Computer‐generated multicomponent calibration designs for optimal analysis sample predictions

Abstract

This paper utilizes variable step size generalized simulated annealing (VSGSA) to design multicomponent calibration samples for spectroscopic data. VSGSA is an optimization procedure which is capable of converging to exact positions of global optima located on multidimensional continuous functions. On the basis of analysis sample response vectors, optimally designed calibration concentration matrices are obtained assuming knowledge of components present. The complexity of response surfaces established by the optimization criteria is described.

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

“…. However, if x (t) is a boundary point of D, such as x (1) in Figure 2, then D (t) should be required to fall in D. Therefore it is possible that the edge length contracts to less than half that of D…”

“…In practice, many optimization problems often encounter the difficulty of being trapped in local optima and call for global optimization solutions. [1][2][3] There are many well-established numerical methods for optimization, such as steepest descent methods, quasi-Newton methods, conjugate gradient methods, simplex methods, etc. However, in order to locate the global optimum, they all require that the objective function be unimodal and/or differentiable.…”

“…These requirements make them inappropriate for practical use. In order to meet the need of a practically useful global optimization method in analytical chemistry, stochastic global optimization methods such as the genetic algorithm (GA) 4,5 and generalized simulated annealing (GSA) 1,2,6,7 have been introduced during recent years. Both the GA and GSA can in some degree avoid the problem of being trapped in local optima and have no special requirements on the objective function.…”

“…SNTO is also tested with complex functions with multilocal optima. A comparison is made with variable step size generalized simulate annealing (VSGSA), 1,11 which is a variation of GSA showing satisfactory results for SNTO.…”

Optimization by Simulated Annealing Theory and Chemometric Applications

“…Ideally, step size should decrease as the temperature is decreased. Kalivas (7) used discrete steplength changes (increase or decrease) throughout the search based on the acceptance rate of the previous 20 A GSA program written by the author in the MATLAB programming language and demonstrated in the appendix uses a set number of stepwise reductions (maxshrinks). Each is made by a specified factor (shrinkfac), and each occurs after a specified number of consecutive unaccepted step attempts (quitreps).…”