[TD07] Two approaches for solving a continuous location problem: Stochastic geometry and Operational Research

Conférence Internationale avec comité de lecture : International Network Optimization Conference, Spa,, January 2007, pp.7,
Résumé: When a network operator has to decide on the location of network facilities on a territory, real data has to be considered in order to optimize the locations. The amount of data can be really huge: for example thousands of connected subscribers can be considered for a specific area. Such large scale problems require the use of efficient solution methods. However, location problems are generally difficult to solve exactly [i,ii]. Several ways exist to obtain good solutions in a limited time: approximation algorithms, heuristics, etc… But the size of the instances is still an issue and one way to circumvent it is to make some abstraction about real data. An approach based on Stochastic Geometry [iii,iv] is currently studied at France Telecom R&D. The idea is to define realistic models for telecommunication network architectures capturing the spatial distribution of the network elements and having a limited number of parameters. The models are probabilistic and the parameters can be set in order to fit, on average, the characteristics of real data. The important point is that these models don't depend on the size of the instances. However, they can't be used to solve exactly specific instances. In this article, we present our first results concerning the comparison between Stochastic Geometry and Operational Research approaches, and discuss the interest of a hybrid of both methods. We focus on a particular Weber problem in a hierarchical network which has been already studied with Stochastic Geometry [v]. We describe how we solve the same problem with O.R. methods. Then we compare the results between the two approaches. In section 2, we describe with further details the location problem. In section 3, we recall the results of the Stochastic Geometry approach and we present our approach using O.R. Finally, in section 4, the results are presented and the first elements of a hybrid method are discussed.




@inproceedings {
title="{Two approaches for solving a continuous location problem: Stochastic geometry and Operational Research}",
author=" M. Trampont and C. Destr ",
booktitle="{International Network Optimization Conference, Spa,}",