A Modified DIviding RECTangles Algorithm for a Problem in Astrophysics

D. Serafino (), G. Liuzzi (), V. Piccialli (), F. Riccio () and G. Toraldo ()
Additional contact information
D. Serafino: Seconda Università degli Studi di Napoli
G. Liuzzi: CNR
V. Piccialli: Università degli Studi di Roma “Tor Vergata”
F. Riccio: Seconda Università degli Studi di Napoli
G. Toraldo: Università degli Studi di Napoli “Federico II”

Journal of Optimization Theory and Applications, 2011, vol. 151, issue 1, No 11, 175-190

Abstract: Abstract We present a modification of the DIRECT (DIviding RECTangles) 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 becomes ineffective on significant instances 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 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-011-9856-9

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