Comparison of alternating variable search and simplex methods of optimisation for inductively coupled plasma optical emission and atomic fluorescence spectrometry

Abstract

The performance of several cyclic alternating variable search (AVS) optimisation methods are compared with two simplex methods with respect to the number of changes of variable required to search a model two-factor response space. The roles of the initial step size and of the variable step size are discussed, and the information produced concerning the shape of the factor space is evaluated. An AVS method which starts with a fixed step size and then changes to a variable step size on second and subsequent cycles is compared with a variable step size simplex for the optimisation of an inductively coupled plasma optical emission spectrometer and of the atomiser, source inductively coupled plasmas in atomic fluorescence spectrometry (the ASIA system). The order in which the variables are taken in the AVS method does not affect the value of the optimum eventually found. Both methods perform satisfactorily for the optical emission work, although the AVS method provides information about the shape of the factor space which is easier to interpret than in the simplex method. However, the simplex method was not always able to satisfy the conditions for termination in the case of the atomic fluorescence studies and was much slower to implement than the AVS method as the latter used direct visual feedback from the output of the lock-in amplifier as a measure of the figure of merit (total fluorescence signal).