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

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.