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Solar panel optimisation problem

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This is my first post on here, so I hope you guys can help!



I am working on an optimisation problem concerning fitting homogeneous regular shapes (i.e. solar panels) within irregular shaped polygons (a standard house roof). I am looking to write a shape fitting algorithm. It wants to be as simple as possible to minimise computing time and of course be quick to code. I have written basic equations for standard roof shapes, but now I want to properly code something for all roof types.


Clearly to be universal the polygon (roof) shape will vary, but the nested shapes (solar panels) are all identical in size, in the same orientation throughout and the shapes are in straight rows.


Does anyone know if using a knapsack algorithm is an appropriate way to go or is this overcomplicating the optimisation problem to much?

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I'm having trouble with the statement "within irregular shaped polygons (a standard house roof)." Is it a standard house roof or is it an irregularly shaped polygon?


I wouldn't call this a knapsack problem there are no weights. I would solve this mathematically using a Lagrange, and this depends entirely on my first question.


Are the rooves going to be rectangular or are they going to be mostly complex shapes. I assume that either way you are wanting to cover them as entirely as possible?


Can the panels be cut? I am assuming no because you said "homogeneous regular shapes. . .".


The math can be a bit tricky, and might require someone to spend some time trying to create a solution that works!

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