# 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

top- [1] L. Ambrosio and P. Tilli, Selected Topics on “Analysis on Metric Spaces”. Appunti dei Corsi Tenuti da Docenti della Scuola, Scuola Normale Superiore, Pisa (2000). Zbl1084.28500
- [2] G. Bouchitté and G. Buttazzo, Characterization of Optimal Shapes and Masses through Monge-Kantorovich Equation. J. Eur. Math. Soc. (JEMS) 3 (2001) 139–168. Zbl0982.49025
- [3] A. Brancolini, Problemi di Ottimizzazione in Teoria del Trasporto e Applicazioni. Master’s thesis, Università di Pisa, Pisa (2002). Available at http://www.sns.it/~brancoli/
- [4] G. Buttazzo, Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations. Pitman Research Notes in Mathematics Series 207. Longman Scientific & Technical, Harlow (1989). Zbl0669.49005MR1020296
- [5] G. Buttazzo and L. De Pascale, Optimal Shapes and Masses, and Optimal Transportation Problems, in Optimal Transportation and Applications (Martina Franca, 2001). Lecture Notes in Mathematics, CIME series 1813, Springer-Verlag, Berlin (2003) 11–52. Zbl1087.49033
- [6] G. Buttazzo, E. Oudet and E. Stepanov, Optimal Transportation Problems with Free Dirichlet Regions, in Variational Methods for Discontinuous Structures (Cernobbio, 2001). Progress in Nonlinear Differential Equations and their Applications 51, Birkhäuser Verlag, Basel (2002) 41–65. Zbl1055.49029
- [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
- [9] K.J. Falconer, The Geometry of Fractal Sets. Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge (1986). Zbl0587.28004MR867284
- [10] L.V. Kantorovich, On the Transfer of Masses. Dokl. Akad. Nauk. SSSR (1942).
- [11] L.V. Kantorovich, On a Problem of Monge. Uspekhi Mat. Nauk. (1948).
- [12] G. Monge, Mémoire sur la théorie des Déblais et des Remblais. Histoire de l’Acad. des Sciences de Paris (1781) 666–704.
- [13] S.J.N. Mosconi and P. Tilli, $\Gamma $-convergence for the Irrigation Problem. Preprint Scuola Normale Superiore, Pisa (2003). Available at http://cvgmt.sns.it/ Zbl1076.49024MR2135803

## Citations in EuDML Documents

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

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