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A modified DIRECT algorithm for a problem in astrophysics

Daniela di Serafino (daniela.diserafino***at***unina2.it)
Giampaolo Liuzzi (giampaolo.liuzzi***at***iasi.cnr.it)
Veronica Piccialli (piccialli***at***disp.uniroma2.it)
Filippo Riccio (filippo.riccio***at***unina2.it)
Gerardo Toraldo (toraldo***at***unina2.it)

Abstract: We present a modification of the DIRECT algorithm, called DIRECT-G, to solve a box-constrained global optimization problem arising in the detection of gravitational waves emitted by coalescing binary systems of compact objects. This is a hard problem since the objective function is highly nonlinear and expensive to evaluate, has a huge number of local extrema and unavailable derivatives. DIRECT performs a sampling of the feasible domain over a set of points that becomes dense in the limit, thus ensuring the everywhere dense convergence; however, it results ineffective on significant istances of the problem under consideration, because it tends to produce a uniform coverage of the feasible domain, by oversampling regions that are far from the optimal solution. DIRECT has been modified by embodying information provided by a suitable discretization of the feasible domain, based on the signal theory, which takes into account the variability of the objective function. Numerical experiments show that DIRECT-G largely outperforms DIRECT and the grid search, the latter being the reference algorithm in the astrophysics community. Furthermore, DIRECT-G is comparable with a genetic algorithm specifically developed for the problem. However, DIRECT-G inherits the convergence properties of DIRECT, whereas the genetic algorithm has no guarantee of convergence.

Keywords: global optimization, DIRECT algorithm, detection of gravitational waves.

Category 1: Global Optimization (Applications )

Category 2: Applications -- Science and Engineering (Other )

Citation: Preprint n. 9/2010, Department of Mathematics, Second University of Naples, Caserta, Italy, October 2010.

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Entry Submitted: 11/02/2010
Entry Accepted: 11/02/2010
Entry Last Modified: 11/28/2010

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