Robust Optimization Approach for Transportation Network Design under Demand Uncertainty

Abstract

This paper reviews our recent developments on applying a robust optimization approach to transportation network design problems where future travel demands are uncertain and traffic flows on the underlying network are in user equilibrium. We assume that the travel demands belong to an uncertainty set instead of having them follow some probability distributions and then design the network against the worst-case scenario realized in the set. The problems are formulated as mathematical programs with complementarity constraints, which are efficiently solvable by a cutting-plane scheme. Numerical examples are provided to demonstrate that the designs from the robust optimization approach perform more stably and guard better against worst-case scenarios than those from traditional deterministic approach. INTRODUCTION Network design problem (NDP) for transportation networks has been extensively studied in the literature. The problem is to determine a plan for modifying a road network (e.g., adding new roads and increasing the capacities of the existing ones) in order to minimize the total system travel cost or to optimize another performance measure subject to a given budget. In the literature, NDP has been formulated as a bi-level optimization problem or, equivalently, mathematical program with equilibrium constraints (MPEC), where users’ responses in travel choices are captured by the lower-level user equilibrium (UE) problem or equilibrium constraints in form of a variational inequality. The formulation is thus nonlinear and non-convex, making it difficult to solve exactly. For an overview on NDP, see, e.g., Magnanti and Wong (1984) and Yang and Bell (1998). NDP can be classified into two general categories depending on how additional capacities are represented, either as continuous or discrete variables. In the literature, many have considered continuous NDP or CNDP because the problem is more computationally tractable. However, an additional capacity is always stated in the unit of one lane in practice, thereby suggesting that discrete NDP or DNDP is more practical. On the other hand, the presence of the integer variables makes DNDP more difficult to solve because the gradient-based ICCTP 2009: Critical Issues in Transportation Systems Planning, Development, and Management ©2009 ASCE 1237