What you can achieve
The MultiSimplex software will let you optimize almost any technical system in a quick and easy way. Numerous examples from our customers show how it can save time for you, and money for your company, e.g.:
- Analytical laboratories have cut analysis time up to 50%.
- Quality characteristics have improved by 50-100%.
- Manufacturing through-puts have increased up to 50%.
- Combustion facilities have cut environmental emissions by 20-30%.
What are savings like this worth to you? $10,000, $100,000 or $1,000,000? With MultiSimplex, you will beat the competition! What if your competitors are already using it?
Key benefits
- Can simultaneously handle several optimization criteria*.
- Find optimum conditions with a minimum of practical trials.
- Practical trials are performed in the direction of improvement.
- Methods used in industry and research for more than 30 years.
Key features
- Basic or modified simplex methods.
- Numerical and graphical evaluation.
- Easy handling of mixture optimization.
- Add and remove variables "on-the-fly".
- Handle many types of optimization problems.
- Tutorials, extensive HTML help system and complete manual.
- Validated to fulfill specifications.
- "Our division manufactures systems for separation of gas mixtures based on hollow fiber membranes. We used the program for conducting an optimization of the fiber spinning process. After 10 trials the performance of the fiber improved by over 20%."
- (Research chemist Kevin Lundy, Permea, Division of Air Products and Chemicals Inc.)
- "Completness, flexibility, and ease of use make the MultiSimplex the best optimization software."
- (Dr. Zhubiao Zhu, Mississippi State University) ”Completeness, flexibility and easy of use make the MultiSimplex® the best optimization software.”
(Dr. Zhubiao Zhu, Mississippi State University)
“The most interesting feature with the MultiSimplex® is it’s ability to optimize several response variables at the same time.”
(Prof. Steven D. Brown in the Journal of Chemometrics.)"Installing the MultiSimplex system on our screening line and TMP refiners gave us quality and production improvements that exceeded our expectations." (Anders Åhlund, Production manager TMP, SCA Graphic, Ortviken mill.)
“Our division manufactures systems for separation of gas mixtures based on hollow fiber membranes. We used the MultiSimplex® program for conducting an optimization of the fiber spinning process. After 10 trials the performance of the fiber improved by over 20 %”
(Kevin Lundy, Permea, Div. of air products and Chemicals)
Optimization in Chemical Industry, Pharmacy and Analytical Chemistry
The methods implemented in MultiSimplex have successfully been used in industry and research for more than 30 years. We are sure that your skill and experience in combination with these methods will give rise to further achievements.
Successful applications:
Chemical and process industry
- Optimized manufacturing conditions for a plastics material
- Continuous improvement of paper manufacturing
- Minimization of air emissions from a power plant
- Optimization of a pelleting machine
- Optimized rubber-blending
Pharmaceutical applications
- Optimized preparation of tablets
- Optimized drug design
Optimization of analytical instruments
- High-performance liquid chromatography (HPLC)
- Nuclear magnetic resonance (NMR) spectroscopy
- Inductive-coupled plasma (ICP) spectroscopy
- Atomic absorption spectroscopy (AAS)
- Flow-injection analysis (FIA)
- Gas chromatography (GC)
- X-ray methods
Software validation process for MultiSimplex®
"Validation means confirmation by examination and provision of objective evidence that the particular requirements for a specific intended use can be consistently fulfilled." (U.S. Food & Drug Administration, 1998, 21CFR820.3)
Our software quality policy is to provide products that consistently fulfill the specifications as presented in our technical documentation (primarily the User's Guide) and sales literature.
Here is how we ensure that MultiSimplex® fulfills our quality commitment:
1. Numerical and graphical output from the software is validated by the following methods:
- Validation by manual calculation, and visual verification of graphs. All algorithms for experimental designs, optimization methods and fuzzy set membership computations are published in the MultiSimplex® User's Guide.
- Validation by calculation with other software. Existing mathematical and statistical software products are used for validation, when the answers cannot be reasonably calculated by hand.
- Validation by comparison with examples in the scientific literature. Data and output from documented examples are used in the above calculations.
2. Software development is performed to ensure that the overall quality goal is met:
- Programming is based on written specifications.
- Programming is done according to defined rules, and the source code is well structured and documented.
- The source code is highly modular, to facilitate error detection, testing and maintenance. A software system is used for version control.
- The software goes through extensive internal pre-release testing, alpha testing, to ensure that the specifications are fulfilled. Especially important is usability testing. Problems are recorded, forwarded to the development team, fixed, and noted.
- Each major new version (x.x) of the software goes through extensive external testing, beta testing, by both qualified scientific experts in the field and ordinary users. Problems are recorded, forwarded to the development team, fixed, and new beta-versions are shipped until all known major problems have been fixed. This assures consistent results across different hardware and software platforms.
- The managing director takes the final decision about release of a new commercially available version, after reviewing the test results from alpha- and beta testing.
- Problems (errors) reported after release are entered into a log, forwarded to the development team, fixed, and noted.
- Service releases are made with fixes to groups of minor problems, or separately if a major problem occur. Service releases are available free of charge to registered users.
3. We assist our customers in performing necessary validation procedures themselves (as regulating authorities may require):
- All algorithms for experimental designs, optimization methods and fuzzy set membership computations are published in the MultiSimplex® User's Guide.
- We provide bibliographic references to the scientific literature describing the methods implemented in the software.
4. We assist our customers in the efficient and correct use of the software:
"Our VOC destruction project was very successful. I used MultiSimplex and obtained good results. The composition of one of our best catalyst coated monoliths was predicted by MultiSimplex. I strongly recommend the program to anyone attempting to optimize a chemical process. I found Multisimplex very user-friendly and I achieved quick results."
(Jimena Cabrera, Research Associate at Eltron Research Inc. in Boulder, CO, USA.)“Applying MultiSimplex software systems to the SNCR-system and combustion air distribution at the Söderenergi heating plant in Södertälje, Sweden, has yielded two important results: 1. Automation of the SNCR-system and combustion process. 2. Substantial emission reductions, 25 % lowers NOx emissions and 60 % lower CO-emissions, when the SNCR-system and combustion process is controlled by MultiSimplex in auto mode. Another economical and environmental benefit is that the NH3 consumption for the SNCR-system has been lowered by 40 %."
(Per Oxelmark, Söderenergi AB)
The Basic Simplex Method
The basic simplex method is easy to understand and apply. The optimization begins with the initial trials. The trial conditions are spread out efficiently. The number of initial trials is equal to the number of control variables plus one. These initial trials form the first simplex. The shapes of the simplex in a one, a two and a three variable search space, are a line, a triangle or a tetrahedron. A geometric interpretation is difficult with more variables, but the basic mathematical approach outlined below can handle the search for optimum conditions.
Geometric interpretation of lower dimensional simplices.
The basic simplex algorithm consists of a few rules:
- The first rule is to reject the trial with the least favorable response value in the current simplex.
A new set of control variable levels is calculated, by reflection into the control variable space opposite the undesirable result. This new trial replaces the least favorable trial in the simplex. This leads to a new least favorable response in the simplex that, in turn, leads to another new trial, and so on. At each step you move away from the least favorable conditions. By that the simplex will move steadily towards more favorable conditions.
- The second rule is never to return to control variable levels that have just been rejected.
The calculated reflection in the control variables can also produce a least favorable result. Without this second rule the simplex would just oscillate between the two control variable levels. This problem is nicely avoided by choosing the second least favorable condition and moving away from it.
An example of a typical optimization sequence with the basic simplex method. Change in the levels for two control variables with the response marked as contours.
Besides the two main rules, two more rules are also used.
- Trials retained in the simplex for a specified number of steps are reevaluated. The reevaluation rule avoids the simplex to be stuck around a false favorable response.
- Calculated trials outside the effective boundaries of the control variables are not made. Instead a very unfavorable response is applied, forcing the simplex to move away from the boundary.
The calculations in the MultiSimplex basic simplex algorithm are outlined in the flow chart. For each simplex the following labels are used: W for the least favorable trial or the trial being rejected, B for the most favorable trial and Nw for the second least favorable trial (i.e. next-to-the worst).
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.
Suggested further reading:
Sequential Simplex Optimization. A Technique for Improving Quality and Productivity in Research, Development, and Manufacturing by Walters, Parker, Morgan and Deming, CRC Press 1991.
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:
National Chiayi University Department of Food Science
National Taipei University of Technology Department of Industrial Engineering & Management
National Kaohsiung University of Science and Technology Department of Civil and Construction Engineering
Minghsin University of Science & Technology Department of Industrial Engineering & Management
Fu Jen Catholic University DEPARTMENT OF INFORMATION MANAGEMENT
Fooyin University Department of Applied Chemistry and Material Science
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