# Optimal networks for mass transportation problems

Alessio Brancolini; Giuseppe Buttazzo

ESAIM: Control, Optimisation and Calculus of Variations (2005)

- Volume: 11, Issue: 1, page 88-101
- ISSN: 1292-8119

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topBrancolini, Alessio, and Buttazzo, Giuseppe. "Optimal networks for mass transportation problems." ESAIM: Control, Optimisation and Calculus of Variations 11.1 (2005): 88-101. <http://eudml.org/doc/245494>.

@article{Brancolini2005,

abstract = {In the framework of transport theory, we are interested in the following optimization problem: given the distributions $\mu ^+$ of working people and $\mu ^-$ of their working places in an urban area, build a transportation network (such as a railway or an underground system) which minimizes a functional depending on the geometry of the network through a particular cost function. The functional is defined as the Wasserstein distance of $\mu ^+$ from $\mu ^-$ with respect to a metric which depends on the transportation network.},

author = {Brancolini, Alessio, Buttazzo, Giuseppe},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {optimal networks; mass transportation problems; Monge-Kantorovich problem; optimal transportation; optimal transportation networks; mass transfer},

language = {eng},

number = {1},

pages = {88-101},

publisher = {EDP-Sciences},

title = {Optimal networks for mass transportation problems},

url = {http://eudml.org/doc/245494},

volume = {11},

year = {2005},

}

TY - JOUR

AU - Brancolini, Alessio

AU - Buttazzo, Giuseppe

TI - Optimal networks for mass transportation problems

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2005

PB - EDP-Sciences

VL - 11

IS - 1

SP - 88

EP - 101

AB - In the framework of transport theory, we are interested in the following optimization problem: given the distributions $\mu ^+$ of working people and $\mu ^-$ of their working places in an urban area, build a transportation network (such as a railway or an underground system) which minimizes a functional depending on the geometry of the network through a particular cost function. The functional is defined as the Wasserstein distance of $\mu ^+$ from $\mu ^-$ with respect to a metric which depends on the transportation network.

LA - eng

KW - optimal networks; mass transportation problems; Monge-Kantorovich problem; optimal transportation; optimal transportation networks; mass transfer

UR - http://eudml.org/doc/245494

ER -

## References

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- [7] G. Buttazzo and E. Stepanov, Optimal Transportation Networks as Free Dirichlet Regions for the Monge-Kantorovich Problem. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 2 (2003) 631–678. Zbl1127.49031
- [8] G. Dal Maso and R. Toader, A Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results. Arch. Rational Mech. Anal. 162 (2002) 101–135. Zbl1042.74002
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- [10] L.V. Kantorovich, On the Transfer of Masses. Dokl. Akad. Nauk. SSSR (1942).
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## Citations in EuDML Documents

top- Alessio Brancolini, Giuseppe Buttazzo, Filippo Santambrogio, Eugene Stepanov, Long-term planning versus short-term planning in the asymptotical location problem
- Alessio Brancolini, Giuseppe Buttazzo, Filippo Santambrogio, Eugene Stepanov, Long-term planning short-term planning in the asymptotical location problem

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