L. C. Evans and W. Gangbo, “Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem,” Memoirs of the American Mathematical Society, Vol. 137, No. 653, 1999, pp. 1-66.

has been cited by the following article:

• TITLE: Numerical Approach of Network Problems in Optimal Mass Transportation

  AUTHORS: Lamine Ndiaye, Babacar Mbaye Ndiaye, Pierre Mendy, Diaraf Seck

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

  JOURNAL NAME: Applied Mathematics, Vol.3 No.5, May 16, 2012

  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.