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I'm trying to place multiple light sources on a 2D plane, in a fashion that satisfies multiple constraints. The 2D scalar distributions are the irradiance distributions of each light source that are functions of a 3D poisition vector and 2 orientation angles.

I want the lights to be set up to satisfy certain constraints as well as possible (maximal homogeneity in a certain area, minimal glare in certain area).

It is not an orthodox packing problem as far as I can tell, since the lit areas have a form that can change substantially by varying the positions and directions of each light source. Additionally, superposition of the irradiance distributions may be needed for an optimal solution.

The only solution I've come up with is a naive minimization of a cost function (using gradient-descent methods, simulated annealing) composed of my constraints. But there may be a more efficient approach to solving such a problem.

Does SCICOMP know a more efficient strategy to tackle this problem? Or an applied mathematics/computer science field dealing with similar problems, so that I may do further research?

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Steepest descent or other "simple" methods are not going to converge to the optimal solution since the problem is not convex. This is easy to see: if you swap two lights, you get the same irradiation. In other words, if you've found one optimum, you can find many others just by swapping lights. What this suggests is that you need an algorithm that allows for global optimization if you really care for finding the best arrangement, not just a local optimum. Of course, global optimizers are also much more expensive than local ones such as the steepest descent method.

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