Sequential simplex technique

A series of 4-phenyltetrafluoroethoxyphenylbenzoyl-ureas was synthesized and evaluated In diet, topical, and chltln synthesis assays. The sequential simplex technique was used to optimize the topical activity. Chltln synthesis activity vks found to be similar to much shorter Inhibitors, yet the topical activity was found to vary widely. 

Since we wished to optimize this series with a minimal expenditure of our synthetic resources, the sequential simplex technique (SSO) was selected (11,12). This strategy is very resource efficient, requiring only n + 1 compounds to start the optimization, where n is the number of physiochemical parameters used to describe the characteristics of a substituent. We selected pi to account for lipophilicity and field (F) and resonance (R) were used to describe the electronic effects of each substituent (14). Verloop s Sterimol parameters (H), minimum van der Waals radius (B] ) and length (L) were selected to describe the size of the substituent. Using cluster analysis, we selected a set of six substituents that cover physiochemical parameter space well (15). These are-listed in Figure 6. 

Techniques used to find global and local energy minima include sequential simplex, steepest descents, conjugate gradient and variants (BFGS), and the Newton and modified Newton methods (Newton-Raphson). 

Walters, F.H., Parker, J Llyod, R., Morgan, S.L., and S.N. Deming, Sequential Simplex Optimization A Technique for Improving Quality and Productivity in Research, Development, and Manufacturing, CRC Press Inc., Boca Raton, Florida, 1991. 

Bindschaedler and Gurny [12] published an adaptation of the simplex technique to a TI-59 calculator and applied it successfully to a direct compression tablet of acetaminophen (paracetamol). Janeczek [13] applied the approach to a liquid system (a pharmaceutical solution) and was able to optimize physical stability. In a later article, again related to analytical techniques, Deming points out that when complete knowledge of the response is not initially available, the simplex method is probably the most appropriate type [14]. Although not presented here, there are sets of rules for the selection of the sequential vertices in the procedure, and the reader planning to carry out this type of procedure should consult appropriate references. 

The optimum found by sequential proceeding, both by Box-Wilson and simplex technique, is that local optimum situated nearest the starting point. It must not inevitably be identical with the global optimum. Therefore, it may be useful to repeat the optimization procedure one or several times. 

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. 

There are two types of unconstrained multivariable optimization techniques those requiring function derivatives and those that do not. An example of a technique that does not require function derivatives is the sequential simplex search. This technique is well suited to systems where no mathematical model currently exists because it uses process data directly. 

The Simplex method (and related sequential search techniques) suffers mainly from the fact that a local optimum will be found. This will especially be the case if complex samples are considered. Simplex methods require a large number of experiments (say 25). If the global optimum needs to be found, then the procedure needs to be repeated a number of times, and the total number of experiments increases proportionally. A local optimum resulting from a Simplex optimization procedure may be entirely unacceptable, because only a poor impression of the response surface is obtained. 

A polynomial was fit to the calibration curve for the thermocouple by means of a minimization of the maximum deviation technique using the Nelder Mead sequential simplex minimization algorithm method.( 5,6, 7) The coefficients of this polynomial are stored in the analysis program and are used to convert thermocouple voltages to temperature values. Y values are converted to dH(t,T)/dt, the heat flow into and out of the sample in mcal/sec. The operator selects a baseline for the analysis by entering the temperatures of the beginning and end points of the baseline. A plot is produced of the raw data with the operator selected baseline shown as illustrated in Figure A. 

F. Maynd, Optimization techniques and pharmaceutical formulation example of the sequential simplex in tableting, Proc. 1st Int. Conf. Pharm. Tech. (APGI), 5, 65-84 (1977). 

The basic simplex optimization method, first described by Spendley and co-workers in 1962 [ 11 ], is a sequential search technique that is based on the principle of stepwise movement toward the set goal with simultaneous change of several variables. Nelder and Mead [12] presented their modified simplex method, introducing the concepts of contraction and expansion, resulting in a variable size simplex which is more convenient for chromatography optimization. 

F. H. Walters, L. R. Parker, Jr., S. L. Morgan, and S. N. Dem-ing, Sequential Simplex Optimization. A Technique for Improving Quality and Productivity in Research, Development and Manufacturing , CRC Press, Boca Raton, FL, 1991. 

As noted in the introduction, energy-only methods are generally much less efficient than gradient-based techniques. The simplex method [9] (not identical with the similarly named method used in linear programming) was used quite widely before the introduction of analytical energy gradients. The intuitively most obvious method is a sequential optimization of the variables (sequential univariate search). As the optimization of one variable affects the minimum of the others, the whole cycle has to be repeated after all variables have been optimized. A one-dimensional minimization is usually carried out by finding the... 

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