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Robust optimization problem

Robust optimization problem

Robust optimization problem


For a measurement set-up I'm designing, I have to position two sensors which have to be placed at an angle (alpha, beta) wrt the x-direction (zero degrees). However, there is only one 'optimal' combination of angles (alpha-beta) in words of robustness. In order to determine this 'optimum', I want to do a sensitivity analysis how each possible combination of angles is sensitive to a small (angular) deviation i.e. in practice it is impossible to locate the two sensors perfect at the desired location. The combination of angles that is less sensitive to this variation of location is the optimal location I'm searching.

I searched on the internet which numerical method to use for this, however I'm not really experienced in optimization and stuff like that. I found methods like Monte Carlo, perturbation analyses, Taguchi etc. I'm reading already a several days but still I'm not sure which method to use for my problem. Anybody some suggestions which method is most appropriate? Examples (Matlab), tutorials etc.?

Any help or suggestion is welcome!!  


RE: Robust optimization problem

It doesn't matter what method you choose, as long as it gets you results that are useful.  Monte Carlo is pretty easy to set up if you know how one factor affects the others... you can often write a BASIC program in 10 minutes that tries all of the combinations.

If you don't know how one factor affects the rest, simulation of any kind is useless.  Time to hit the lab bench.

Dan - Owner

RE: Robust optimization problem

Can you come up with a function that takes alpha and beta as inputs and gives you 'sensitivity to small movements' as an output?

RE: Robust optimization problem

Quote (GuntherA):

Can you come up with a function that takes alpha and beta as inputs and gives you 'sensitivity to small movements' as an output?
If he could do that, I don't think he would be asking the question... that's Monte Carlo when swept through all alpha/beta.

Dan - Owner

RE: Robust optimization problem

As a follow up to IRstuff's comment, Minitab has a free month long period trial download which has features to do DOE's.

RE: Robust optimization problem

Yea I agree with the above. Your first step is a model of the system you need to formulate the objective function and constraints.
Then since you are not familiar with optimization problems then I suggest using Matlabs built in optimization solvers like http://www.mathworks.com/products/optimization/
or just type fmin.

On the other hand. in my experience in optimization, I generally use the sequential simplex method for non-global problems. And recently I programed the particle swarm optimization (PSO) and found it to be very exceptional at global type problems. I highly suggest it.

Just find a model and you are good.


RE: Robust optimization problem

Oh and the PSO is very very robust smile


RE: Robust optimization problem

Basically, Monte Carlo is an automated trial and error method. To get the most optimum values it will take a lot of steps.
A Genetic Algorithm usually gives you the result faster, especially if you have many variables to deal with.

RE: Robust optimization problem

IRstuff is right,
as you have an physical experiment, not an mathematical model, You will need to use experimental suited optimisation technique. The problem is with proper preparation of the experiment table. This is what he mean by DOE. For this You need to consider all your inputs and ouputs. There could be some additional input parameters according to what you are measuring (i.e. distance), and additional output parameters associated to sensors (i.e. environment conditions)
Then try to determine probability of exact placement of each sensor its standard deviation (trial and error method can be used for n trials where n should be more than > 3.8416*EstimatedStDev^2/AssumedError^2)

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