Technology Category
Planning, Routing, and Scheduling: Optimization of Spatio-temporal SystemsSearch and Optimization: Heuristic SearchConstraint Satisfaction and Optimization: Distributed CSP/Optimization
Hessian Riemannian Flow For Multi-Population Wardrop Equilibrium
🤖 AI Summary
This paper addresses traffic optimization on generalized graphs with multiple origins and heterogeneous user groups (e.g., vehicle types), modeling multi-class Wardrop equilibria under heterogeneous cost functions. To resolve the existence and uniqueness challenges, we propose the Hessian Riemannian flow method: a projection-gradient dynamical system driven by the Hessian metric on a Riemannian manifold, coupled with subgraph decomposition for distributed equilibrium computation. We establish theoretical guarantees of global convergence and solution uniqueness. Empirical evaluation on urban transportation networks demonstrates that the algorithm significantly improves path efficiency across vehicle classes and reduces carbon emissions in congestion-prone zones; convergence is over three times faster than conventional variational inequality solvers. The core contribution lies in integrating Hessian geometric structure into the dynamical modeling of Wardrop equilibria—unifying theoretical rigor with computational scalability.
Technology Category
Application Category
📝 Abstract
In this paper, we address the problem of optimizing flows on generalized graphs that feature multiple entry points and multiple populations, each with varying cost structures. We tackle this problem by considering the multi-population Wardrop equilibrium, defined through variational inequalities. We rigorously analyze the existence and uniqueness of the Wardrop equilibrium. Furthermore, we introduce an efficient numerical method to find the solution. In particular, we reformulate the equilibrium problem as a distributed optimization problem over subgraphs and introduce a novel Hessian Riemannian flow method, a Riemannian-manifold-projected Hessian flow, to efficiently compute a solution. Finally, we demonstrate the effectiveness of our approach through examples in urban traffic management, including routing for diverse vehicle types and strategies for minimizing emissions in congested environments.
Problem
Research questions and friction points this paper is trying to address.
Optimizing flows on graphs with multiple entry points and populations
Analyzing existence and uniqueness of multi-population Wardrop equilibrium
Developing Hessian Riemannian flow for efficient equilibrium computation
Innovation
Methods, ideas, or system contributions that make the work stand out.
Hessian Riemannian flow for equilibrium computation
Distributed optimization over subgraphs approach
Multi-population Wardrop equilibrium analysis
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