Designing optimal networks for multicommodity transport problem

@article{Lonardi2021DesigningON,
  title={Designing optimal networks for multicommodity transport problem},
  author={Alessandro Lonardi and Enrico Facca and Mario Putti and Caterina De Bacco},
  journal={Physical Review Research},
  year={2021}
}
Designing and optimizing different flows in networks is a relevant problem in many contexts. While a number of methods have been proposed in the physics and optimal transport literature for the onecommodity case, we lack similar results for the multi-commodity scenario. In this paper we present a model based on optimal transport theory for finding optimal multi-commodity flow configurations on networks. This model introduces a dynamics that regulates the edge conductivities to achieve, at… 

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References

SHOWING 1-10 OF 32 REFERENCES

OPTIMAL PATHS RELATED TO TRANSPORT PROBLEMS

In transport problems of Monge's types, the total cost of a transport map is usually an integral of some function of the distance, such as |x - y|p. In many real applications, the actual cost may

STRUCTURE

Network extraction by routing optimization

TLDR
This work introduces a method to extract network topologies from dynamical equations related to routing optimization under various parameters’ settings and proposes a principled model to address the filtering in the last step, and gives a quantitative interpretation in terms of a transport-related cost function.

Adaptation and optimization of biological transport networks.

TLDR
The adaptation dynamics minimizes the global energy consumption to produce optimal networks, which may possess hierarchical loop structures in the presence of strong fluctuations in flow distribution, and shows that there may exist a new phase transition as there is a critical open probability of sinks.

Fluctuations and redundancy in optimal transport networks.

  • F. Corson
  • Computer Science
    Physical review letters
  • 2010
TLDR
It is shown here that it is contingent on the assumption of a stationary flow through the network that optimal networks are trees, and when time variations or fluctuations are allowed for, a different class of optimal structures is found, which share the hierarchical organization of trees yet contain loops.

Optimal transport in multilayer networks

TLDR
A model where optimal flows on different layers contribute differently to the total cost to be minimized is proposed, done by means of a parameter that varies with layers, which allows to flexibly tune the sensitivity to the traffic congestion of the various layers.

Discontinuous transition to loop formation in optimal supply networks

TLDR
It is demonstrated that loops emerge discontinuously when decreasing the costs for new edges for both an edge-damage model and a fluctuating sink model, and an intimate relationship among betweenness measures and optimal tree networks is unveiled.

The multicommodity network flow problem: state of the art classification, applications, and solution methods

TLDR
A taxonomic review of the MCNF literature published between 2000 and 2019 is presented, based on an adapted version of an existing comprehensive taxonomy, which categorizes 263 articles into two main categories of applications and solution methods.

and s

Optimal Transport Flows for Distributed Production Networks.

TLDR
This work shows how optimizing the transport time yields network topologies that match those observed in the insulin-producing pancreatic islets, and obtained flow networks are broadly independent of how the flow velocity depends on the flow flux, but continuous and discontinuous phase transitions appear at extreme flux dependencies.