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A Modified DIviding RECTangles Algorithm for a Problem in Astrophysics

Author

Listed:
  • 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”)

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.

Suggested Citation

  • D. Serafino & G. Liuzzi & V. Piccialli & F. Riccio & G. Toraldo, 2011. "A Modified DIviding RECTangles Algorithm for a Problem in Astrophysics," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 175-190, October.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:1:d:10.1007_s10957-011-9856-9
    DOI: 10.1007/s10957-011-9856-9
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    References listed on IDEAS

    as
    1. Giampaolo Liuzzi & Stefano Lucidi & Veronica Piccialli, 2010. "A partition-based global optimization algorithm," Journal of Global Optimization, Springer, vol. 48(1), pages 113-128, September.
    2. Daniela di Serafino & Susana Gomez & Leopoldo Milano & Filippo Riccio & Gerardo Toraldo, 2010. "A genetic algorithm for a global optimization problem arising in the detection of gravitational waves," Journal of Global Optimization, Springer, vol. 48(1), pages 41-55, September.
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    Cited by:

    1. Rudolf Scitovski, 2017. "A new global optimization method for a symmetric Lipschitz continuous function and the application to searching for a globally optimal partition of a one-dimensional set," Journal of Global Optimization, Springer, vol. 68(4), pages 713-727, August.
    2. Ratko Grbić & Emmanuel Nyarko & Rudolf Scitovski, 2013. "A modification of the DIRECT method for Lipschitz global optimization for a symmetric function," Journal of Global Optimization, Springer, vol. 57(4), pages 1193-1212, December.
    3. G. Liuzzi & S. Lucidi & V. Piccialli, 2016. "Exploiting derivative-free local searches in DIRECT-type algorithms for global optimization," Computational Optimization and Applications, Springer, vol. 65(2), pages 449-475, November.
    4. Remigijus Paulavičius & Lakhdar Chiter & Julius Žilinskas, 2018. "Global optimization based on bisection of rectangles, function values at diagonals, and a set of Lipschitz constants," Journal of Global Optimization, Springer, vol. 71(1), pages 5-20, May.
    5. Renato Bruni & Fabio Celani, 2019. "Combining Global and Local Strategies to Optimize Parameters in Magnetic Spacecraft Control via Attitude Feedback," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 997-1014, June.
    6. Remigijus Paulavičius & Julius Žilinskas, 2014. "Simplicial Lipschitz optimization without the Lipschitz constant," Journal of Global Optimization, Springer, vol. 59(1), pages 23-40, May.
    7. Remigijus Paulavičius & Yaroslav Sergeyev & Dmitri Kvasov & Julius Žilinskas, 2014. "Globally-biased Disimpl algorithm for expensive global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 545-567, July.

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