Hello,

This is a rather simple optimization problem and almost any algorithm could do the job. If I understand right, you have a problem with 3 design variables (3 rotation angles). You have made an algorithm (function f) that takes these 3 variables and calculates the area of the shadow.

If function f is in analytical form then (generally speaking) you can try to minimize it yourself. You can do it by calculating the derivatives of f in respect to the 3 variables and then setting the derivatives equal to zero.

In most cases, f is not available in analytical form, but rather in algorithmic form (computer function). In these cases you have to use an optimizer. If you can program f in Excel then the most simple solution is to use the Excel Solver which is a very good optimizer (you have to install Excel Solver separately, it is not activated by default in Excel). Excel Solver presupposes that you have the 3 design variables in 3 cells and the objective function in another cell - also constraint values in other cells if you have some. It is very easy to use and rather efficient.

If you cannot have f in excel but you have it on a computer code, then you have to link an optimizer to your code. Any optimizer would do, you can start with a mathematical optimizer and then try also an evolutionary optimizer such as GA. If this is the case, you can provide us more information on the computer code you have for the calculation of the objective function (code language, structure, etc) and we can suggest more appropriate solutions.

I hope my answer helps!

Hello,

You should take into account that the problem is multi-extremal, ant that proper global optimization techniques should be applied. An alternative to minimizing vrt the body position is to minimize vrt the position of the source of light.

In our paper:

http://liu.diva-portal.org/smash/record.jsf?pid=diva2%3A354877&dswid=-9412

http://liu.diva-portal.org/smash/get/diva2:354877/FULLTEXT01.pdf

a robot is viewed as a source of light and the corresponding shade volume is minimized.

Hello,

You should take into account that the problem is multi-extremal, ant that proper global optimization techniques should be applied. An alternative to minimizing vrt the body position is to minimize vrt the position of the source of light.

In our paper:

http://liu.diva-portal.org/smash/record.jsf?pid=diva2%3A354877&dswid=-9412

http://liu.diva-portal.org/smash/get/diva2:354877/FULLTEXT01.pdf

a robot is viewed as a source of light and the corresponding shade volume is minimized.

Hello,

You should take into account that the problem is multi-extremal, ant that proper global optimization techniques should be applied. An alternative to minimizing vrt the body position is to minimize vrt the position of the source of light.

In our paper:

http://liu.diva-portal.org/smash/record.jsf?pid=diva2%3A354877&dswid=-9412

http://liu.diva-portal.org/smash/get/diva2:354877/FULLTEXT01.pdf

a robot is viewed as a source of light and the corresponding shade volume is minimized.

Dear Sirs,

Thank you for your responses, I really appreciate it.

The objective function doesn’t have an analytical Jacobian and it has multiple minima probably depending on geometry complexity. I use Python language for coding this problem. I tried some global minimizers like Particle Swarm and Surrogate model optimization. In some cases these methods work but often fail even for a simple geometry. I have only a little experience with global optimization, please could You give any advice how to implement GA or another glob. minimization?