Sequential number-theoretic optimization (SNTO) method applied to chemical quantitative analysis

Lin Zhang, Yi-Zeng Liang*, Ru-Qin Yu, Kai-Tai Fang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

14 Citations (Scopus)


A sequential number-theoretic optimization (SNTO) method recently developed in statistics was introduced as a global optimization procedure in constrained background bilinearization (CBBL) for the quantification of real two-way bilinear data. SNTO searches for the global optimum among points uniformly scattered in the search space and convergence of the algorithm is quickened through sequential contraction of that space. Since the global optimization performance of SNTO is closely related to the number of points scattered, a new practical approach for selection of the number of points scattered in the original search space by trial tests is proposed in this paper in order to increase the possibility of locating the global optimum. The performance of SNTO has also been tested with mathematical models with multiple local optima. In comparison with another global optimization method, variable step size simulated annealing (VSGSA), SNTO achieved satisfactory results for both mathematical models and a real analytical system. The clarity and simplicity of the idea of SNTO together with its convenience for implementation make SNTO a promising tool in chemometrics.

Original languageEnglish
Pages (from-to)267-281
Number of pages15
JournalJournal of Chemometrics
Issue number3
Publication statusPublished - May 1997
Externally publishedYes

Scopus Subject Areas

  • Analytical Chemistry
  • Applied Mathematics

User-Defined Keywords

  • Constrained background bilinearization
  • Global optimization
  • Sequential number-theoretic optimization method
  • Variable step size simulated annealing


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