### Sergio García Quilles (University of Edinburgh)

#### Solving large p-median models using a radius formulation

*Wednesday 20 November 2013 at 15.30, JCMB 6206*

##### Abstract

One of the most classical problems in Discrete Location is the p-median
problem. It consists in, given a finite set of points, decide where to locate
a fixed number p of facilities (the medians) and how to allocate the
non-median points to the median nodes in such a way that total cost (usually
distance) be minimum. It is a problem with many applications: clustering,
emergency services, image processing, political districting, etc. However, it
is difficult to solve large instances in an efficient way due to the fact that
the classical formulation has a quadratic number of variables and constraints.
Recently, it has been developed an alternative formulation called radius
formulation that allows to solve much larger instances very efficiently. This
formulation and the algorithm used to solve it will be detailed in the first
part of the talk. In the second part, it will be shown that a similar idea can
be used to solve a problem of clustering with feature selection, problem that
can be seen as "double p-median" problem.

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