Supermodified simplex

In the modified algorithm the initial simplex, BNW, can be submitted to five different operations refiection, expansion, contraction, contraction with direction change and massive contraction. In the supermodified simplex (Routh et al., 1977), the selection of options is amplified. 

Fig. 8.8. The supermodified simplex, (a) The responses observed at W and R would indicate an expansion of the modified simplex, (b) With this response surface expansion would not be the best movement. A P value of about 1.3 would produce a larger response, (c) For the concave surface the R vertex is maintained.

In the cases of violations of established experimental hmits for the variables being optimized, the choice of a new supermodified simplex is more complicated than for the other algorithms, because the response at the R vertex (that could be impossible to determine) is necessary to calculate Popt- The reader can discover how to treat this problem in Morgan et al. (1990). 

The biggest disadvantage of the supermodified simplex is that the definition of each new simplex requires an extra experiment, made at point P. Some researchers have preferred to avoid this additional effort, using the average of the responses at all the vertexes of the simplex (except W) as an estimate of the response at P. This variant of the supermodified algorithm has been tested on several response surfaces (Brown, 1990). 

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