Hessian Riemannian Flow For Multi-Population Wardrop Equilibrium
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912341137817600 |
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| author | Bakaryan, Tigran Aoun, Christoph Ribeiro, Ricardo de Lima Hovakimyan, Naira Gomes, Diogo |
| author_facet | Bakaryan, Tigran Aoun, Christoph Ribeiro, Ricardo de Lima Hovakimyan, Naira Gomes, Diogo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16028 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hessian Riemannian Flow For Multi-Population Wardrop Equilibrium Bakaryan, Tigran Aoun, Christoph Ribeiro, Ricardo de Lima Hovakimyan, Naira Gomes, Diogo Systems and Control Multiagent Systems Optimization and Control 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. |
| title | Hessian Riemannian Flow For Multi-Population Wardrop Equilibrium |
| topic | Systems and Control Multiagent Systems Optimization and Control |
| url | https://arxiv.org/abs/2504.16028 |