## Section: Contracts and Grants with Industry

### Optimization of sensors location and activation — contract with DGA / Techniques navales

Participant : François Le Gland.

INRIA contract ALLOC 4233 — April 2009 to September 2011.

This is a collaboration with Sébastien Paris (université Paul Cézanne), related with the supervision of the PhD thesis of Mathieu Chouchane.

The objective of this project is to optimize the position and activation times of a few sensors deployed by a platform over a search zone, so as to maximize the probability of detecting a moving target. The difficulty here is that the target can detect an activated sensor before it is detected itself, and it can then modify its own trajectory to escape from the sensor. Because of the many constraints including timing constraints involved in this optimization problem, a stochastic algorithm is preferred here over a deterministic algorithm. The underlying idea is to replace the problem of maximizing a cost function (the probability of detection) over the possible configurations (admissible position and activation times) by the apparently simpler problem of sampling a population according to a probability distribution depending on a small parameter, which asymptotically concentrates on the set of global maxima of the cost function, as the small parameter goes to zero. The usual approach here is to use the cross–entropy method [65] , [33] .

The contribution of ASPI has been to propose a multilevel splitting algorithm, in order to evaluate the probability of detection for a given configuration. When this probability is small, these methods are known to provide a significant reduction in the variance of the relative error.