Firstly, please don't tell me about how "useless" static analysis and optimization is. I know it has limits, but I believe I am a stronger player because of it, therefore I will use it.
Secondly, please don't tell me "no forts". I am optimizing MPNW (DPNW + OPNW at a fixed off/def ratio). I may choose to run fewer forts due to "intangible" considerations, but I want to know the "optimal" number of each.
So the goal: find a way to take X% land at B% BE with M military units per acre (of strength O and D for off and def respectively) with a finial off/def ratio of R (aka, 3:2 or 2:1) and a fixed NWPA (before stables), and divide X up into TG, Fort, and Stables such that MPNW is maximized.
The question - how? I tried one approach in my simulation spreadsheet, but upon reexamining it, it stinks. It does better than splitting in 3rds, but it is clearly not optimal. No matter how high BE goes, it still has at least .1% stables. It was based on the idea of starting at the "corners" and moving towards the center, with the movement based on how much it "helped". It doesn't deal with discontinuities, and it doesn't deal with cases where optimal of a building is 0.
I also know I *could* write a "grid" approximation and refinement algorithm. Break the area up into 100 cubes, calc at each point, find the best 1, and do the same in a smaller grid around that point. This is NOT an algorithm that can be done effectively in a spreadsheet however, and it therefore requires rewriting the whole sim in C. (And worsening the user interface... cause I'm not writing a nice slick one in C just for this.)
So what else is available? Are there any good approximations that a spreadsheet can do? Are there any simplifications to the systems of equations we can make? Or is it just too hard?