Designing optimal networks for multicommodity transport problem

Lonardi, Alessandro; Facca, Enrico; Putti, Mario; Bacco, Caterina De

doi:10.1103/physrevresearch.3.043010

Cited by 15 publications

(37 citation statements)

References 27 publications

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“…Recent studies [25,26] have shown that this theoretical formalism can be adapted to address multicommodity scenarios, generalizing well-established results for unicommodity models [27][28][29][30][31][32][33]. The works of Lonardi et al [25] and Bonifaci et al [26] focus on a theoretical characterization of the problem, drawing a formal connection between optimal transport and an equivalent dynamical system that is formulated in terms of physical quantities like conductivities and fluxes. They provide theoretical guarantees that are valid for a particular choice of the transport cost function.…”

Section: Introductionmentioning

confidence: 79%

“…( 2) regulates the time evolution of the conductivities by means of a feedback mechanism where the higher the flux on an edge, the larger its conductivity µ e . All commodities share one unique infrastructure, so we follow [25] and assume that µ e is the same for all i.…”

Section: A Multicommodity Routing On Networkmentioning

confidence: 99%

“…The growth in time of µ e is governed by the function f (•), that in multicommodity optimal transport settings is typically an increasing and differentiable function of some norm of the fluxes [25,26]. The aim of our work is to investigate how different expressions of f (•) result in different distributions of passengers flows, thus we focus on the following two choices: (i) f (x) = ||x|| 2 2 (2-norm), and (ii) f (x) = ||x|| 2 1 (1-norm).…”

Section: A Multicommodity Routing On Networkmentioning

confidence: 99%

“…The aim of our work is to investigate how different expressions of f (•) result in different distributions of passengers flows, thus we focus on the following two choices: (i) f (x) = ||x|| 2 2 (2-norm), and (ii) f (x) = ||x|| 2 1 (1-norm). The first is supported by theoretical groundings as derived in [25]. However, it may not be the most appropriate one in applications involving transport of passengers, as the 2-norm does not have a straightforward interpretation in these cases.…”

Section: A Multicommodity Routing On Networkmentioning

confidence: 99%

“…The first choice is more intuitive, since counting the total number of users in a network is a natural metric to evaluate its occupancy. However, the second one provides strong theoretical guarantees in terms of optimal transport theory [25,26].…”

Section: Introductionmentioning

confidence: 99%

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Multicommodity routing optimization for engineering networks

Lonardi,

Putti,

De Bacco

2021

Preprint

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Optimizing passengers routes is crucial to design efficient transportation networks. Recent results show that optimal transport provides an efficient alternative to standard optimization methods. However, it is not yet clear if this formalism has empirical validity on engineering networks. We address this issue by considering different response functions-quantities determining the interaction between passengers-in the dynamics implementing the optimal transport formulation. Particularly, we compare a theoretically-grounded response function with one that is intuitive for settings involving transportation of passengers, albeit lacking theoretical justifications. We investigate these two modeling choices on the Paris metro and analyze how they reflect on passengers' fluxes. We measure the extent of traffic bottlenecks and infrastructure resilience to node removal, showing that the two settings are equivalent in the congested transport regime, but different in the branched one. In the latter, the two formulations differ on how fluxes are distributed, with one function favoring routes consolidation, thus potentially being prone to generate traffic overload. Additionally, we compare our method to Dijkstra's algorithm to show its capacity to efficiently recover shortest-path-like graphs. Finally, we observe that optimal transport networks lie in the Pareto front drawn by the energy dissipated by passengers, and the cost to build the infrastructure.

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Section: Introductionmentioning

confidence: 79%

Section: A Multicommodity Routing On Networkmentioning

confidence: 99%

Section: A Multicommodity Routing On Networkmentioning

confidence: 99%

Section: A Multicommodity Routing On Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multicommodity routing optimization for engineering networks

Lonardi,

Putti,

De Bacco

2021

Preprint

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Similarity and economy of scale in urban transportation networks and optimal transport-based infrastructures

Leite,

De Bacco

2024

Nat Commun

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Designing and optimizing the structure of urban transportation networks is a challenging task. In this study, we propose a method inspired by optimal transport theory and the principle of economy of scale that uses little information in input to generate structures that are similar to those of public transportation networks. Contrarily to standard approaches, it does not assume any initial backbone network infrastructure but rather extracts this directly from a continuous space using only a few origin and destination points, generating networks from scratch. Analyzing a set of urban train, tram and subway networks, we find a noteworthy degree of similarity in several of the studied cases between simulated and real infrastructures. By tuning one parameter, our method can simulate a range of different subway, tram and train networks that can be further used to suggest possible improvements in terms of relevant transportation properties. Outputs of our algorithm provide naturally a principled quantitative measure of similarity between two networks that can be used to automatize the selection of similar simulated networks.

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Multicommodity routing optimization for engineering networks

Lonardi

Putti

Bacco

2022

Sci Rep

Self Cite

View full text Add to dashboard Cite

Optimizing passengers routes is crucial to design efficient transportation networks. Recent results show that optimal transport provides an efficient alternative to standard optimization methods. However, it is not yet clear if this formalism has empirical validity on engineering networks. We address this issue by considering different response functions—quantities determining the interaction between passengers—in the dynamics implementing the optimal transport formulation. Particularly, we couple passengers’ fluxes by taking their sum or the sum of their squares. The first choice naturally reflects edges occupancy in transportation networks, however the second guarantees convergence to an optimal configuration of flows. Both modeling choices are applied to the Paris metro. We measure the extent of traffic bottlenecks and infrastructure resilience to node removal, showing that the two settings are equivalent in the congested transport regime, but different in the branched one. In the latter, the two formulations differ on how fluxes are distributed, with one function favoring routes consolidation, thus potentially being prone to generate traffic overload. Additionally, we compare our method to Dijkstra’s algorithm to show its capacity to efficiently recover shortest-path-like graphs. Finally, we observe that optimal transport networks lie in the Pareto front drawn by the energy dissipated by passengers, and the cost to build the infrastructure.

show abstract

Designing optimal networks for multicommodity transport problem

Cited by 15 publications

References 27 publications

Multicommodity routing optimization for engineering networks

Multicommodity routing optimization for engineering networks

Similarity and economy of scale in urban transportation networks and optimal transport-based infrastructures

Multicommodity routing optimization for engineering networks

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