In the absence of mathematical expression, how can i optimize a problem with minimum effort ? Which technique to use ? What will be the approach like ?
Will DOE ( Design Of Experiments), may be taguchi method, be helpful ? If yes how ?
Thanks !
Rajesh.
Do you refer to a black-box problem? (i.e. when the maths of the underlying problem are unknown)
If so you may try any convenient variant of evolutionary algorithms. You can check some available EA frameworks here:
http://en.wikipedia.org/wiki/Java_Evolutionary_Computation_Toolkit
http://en.wikipedia.org/wiki/Paradiseo
http://en.wikipedia.org/wiki/MOEA_Framework
@ Juan, thanks for the info.
Even if I use any evolutionary algorithms, like genetic algorithm, there should be some thing to drive it. I mean the fitness function, may be an neural network. And for which you need many data points, which I don't have.
Hi Dear,
You can use Neural Fuzzy at first to train your data then when it was trained, it means you have relationships between inputs and outputs, therefore then you can apply optimization method.
regards
I. Shafieenejad
@ Iman, thanks for the update.
But for training and developing the network, a sufficiently large data set is required, right. Which I don't have.
As Iman suggensted, you can use neural network. Give the inputs and outputs. train the network. It will find the pattern and be able to give out outputs when u give inputs outside the rage of training data. The more the no of neurons the better the results. This is just a simple statement. There are a lot mor to it.
@ Tawfiqur, thanks for the update.
But as I already mentions, I don't have much data sets to work with.
do you have any clue on some possible mathematical expression or on the physic behind the data? what kind of data do you have? You might use some candidates of models and try to figure out which of them is the proper one. At the end you might be able to pick one of those models and introduce some corrections (if necessary). Another option might be to do some Principal Component Analysis or Factor Analysis of the data, to see how many factors are driving the system output. This might give you other clues on the number of parameters that your model needs.
Hi,
DOE would be the easiest solution provided you are not interested in clarifying what the constitutive relationships are. You might be able to do this afterwards, once the data has been collected and the statistically significant independent variables identified; however this is not always possible and ultimately it's down to you and how much expertise you have with regards to the process.
DOE might be a bit of a problem if your experimental area is not regular, in which case you need to resort to D-optimal designs.
If you provide more info I will be happy to help to a larger extent.
cheers
In this thread ppl suggest some method.. but the setup is completely unknown.. We need to know more about this before anyone can answer.
What kind of data do you have? How many points, data type (e.g. continuous, categorical, etc)
You say you don't have much data.. but how much exactly?
Do you have access to the black box to generate more data? If not, then you have to build a very simple model..
cheers
I think if you relate your physical problem with optimization problem set. you can easily get your membership function for input and output data, then you can apply your optimization technique on that membership function. may it help you.
if your problem is like y = f(xi), where xi are the input variables. You can use linear perturbation method to evaluate the variation of y with a particular x, keeping other xi constant to generate data. Here you don't know the expression for f. But your data set may have some insights to construct a trail function at least
"Metamodeling" or "surrogate modeling" is one answer for your problem.
To do that, you need to generate a DOE and carefully fit an appropriate curve (surrogate model) to your data. Of course the accuracy of your surrogate model depends on the number of data you generated in the DOE.
There are numerous surrogate modeling (metamodeling) methods reported in the literature you may want to review.
Hope it helps.
Hi Dear,
in contrast if you have many data. processing time for training neural fuzzy is one of your problems. So, if you have some data it is better. for example 50 data can train your system. However, sensitivity of your system is problem that only you can answer it. Finally I suggest one time you examine this method.
regards,
I. Shafieenejad
@ Alessandro, thanks for the info.
This is more a general research, where I am trying to apply optimization methods to problems where one don't know whether the existing or improved design is in fact the optimum or not. More from CFD point of veiw. It would be computationally expensive to run multiple iterations, in order to get data sets.
Under such circumstances, if there is any way out. It would be great.
Thanks for your help.
Rajesh.
@ Filomeno, thanks for the info.
the data sets I have is numerical results. Can you give me a better insight in to DOE. Appreciate your help, thanks.
@ Tobias, thanks for the info.
the results that I have are numerical results. I can generate more data, but it would be computationally expensive. That is why I am looking for any other method, which is much simpler and serves the purpose.
Appreciate your help.
@ Kanhaiya, thanks for the help.
But what I am looking is not a conventional ways out, but more a simpler way. Like a "jugaad".
@ Sasi, thanks for the insight. Would you please provide me a better insight, it seems promising. Do you have any material on it ? Anything would be a great help.
What if there are more independent variables, say for example for 2 independent variable.
y=f(x,z)
Appreciate your help.
Rajesh.
@ Rouhi, thanks for your help.
It seems promising. Do you have any materials in regard to this. It would be a great help. And how to generate DOE ?
Appreciate your help.
Rajesh.
@ Iman, thanks for the info.
I am aware of this method, but the problem is to generate 50 sets of data might takes more time. What I am looking forward is much generic method.
Appreciate your help, thanks.
Rajesh.
Dear Mr. Rajesh
The problem is really interesting. When I starting working on one of the research problem, faced the similar issue and wondered a lot in finding the appropriate approach. Taguchi method and full factorial approach can be utilized for this purpose, where effect of various factors on different levels can be assessed. Both the approaches are equally good but I will recommend Taguchi because you can reach to some conclusion in time effective manner.
Well, for creating Taguchi design two approaches can be applied.
1. Manual
2. Simulation.
Manual approach need to be done on paper and needs lots computation and evaluation whereas simulation based approach is much better. For the simulation purpose you can use Minitab 15 or Minitab 17. The trial version for both is avialabe online.
Visit: http://it.minitab.com/en-us/products/minitab/free-trial.aspx
Its 30 days trial version. This tool is very easy to run and gives accurate results. You can utilize the help given with the tool to understand the step-by-step working and to interpret the response.
At the end you will be in a position to report or identify the appropriate combination of factors that can be used to conduct the final experiment to receive the optimized results.
If you need any help then discusses, will happy to help upto best of my knowledge.
Thank you so much.
-Hari
Rajesh,
if you are not familiar with DOE I suggest you take a quick look at Montgomery's book "Design of experiments" and download a trial version of Stat-Ease design expert. For your sort of application and need, it should be pretty straightforward.
@ Hari, thanks for the update. It seems promising, I will go in deep.
Appreciate your help.
Rajesh.
@ Filomeno, thanks for the update. I will do that.
Appreciate your help.
Rajesh.
This is a wide assumption having large number of possibilities. You need to give specific conditions of your problem to be solved. Then may some body can help.
@Rajesh
I used surrogate modeling based design optimization in a number of my recent publications that are listed in my RG page. You may want to take a look at them (esp. in the introcution parts on metamodeling approaches) to find some references useful for what you need.
Good luck,
Mohammad
@ Mohammad, thanks for the info.
I will go through it.
Appreciate your help.
Rajesh.
@ Fouad, thanks for the info.
Yes, ANN is an option to generate a driving function. But I don't have sufficient data point to generate an ANN.
@ Farhad, thanks for the info.
I will go through it. Appreciate your help.
Use the surrogate models or approximation
Response surface methodology (RSM)
Kriging
Neural networks
or Regression Support Vector (RSV)
Rajesh, check my profile on Research Gate. There is a description of the so-called Sequential Simplex Search. This method was specifically developed for the situation when the results of experiments are not calculated through a mathematical expression but rather evaluated qualitatively. However, there are miracles in the world, and to be able to use the method you must be able for any two results of your experiment to determine which one is better (or worse). Feel free to contact me directly for more details.
The non lineal programming and discreet programming numeric methods, as well as metaheuristics don't need analytic descriptions of the models relationships. In quality of models complex calculation procedures characteristics of each specialty or thematic could be used, including those that require to find approaximation functions, using implicit calculation procedures, etc. If the efficiency indicators and the variables that require to be restricted can be calculated by certain algorithm, then you can use some of the mentioned methods. I am attaching you a work that could be useful.for you
If you go back to the methods of optimization techniques illuastrated in the new published literature, you can find methods of optimization depending on graphical representations or numerical procedures.
