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Section: Contracts and Grants with Industry


Participants : Pierre Del Moral, Alexandru-Adrian Tantar, Emilia Tantar.

The objective of this contract (10kE, 2009) is to implement interacting particle algorithms for the optimization of networks of sparse antenna arrays.

Sparse antenna arrays represent a topic of major interest in the electromagnetic measures domain, communications, etc., offering cost and space efficient solutions. From a formal point of view, the optimization of a sparse antenna array, with respect to various constraints, can be modeled over a set of continuous functions, e.g. describing directivity, lobes. Nonetheless, as a result of the non-convex and highly multi-modal nature of the functions to be optimized, classical algorithms are generally ineffective. Extending previous approaches, a Kullback-Leibler cross-entropy based stochastic paradigm has been first considered for the study, the algorithm relying on iterative adaptive changes of the probability density functions in order to explore the search space.

As a second part of the study, an extension has been proposed by adopting an evolutionary based approach. Different designs have been considered ranging from simple direct local search methods to highly complex hybrid constructions, e.g. relying on island-based models of differential evolution and evolutionary algorithms. A significant improvement of the formerly obtained results was attained, superseding the cross-entropy based approaches, previously addressed in the project. Compared to the initial solutions, the newly obtained arrays provided a higher directivity and a reduced coupling with the enclosing environment, i.e. the objectives to be attained.

Furthermore a multi-objective formulation was introduced, in order to provide a set of good compromise (Pareto) approximate solutions. In this context a new interacting particle approach was proposed and experimentally tested. Its performance guarantees (the convergence and quality of the offered solutions) remain to be theoretically addressed.


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