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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 541782, 8 pages
Research Article

A Nondominated Genetic Algorithm Procedure for Multiobjective Discrete Network Design under Demand Uncertainty

1Institute of Transportation Engineering, Tsinghua University, Beijing 100084, China
2China Academy of Urban Planning and Design, Beijing 100044, China

Received 9 December 2014; Accepted 12 January 2015

Academic Editor: Wei (David) Fan

Copyright © 2015 Bian Changzhi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper addresses the multiobjective discrete network design problem under demand uncertainty. The OD travel demands are supposed to be random variables with the given probability distribution. The problem is formulated as a bilevel stochastic optimization model where the decision maker’s objective is to minimize the construction cost, the expectation, and the standard deviation of total travel time simultaneously and the user’s route choice is described using user equilibrium model on the improved network under all scenarios of uncertain demand. The proposed model generates globally near-optimal Pareto solutions for network configurations based on the Monte Carlo simulation and nondominated sorting genetic algorithms II. Numerical experiments implemented on Nguyen-Dupuis test network show trade-offs among construction cost, the expectation, and standard deviation of total travel time under uncertainty are obvious. Investment on transportation facilities is an efficient method to improve the network performance and reduce risk under demand uncertainty, but it has an obvious marginal decreasing effect.