Dynamic Data Structures for a Direct Search Algorithm

  • Authors:

  • Jian He;Layne T. Watson;Naren Ramakrishnan;Clifford A. Shaffer;Alex Verstak;Jing Jiang;Kyung Bae;William H. Tranter

  • Affiliations:

  • Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA;Departments of Computer Science and Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA. ltw@cs.vt.edu;Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA;Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA;Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA;Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA;Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA;Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

  • Venue:
  • Computational Optimization and Applications
  • Year:
  • 2002

Quantified Score

Hi-index 0.01

Visualization

Abstract

The DIRECT (DIviding RECTangles) algorithm of Jones, Perttunen, and Stuckman (Journal of Optimization Theory and Applications, vol. 79, no. 1, pp. 157–181, 1993), a variant of Lipschitzian methods for bound constrained global optimization, has proved effective even in higher dimensions. However, the performance of a DIRECT implementation in real applications depends on the characteristics of the objective function, the problem dimension, and the desired solution accuracy. Implementations with static data structures often fail in practice, since it is difficult to predict memory resource requirements in advance. This is especially critical in multidisciplinary engineering design applications, where the DIRECT optimization is just one small component of a much larger computation, and any component failure aborts the entire design process. To make the DIRECT global optimization algorithm efficient and robust on large-scale, multidisciplinary engineering problems, a set of dynamic data structures is proposed here to balance the memory requirements with execution time, while simultaneously adapting to arbitrary problem size. The focus of this paper is on design issues of the dynamic data structures, and related memory management strategies. Numerical computing techniques and modifications of Jones' original DIRECT algorithm in terms of stopping rules and box selection rules are also explored. Performance studies are done for synthetic test problems with multiple local optima. Results for application to a site-specific system simulator for wireless communications systems (S4W) are also presented to demonstrate the effectiveness of the proposed dynamic data structures for an implementation of DIRECT.