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A DIRECT-based approach exploiting local minimizations for the solution of large-scale global optimization problems

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Abstract

In this paper we propose a new algorithm for solving difficult large-scale global optimization problems. We draw our inspiration from the well-known DIRECT algorithm which, by exploiting the objective function behavior, produces a set of points that tries to cover the most interesting regions of the feasible set. Unfortunately, it is well-known that this strategy suffers when the dimension of the problem increases. As a first step we define a multi-start algorithm using DIRECT as a deterministic generator of starting points. Then, the new algorithm consists in repeatedly applying the previous multi-start algorithm on suitable modifications of the variable space that exploit the information gained during the optimization process. The efficiency of the new algorithm is pointed out by a consistent numerical experimentation involving both standard test problems and the optimization of Morse potential of molecular clusters.

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Authors and Affiliations

  1. IASI—Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, CNR—Consiglio Nazionale delle Ricerche, Viale Manzoni 30, 00185, Roma, Italy

    G. Liuzzi

  2. Dipartimento di Informatica e Sistemistica “Antonio Ruberti”, Università degli Studi di Roma “La Sapienza”, via Ariosto 25, 00185, Roma, Italy

    S. Lucidi

  3. Dipartimento di Ingegneria dell’Impresa, Università di Roma “Tor Vergata”, Via del Politecnico 1, 00133, Roma, Italy

    V. Piccialli

Authors
  1. G. Liuzzi
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  2. S. Lucidi
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  3. V. Piccialli
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Correspondence to S. Lucidi.

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Paper presented at the Erice 2007 workshop.

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Liuzzi, G., Lucidi, S. & Piccialli, V. A DIRECT-based approach exploiting local minimizations for the solution of large-scale global optimization problems. Comput Optim Appl 45, 353–375 (2010). https://doi.org/10.1007/s10589-008-9217-2

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  • DOI: https://doi.org/10.1007/s10589-008-9217-2

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