Journal of Optimization Theory and Applications

, Volume 151, Issue 1, pp 175–190 | Cite as

A Modified DIviding RECTangles Algorithm for a Problem in Astrophysics

  • D. di Serafino
  • G. Liuzzi
  • V. Piccialli
  • F. Riccio
  • G. Toraldo


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.


Global optimization DIRECT algorithm Detection of gravitational waves 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • D. di Serafino
    • 1
  • G. Liuzzi
    • 2
  • V. Piccialli
    • 3
  • F. Riccio
    • 1
  • G. Toraldo
    • 4
  1. 1.Dipartimento di MatematicaSeconda Università degli Studi di NapoliCasertaItaly
  2. 2.Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”CNRRomeItaly
  3. 3.Dipartimento di Informatica, Sistemi e ProduzioneUniversità degli Studi di Roma “Tor Vergata”RomeItaly
  4. 4.Dipartimento di Ingegneria Agraria e Agronomia del TerritorioUniversità degli Studi di Napoli “Federico II”Portici (NA)Italy

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