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

  • Authors:

  • G. Liuzzi;S. Lucidi;V. Piccialli

  • Affiliations:

  • IASI--Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti", CNR--Consiglio Nazionale delle Ricerche, Roma, Italy 00185;Dipartimento di Informatica e Sistemistica "Antonio Ruberti", Università degli Studi di Roma "La Sapienza", Roma, Italy 00185;Dipartimento di Ingegneria dell'Impresa, Università di Roma "Tor Vergata", Roma, Italy 00133

  • Venue:
  • Computational Optimization and Applications
  • Year:
  • 2010

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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.