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.