Computational Optimization and Applications

, Volume 30, Issue 3, pp 297–318

Application of Deterministic Low-Discrepancy Sequences in Global Optimization

Article

DOI: 10.1007/s10589-005-4615-1

Cite this article as:
Kucherenko, S. & Sytsko, Y. Comput Optim Applic (2005) 30: 297. doi:10.1007/s10589-005-4615-1

Abstract

It has been recognized through theory and practice that uniformly distributed deterministic sequences provide more accurate results than purely random sequences. A quasi Monte Carlo (QMC) variant of a multi level single linkage (MLSL) algorithm for global optimization is compared with an original stochastic MLSL algorithm for a number of test problems of various complexities. An emphasis is made on high dimensional problems. Two different low-discrepancy sequences (LDS) are used and their efficiency is analysed. It is shown that application of LDS can significantly increase the efficiency of MLSL. The dependence of the sample size required for locating global minima on the number of variables is examined. It is found that higher confidence in the obtained solution and possibly a reduction in the computational time can be achieved by the increase of the total sample size N. N should also be increased as the dimensionality of problems grows. For high dimensional problems clustering methods become inefficient. For such problems a multistart method can be more computationally expedient.

Keywords

global optimization stochastic optimization low-discrepancy sequences multi level single linkage method 

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Imperial College LondonUK
  2. 2.Moscow Engineering Physics InstituteMoscowRussia