Primal-Dual Gradient Methods for Searching Network Equilibria in Combined Models with Nested Choice Structure and Capacity Constraints

TL;DR

This paper develops primal-dual gradient methods to solve network equilibrium models with capacity constraints, extending existing models to include stable dynamics and providing convergence guarantees through theoretical analysis and numerical experiments.

Contribution

It introduces an extension of the combined network equilibrium model to include stable dynamics with capacity constraints and proposes accelerated gradient methods with proven convergence.

Findings

Effective solution methods for capacity-constrained network equilibrium models.

Theoretical convergence guarantees for the proposed algorithms.

Numerical validation on Moscow and Berlin transportation networks.

Abstract

We consider a network equilibrium model (i.e. a combined model), which was proposed as an alternative to the classic four-step approach for travel forecasting in transportation networks. This model can be formulated as a convex minimization program. We extend the combined model to the case of the stable dynamics (SD) model in the traffic assignment stage, which imposes strict capacity constraints in the network. We propose a way to solve corresponding dual optimization problems with accelerated gradient methods and give theoretical guarantees of their convergence. We conducted numerical experiments with considered optimization methods on Moscow and Berlin networks.