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Characterization of optimal shapes and masses through Monge-Kantorovich equation

Guy Bouchitté, Giuseppe Buttazzo (2001)

Journal of the European Mathematical Society

We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both cases some examples are presented.

Choix multicritères dans le risque et variables multidimensionnelles: proposition de méthode et application aux réseaux de transport d'énergie

Bertrand Munier, Nathalie Taverdet-Popiolek (2010)

RAIRO - Operations Research

This paper presents an application of Multiple Attribute Utility Theory on strategic choices concerning energy transportation. The environmental assessment of a network reinforcement strategy is emphasized. Our assessment brings about to consider multidimensional variables in MCDM. However, Multi-Attributed Utility Theory (MAUT) cannot, as a practical matter, manage such variables. We therefore work out a methodology to transform multidimensional variables into unidimensional ones. We apply...

Combination of mobile agent and evolutionary algorithm to optimize the client transport services

Hayfa Zgaya, Slim Hammadi, Khaled Ghédira (2008)

RAIRO - Operations Research

This paper presents a migration strategy for a set of mobile agents (MAs) in order to satisfy customers' requests in a transport network, through a multimodal information system. In this context, we propose an optimization solution which operates on two levels. The first one aims to constitute a set of MAs building their routes, called Workplans. At this level, Workplans must incorporate all nodes, representing information providers in the multimodal network, in order to explore it completely....

Construction of a Φ-function for two convex polytopes

Y. Stoyan, J. Terno, M. Gil, T. Romanova, G. Scheithauer (2002)

Applicationes Mathematicae

The analytical description of Φ-functions for two convex polytopes is investigated. These Φ-functions can be used for mathematical modelling of packing problems in the three-dimensional space. Only translations of the polytopes are considered. The approach consists of two stages. First the 0-level surface of a Φ-function is constructed, and secondly, the surface is extended to get the Φ-function. The method for constructing the 0-level surface is described in detail.

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