic assignment algorithm, whereas the stochastic nature was addressed through simulations. Numerical experiments were conducted to evaluate the applicability of the stochastic NDP models and the solution procedure. Results from the three experiments show that the solution procedures are quite robust to different parameter settings.展开更多
In this paper, we propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]....In this paper, we propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]. We study the statistical properties of obtained SAA estimators. In particular we show that under moderate conditions a sequence of weak stationary points of SAA programs converge to a weak stationary point of the true problem with probability approaching one at exponential rate as the sample size tends to infinity. To implement the SAA method more efficiently, we incorporate the method with some techniques such as Scholtes＇ regularization method and the well known smoothing NCP method. Some preliminary numerical results are reported.展开更多
基金Supported by the National Science Foundation (No. CMS-0134161) of the United Statesthe Visiting Professor Fellowship from the University of Seoul, Korea
文摘The network design problem （NDP） is one of the most difficult and challenging problems in transportation. Traditional NDP models are often posed as a deterministic bilevel program assuming that all relevant inputs are known with certainty. This paper presents three stochastic models for designing transportation networks with demand uncertainty. These three stochastic NDP models were formulated as the expected value model, chance-constrained model, and dependent-chance model in a bilevel programming framework using different criteria to hedge against demand uncertainty. Solution procedures based on the traffic assignment algorithm, genetic algorithm, and Monte-Carlo simulations were developed to solve these stochastic NDP models. The nonlinear and nonconvex nature of the bilevel program was handled by the genetic algorithm and traffic assignment algorithm, whereas the stochastic nature was addressed through simulations. Numerical experiments were conducted to evaluate the applicability of the stochastic NDP models and the solution procedure. Results from the three experiments show that the solution procedures are quite robust to different parameter settings.
文摘In this paper, we propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]. We study the statistical properties of obtained SAA estimators. In particular we show that under moderate conditions a sequence of weak stationary points of SAA programs converge to a weak stationary point of the true problem with probability approaching one at exponential rate as the sample size tends to infinity. To implement the SAA method more efficiently, we incorporate the method with some techniques such as Scholtes＇ regularization method and the well known smoothing NCP method. Some preliminary numerical results are reported.
