Numerical Approach of Network Problems in Optimal Mass Transportation

Affiliation(s)

Laboratory of Mathematics of Decision and Numerical Analysis (LMDAN), FASEG, University of Cheikh Anta Diop, Dakar, Senegal.

Unité Mixte Internationale, UMMISCO, Institut de Recherche pour le Développement, Bondy, France.

Laboratory of Mathematics of Decision and Numerical Analysis (LMDAN), FASEG, University of Cheikh Anta Diop, Dakar, Senegal.

Unité Mixte Internationale, UMMISCO, Institut de Recherche pour le Développement, Bondy, France.

Abstract

In this paper, we focus on the theoretical and numerical aspects of network problems. For an illustration, we consider the urban traffic problems. And our effort is concentrated on the numerical questions to locate the optimal network in a given domain (for example a town). Mainly, our aim is to find the network so as the distance between the population position and the network is minimized. Another problem that we are interested is to give an numerical approach of the Monge and Kantorovitch problems. In the literature, many formulations (see for example [1-4]) have not yet practical applications which deal with the permutation of points. Let us mention interesting numerical works due to E. Oudet begun since at least in 2002. He used genetic algorithms to identify optimal network (see [5]). In this paper we introduce a new reformulation of the problem by introducing permutations . And some examples, based on realistic scenarios, are solved.

In this paper, we focus on the theoretical and numerical aspects of network problems. For an illustration, we consider the urban traffic problems. And our effort is concentrated on the numerical questions to locate the optimal network in a given domain (for example a town). Mainly, our aim is to find the network so as the distance between the population position and the network is minimized. Another problem that we are interested is to give an numerical approach of the Monge and Kantorovitch problems. In the literature, many formulations (see for example [1-4]) have not yet practical applications which deal with the permutation of points. Let us mention interesting numerical works due to E. Oudet begun since at least in 2002. He used genetic algorithms to identify optimal network (see [5]). In this paper we introduce a new reformulation of the problem by introducing permutations . And some examples, based on realistic scenarios, are solved.

Keywords

Optimal Mass Transportation; Network; Urban Traffic; Monge-Kantorovich Problem; Global Optimization

Optimal Mass Transportation; Network; Urban Traffic; Monge-Kantorovich Problem; Global Optimization

Cite this paper

L. Ndiaye, B. Ndiaye, P. Mendy and D. Seck, "Numerical Approach of Network Problems in Optimal Mass Transportation,"*Applied Mathematics*, Vol. 3 No. 5, 2012, pp. 457-466. doi: 10.4236/am.2012.35069.

L. Ndiaye, B. Ndiaye, P. Mendy and D. Seck, "Numerical Approach of Network Problems in Optimal Mass Transportation,"

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