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

**ConfÃ©rence Internationale avec comitÃ© de lecture : **
International Network Optimization Conference, Spa,,
January 2007,

pp.7,

**motcle: **

**RÃ©sumÃ©: **
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, etcâ€¦ 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.

**Commentaires: **
http://www.poms.ucl.ac.be/inoc2007/Papers/author.85/paper/paper.85.pdf

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