Here we present a brief introduction to the methods used in MultiSimplex. More details
are given in the the following pages:
Method Overview
The optimization of technical systems is the process of adjusting the control variables
to find the levels that achieve the best possible outcome (response). Usually many
conflicting responses must be optimized simultaneously. In the lack of systematic
approaches the optimization is done by "trial-and-error" or by changing one
control variable at a time while holding the rest constant. Such methods are not efficient
in finding the true optimum.
In 1962 an efficient sequential optimization method called the basic simplex method was
presented by Spendley et al. This method will find the true optimum of a response with
fewer trials than the non-systematic approaches or the one-variable-at-a-time method. The
simplex method has been improved by active workers in the field, to what is called the
modified simplex method (see e.g. Nelder and Mead, 1965; Åberg and Gustavsson, 1982 and
Betteridge et al, 1985). The two simplex methods are the optimization algorithms used in
the MultiSimplex software.
The MultiSimplex software also use modified first design
matrices to start the optimization. These D-optimal linear designs
have been shown to perform better than previous approaches in a
normal experimental situation (Öberg, 1998).
The simplex algorithms can handle only one response at a time, but usually there are
many response variables to optimize simultaneously. A method to form a joint response
measure, from the individual response variables, is therefore needed.
Zadeh introduced such a method in 1965, with the concept of "fuzzy sets".
Fuzzy set theory provides flexible and efficient techniques for handling different and
conflicting optimization criteria (see Otto, 1988). The fuzzy set membership functions are
the means for handling multiple responses in the MultiSimplex software.
The MultiSimplex software rests on a firm basis combining two established and popular
methods. Together these two methods can simultaneously handle both multiple control
variables and multiple response variables.
- Please note:
- The sequential simplex methods used in the MultiSimplex software should not
be confused with the simplex method for linear programming (a method to solve a linear
program by progressing from one extreme point of the feasible polyhedron to an adjacent
one).
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Reality is nonlinear and multivariate! MultiSimplex is designed as a true multivariate
nonlinear optimization tool. It seeks the optimum step-by-step, with a minimum of trials.
The main principle behind MultiSimplex is to put you in charge of everything.
MultiSimplex calculates from purely mathematical considerations and has no intelligence of
it’s own. It is your experience and skill as a working professional that is
important. In every step during the optimization you can change both the optimization
objectives and how the software operates. The preset optimization procedures will usually
work nicely, but there is always reason to try out a "flash of genius" (when it
occurs). In every step the software will also automatically check that you are not
violating the basic principles for the algorithms, and warn you if you do.
Spendley, W., Hext, G. R., Himsworth, F. R. Sequential application of simplex
designs in optimisation and evolutionary operation. Technometrics 4(1962):4 441-461.
Nelder, J. A., Mead, R. A simplex method for function minimization. Computer
Journal 7(1965) 308-313.
Åberg, E. R., Gustavsson, A. G. T. Design and evaluation of modified simplex
methods. Analytica Chimica Acta 144(1982) 39-53.
Betteridge, D., Wade, A. P., Howard, A. G. Reflections on the modified simplex - II.
Talanta 32(1985):8B 723-734.
Öberg, T. Importance of the first design matrix in
experimental simpplex optimization. Chemometrics and
Intelligent Laboratory Systems 44(1998) 147-151
Zadeh, L. A. Fuzzy sets. Information and Control 8(1965) 338-363.
Otto, M. Fuzzy theory explained. Chemometrics and Intelligent Laboratory Systems
4(1988) 101-120.
More details are given in the the following pages:
You can have your own copy of MultiSimplex within a few days. Place
your order with us, or one of our local distributors.
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