# Sequential Simplex Optimization

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Viewing 17 posts - 1 through 17 (of 17 total)
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• #44543

Ropp
Participant

Does anyone how any views pro or con regarding the use of sequential simplex optimization as a method for optimizing a process versus response surface methods or others.

Thanks,

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#142915

Hans
Participant

Dave,
I am not quite sure if I understand your question correctly. The simplex method is based on matrix algebra in that a set of simultaneous constraints equations is solved through the inverse matrix. It is typically discussed under linear programming and the methodology is used in “mixture experiments” in for a example simplex lattice designs. or simplex centroids. These design are a class of response surface experiments in which the product under investigation contains several components (in chemisty for example a 30% component A may be compared with a 70% component B, versus 10% of A and 90% of B).
In response surface designs (in a narrwer sense) experimental factor levels are varied to determine the combination of settings that produces an optimum desired outcome. Sequential experimentation are often used when only small numbers of experimental trials are run. Multiple response optimization looks at the optimal settings of several factors simultaneously. (However, you are not dealing with percentages of A vs. B, but with factor settings of A vs. B).
Thus, I think you are dealing with two types of applications: Mixture designs vs. Response Survade Designs. Within Response surface designs you are looking at sequential vs. simultaneous optimization. Thus, it is diffiuclt to say which one is “the best”. It depends on your problem, etc. Robert Butler is probably the most competent person on this site to further elaborate if needed. And correct me if I am wrong.
Regards

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#142916

Hans
Participant

Two more observations:
Within response surface methods there is an orthogonal design called simplex.
Also, many response optimization techniques are based on non-linear programming (simplex is a form of linear programming). However, there is an approach to reformulate quadratic programming problems and obtaining the solution using the simplex method. Mixtures experiments primarily use linear programming using simplex.
Your question is somewhat complicated by the fact that you dichotomize simplex and response surface designs. So, on the one hand you have a fitting of a first-order model using simplex. On the other hand, you have the algorithm of solving a constrained optimization problem via nonlinear programming methods. However, this approach can in some instances be reformulated into a linear programming problem solved by the simplex method.
I have been accused of using the Thesaurus Dictionary to often. However, it seems to be worth disentangling the two layers of your question before giving you an answer. (50% of the answer is the question). Regards.

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#142918

Anonymous
Guest

Dave,
Simplex is a evolutionary operations procedure – EVOP. One of the world’s largest chocolate manufacturing companies uses Simplex to sequentiually ‘optimise’ their processes.
Sometimes, sequentially ‘controlled’ tweaks is necessary to adjust a process when the variation in incoming materials is uncontrollable. For example, in the manufacture of CIJ ink manufacturing where several responses have to be adjusted as a function of several raw materials, such as polymer and dye viscosity, surface tension, conductivity, etc.
Andy

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#142922

Hans
Participant

Andy,
In this case we have three types of research designs: evolutionary design, response surface designs and mixture experiments, that all may use simplex as the linear programming algorithm to optimize the response. In that case, the question is on the design and the appropriate application, because simplex is simplex is simplex. Just curious. Regards.

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#142930

Robert Butler
Participant

All of the simplex methods with which Im familiar involve setting up an initial test space comprised of n+1 experiments where n is the number of X variables of interest.  The term simplex comes from the geometric term for shapes based on the n and n+1.

If we consider only 2 X’s the basic idea is as follows:

If you have 2 Xs the initial shape of the search region is in the form of a triangle in the X1, X2 plane.  You take your measurements at each of the three experimental points as defined by the triangle (the vertices).  The program examines their values using a search algorithm which will define the direction of improvement for the Y variable of interest. Once this direction is defined the program identifies a new experiment in the direction of improvement. In the case of 2 variables this will result in a new triangle defined by the two best vertices of the old triangle and the new test point. The new experiment is run and the process repeats itself until either some pre-set level of optimization is reached or the process can find no direction along which to improve the Y value of interest.

As far as I know the biggest drawback to simplex methods is they only focus on the optimization of a single Y response.  This is fine as long as you only have one product property of interest.  If, as has always been the case for me, you have more than one Y and/or you need to be sure that other Ys of interest dont move off of nominal this method doesnt have much to offer.

Even if the problem of one-Y-at-a-time has been addressed since the last time I looked at one of these packages there is still the fact that data from such an effort will have a lot of confounding with the various Xs.  This means you will be out of luck if you have follow up questions and you want to go back and attempt to answer them using regression methods.

I can see where simplex methods might be useful for the kind of tweaking Andy U mentioned since a single tweaking of a single Y probably wont result in too much degradation of other Ys of interest.

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#142932

michael spearman
Participant

Mr. Butler, I enjoyed your post, do you have any written information on this subject in detail? If you do, could you please forwarded it to me, or tell me where I could get it from, or a good reference to it.
Any good books out their on this???????
Thank you

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#142937

Hans
Participant

Robert,
As always excellent summary. I would like to add one comment on the simplex method. Simplex is part of linear programming and thus optimizes one response (a single objective function) as you correctly point out. Goal programming is used when there are multiple (most often conflicting objectives). However, there is a “modified simplex procedure” that is sometimes being used in goal programming applications. Thus, it is possible that a statistical program may use a modified simplex procedure where other goal programming techniques could be used. Regards
If anyone cares about linear and goal programming a good reference is Moore, Lee, and Taylor (1993). Management Science. Simon & Schuster, Inc. (chapters 2 and 13).

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#142938

Anonymous
Guest

Robert,
In chocolate manufacture there are several correlated Y’s, and each small tweak has to be evaluated in terms of all the responses, while continuing to manufacture. It is not an ‘off-line’ DOE procedure, which is another reason for using small tweaks!!!
Similarly, during CIJ ink manufacture, each controlled tweak has to be considered in terms of viscosity, drop formation (surface tension) conductivity, and print quality.  The turn-around time for the test is about 30 mins., because a shear mixer has to be given time to mix in any adjustment chemicals, and then all the measurements have to be repeated, including loading the ink into the CIJ printer, ‘blowing off solvent to bring it into spec. quickly, and printing. It is a tedious procedure.
Cheers,
Andy

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#142940

Anonymous
Guest

Hi Hans,
I only know a little about the EVOP Simplex. I’ve never heard of the others you mentioned except RSM. I did try RSM a few times until I found out why it would work for me.
Cheers,
Andy

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#142942

Hans
Participant

Do you have a reference of the EOVP Simplex? I could not find anything, in any of my books on DOE etc. Thanks, Hans

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#142954

Anonymous
Guest

Hans,
I found this one …
http://www.multisimplex.com/
When I looked into this a few years ago, I bought some software and an eBook from someone on the internet. I can’t remember the name.
I’m currently searching my backups – if I find anything I’ll contact you directly.
Cheers,
Andy

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#142956

Anonymous
Guest

Hans,
I’ve now found the eBook the guy sent me. The title is: “Sequential Simplex Optimization” by Walters, Parker, Morgan, and Deming. (It is a very good book.)
Publishers email: [email protected]
No sign of the software though ..
Cheers,
Andy

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#142957

Hans
Participant

Thanks! I appreciate it!

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#142959

Hans
Participant

Andy,
This link really clarified the issue for me and why it is so difficult to find anythig on the topic in regular text books.
The authors basically use the simplex algorithm as their underlying mathematical optimization tool. By using sequential methodology and combining the “simple” simplex with the “modified” simplex algorithm the creators of the approach/program avoid using different types of algorithms for response surface, evolutionary operation and mixture experiments.
This is a very clever way of reducing programming costs for different modules. The price the user pays is in only having the ability to do sequential analysis. Robert pointed the drawbacks out very succinctly in his response to the thread.
So to Dave’s original question: are there pros and cons: Pros: Sequential Simplex Optimization simplifies the mathematical operations performed for EVOP, Response Surface or Mixture Experiments. It unifies the three concepts under one mathematical algorithm. Cons: You have to deal with the sequentiality of the experimental design. Again, thanks for sharing the link!

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#142969

Robert Butler
Participant

Thanks to Andy for providing an update on the status of the current simplex packages and also thanks to Hans for taking the time to look at them and summarize what they are doing.
As has already been noted – it would appear the problem with the newer simplex methods which permit the optimization of multiple Y’s are the same as the earlier versions – namely they will find you an optimum but the results of the experiments run using simplex methods cannot be used to build regression models capable of describing the effects of changing the various X’s in the process.

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#142992

Anonymous
Guest

Yes, it’s an ‘optimization’ procedure only, but a very effective one in my experience. The key is to make small changes, otherwise any correlation or collinearity make it exremely confusing! (Usually, the goal is to bring several Y’s into a tolerance window.)
It was shortly after I investigated this procedure that I decided to run a full factorial with on outer array replication and analyse it using ‘Taguchi Methods.’ To my surprise I found the use of an ‘outer array’ eliminated the interaction effects estimated in the usual way, by essentially pinned the levels of factors having level uncertainty (central limit) which has a particular advantage when the chemical activity of an ingedient is unknown. I also modelled this in Minitab using ‘what if data.’
As you know measuring quantities of chemicals accurately and precisely is not sufficient to set a factor level, because the level can change between trials and during replication. Therefore, I believe Dr. Box’s view of Taguchi Methods is in error.
This is why I now claim some DOE are over defensive against interactions, which is has a greater impact on efficiency than design resolution. (I don’t don’t the existence of non-linear effects, but a prediciton is a better test of their presence than a full model.)
Clearly, there is a link between the two cases – both suffer independent variable uncertainty with regard to chemical activity. Unfortunately, I don’t know if the use of NIR spectrosocy would be sufficient to set factor levels. (I’ve haven’t had a suitable contract to investigate this further.) In fact, I’ve only had four months in the past two years, which is why I’m now looking at a new career. I’ve had several interviews but no one appears to like me; or nature’s justice is pushing me along another path.
This why I should like to ‘pass the ball’ so to speak ..
Cheers,
Andy

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