Optimization using the super-modified simplex method

Abstract

Morgan, E., Burton, K.W. and Nickless, G., 1990. Optimization using the super-modified simplex method. Chemometrics and Intelligent Laboratory Systems, 8: 97–107. The super-modified simplex method represents an advance over the modified simplex method. It has an ability to change its size and orientate itself to fit a response surface by second-order and gaussian estimation of the position of an optimal vertex from previously obtained responses. The super-modified simplex is essentially a set of rules which, like other simplex methods, can be presented as a flow chart. Restrictions to the positions that the optimal vertex may take are also presented since these enable the super-modified simplex to maintain its symmetry during the optimization process and make effective progress towards an optimum. Attempted boundary violations by both the second-order and gaussian super-modified simplex methods are also dealt with since they behave quite differently to other simplex techniques. Finally an example is presented with some of the required calculations to demonstrate movement of the simplex across a response surface. This tutorial should act as an introduction to the super-modified simplex method for students and scientists who are interested in learning about the technique without having to search through all the available literature.