MultiSimplex is a Windows-based software for sequential design of experiments and optimization. MultiSimplex is used to improve:
- Quality of products.
- Efficiency of processes.
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Performance of analytical instruments
The optimization is based on practical trials that are performed step-by-step. Together with your skill and your experience, the efficient and systematic search strategies of the optimization algorithms form a powerful tool.
Optimization Methods
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).
The Philosophy Behind MultiSimplex
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.
Literature
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:
