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A Modified DIviding RECTangles Algorithm for a Problem in Astrophysics

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Seconda Università degli Studi di Napoli, via Vivaldi 43, 81100, Caserta, Italy

    D. di Serafino & F. Riccio

  2. Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, CNR, viale Manzoni 30, 00185, Rome, Italy

    G. Liuzzi

  3. Dipartimento di Informatica, Sistemi e Produzione, Università degli Studi di Roma “Tor Vergata”, viale del Politecnico 1, 00133, Rome, Italy

    V. Piccialli

  4. Dipartimento di Ingegneria Agraria e Agronomia del Territorio, Università degli Studi di Napoli “Federico II”, via Università 100, 80055, Portici (NA), Italy

    G. Toraldo

Authors
  1. D. di Serafino
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  2. G. Liuzzi
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  3. V. Piccialli
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  4. F. Riccio
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  5. G. Toraldo
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Corresponding author

Correspondence to G. Toraldo.

Additional information

Communicated by Ryan P. Russell.

We thank Stefano Lucidi for useful discussions on DIRECT and on strategies to accelerate its convergence. We are also thankful to the anonymous Referees and the journal Editors for their careful reading of the paper and their insightful comments that helped us improving the paper. This work was supported by the Italian Ministry for Education, University and Research, under the PRIN Project Nonlinear Optimization, Variational Inequalities and Equilibrium Problems.

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di Serafino, D., Liuzzi, G., Piccialli, V. et al. A Modified DIviding RECTangles Algorithm for a Problem in Astrophysics. J Optim Theory Appl 151, 175–190 (2011). https://doi.org/10.1007/s10957-011-9856-9

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  • DOI: https://doi.org/10.1007/s10957-011-9856-9

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