Solving Continuous Network Design Problem with Generalized Geometric Programming Approach

Abstract

To satisfy growing travel demand and reduce traffic congestion, the continuous network design problem (CNDP) is often proposed to optimize road network performance by the expansion of road capacity. In the determination of the equilibrium travel flow pattern, equilibrium principles such as deterministic user equilibrium (DUE) and stochastic user equilibrium (SUE) may be applied to describe travelers’ route choice behavior. Because of the different mathematical formulation structures for the CNDP with DUE and SUE principles, most of the existing solution algorithms have been developed to solve the CNDP for either DUE or SUE. In this study, a more general solution method is proposed by applying the generalized geometric programming (GGP) approach to obtain the global optimal solution of the CNDP with both DUE and SUE principles. Specifically, the original CNDP problem is reformulated into a GGP form, and then a successive monomial approximation method is employed to transform the GGP formulation into a standard geometric programming form, which can be cast into an equivalent nonlinear but convex optimization problem whose global optimal solution can be guaranteed and solved by many existing solution algorithms. Numerical experiments are presented to demonstrate the validity and efficiency of the solution method.

A Continuous Transportation Network Design Problem with the Consideration of Road Congestion Charging

“…The first study of CNDPs based on SUE traffic assignment was presented by Davis [16], in which two different methods considering the effects of stochastic user equilibria were proposed for solving CNDPs, and these methods were applied to several test networks. Liu and Wang [17] and Du and Wang [18] proposed different methods for achieving the global solution of a CNDP by considering the SUE assumption. Similar to this study, Long et al [19] developed a bilevel programming model to solve the turning restriction design problem with SUE.…”

Improving the Performance of the Bilevel Solution for the Continuous Network Design Problem

“…After almost two decades, Liu and Wang [23] considered CNDP with SUE traffic assignment by using the logit route choice model, aiming to determine the global optimum solution. Du and Wang [24] proposed the generalized geometric programming method to achieve the global solution for CNDP by considering both DUE and SUE assumptions. As another type of road network design problems, the discrete network design problem (DNDP) with SUE constraint has been studied by Chen and Alfa [25].…”