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This paper aims to provide a state-of-the-art review of the transport network design problem (NDP) under uncertainty and to present some new developments on a biobjective reliable network design problem (BORNDP) model that explicitly optimizes the capacity reliability and travel time reliability under demand uncertainty. Both are useful performance measures that can describe the supply-side reliability and demand side reliability of a road network. A simulation-based multi-objective genetic algorithm (SMOGA) solution procedure, which consists of a traffic assignment algorithm, a genetic algorithm, a Pareto filter, and a Monte-Carlo simulation, is developed to solve the proposed BORNDP model. A numerical example based on the capacity enhancement problem is presented to demonstrate the tradeoff between capacity reliability and travel time reliability in the NDP.

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Uncertainties are unavoidable in engineering applications. A new model is proposed for designing networks under uncertainty of future demands. The objective is to minimize the total travel time budget required to satisfy the total travel time reliability constraint while considering the route choice behavior of network users. The model adopts the value-at-risk risk measure instead of the utility function to model planner risk preferences. It allows the planners to specify their risk preferences by using a confidence level of alpha on the total travel time reliability. This alpha reliable network design model is formulated as a stochastic bilevel optimization problem. The upper-level subprogram is a variant of the chance-constrained model that minimizes the total travel time budget subject to a chance constraint with a user-specified confidence level, a budget constraint, and design variable constraints; the lower-level subprogram is a user-equilibrium problem under demand uncertainty. A simulation-based genetic algorithm procedure is developed to solve this complex network design problem (NDP). Two numerical examples are presented to illustrate the features of the proposed NDP model.

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