Simplex optimisation

The results of the simplex optimisation are essentially the same as those produced by the Newton-Gauss fit on p.166. The main difference is the lack of the standard deviations of the parameters and longer computation times. 

The second approach to optimisation is a model independent one. One of these model independent methods is the sequential simplex [24,25] used by Shek et al. [26], The method is claimed to be ideally suited for the optimisation of formulations [27] because of the relatively low number of experiments to be performed. 

In this particular situation two criteria are optimised. The overall responses of the vertices of the present simplex are compared and the simplex moves away from low responses. The optimisation route depends on the measured values of R and i 2 the values of a and b, which have to be chosen before the start of the optimisation procedure. Suppose in the progress of the optimisation procedure the following results are obtained ... 

Figure 4.15 Illustration of the sequential simplex optimisation procedure in a mixture of three components. Point A is the result of situation A, point B is the result of situation B...

Although application of chemometrics in sample preparation is very uncommon, several optimisation techniques may be used to optimise sample preparation systematically. Those techniques can roughly be divided into simultaneous and sequential methods. The main restrictions of a sequential simplex optimisation [6,7] find their origin in the complexity of the optimisation function needed. This function is a predefined function, often composed of several criteria. Such a composite criterion may lead to ambiguous results [8]. Other important disadvantages of simplex optimisation methods are that not seldom local optima are selected instead of global optima and that the number of experiments needed is not known beforehand. 

We will present the basics of the simplex method with the aid of a simulation and then describe the algorithm. As an example, Soylak et al. [18] optimised a procedure to preconcentrate lead (the studied response, Y) using a 2 factorial design in which the factors were ... 

Below, a pseudo-code is presented to perform a simplex optimisation (using the original algorithm). 

A pseudo-code is presented below to perform a modified simplex optimisation. 

Relevant variables influencing vapour generation of Sb(III) with bromide were screened using an experimental design. Then they were optimised using a simplex algorithm... 

An experimental design was applied to study which variables determined the measurement of total reduced sulfur species in natural waters and sediments. Then, a simplex optimisation of relevant variables was made... 

Table 2.35 Examples of practical applications of simplex optimisation in atomic spectrometry.

Cr without flames were optimised by simplex. The effects of matrix concomitants were also studied... 

Fe in water-methanol were simplex optimised (ashing temperature, ashing time), ramp and atomisation temperature)... 

A separation procedure was developed after a simplex optimisation of a nitric acid digestion to determine lanthanides and yttrium in rare earth ores and concentrates... 

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