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

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.