Engineer for automatic furniture layout algorithm

Given the shape of a room, and a large database of furniture with its dimensions, produce the best few layouts to furnish that room, according to the room type — a small number of options, each genuinely different from the others, and every one of them obeying the interior design rules: how much clear space a piece needs, walkability paths, what faces what, distance range between the TV and the sofa, etc. You do not need to be an interior designer. We have a set of interior design rules and more may be researched if needed. This is a mathematics and algorithms job. We may also provide you access to our interior designer to answer question about the rules and layout if need be. The ultimate goal is to produce the arrangements a designer would have drawn, and knowing that it is the best of the many we generated. We have engineered the start of a method/solution, we are looking for an engineer to finish it, amend it, or replace it with something better. Must have: - Strong applied mathematics and algorithms. - You have built a program of that kind before — one that had to pick the best few options out of a very large number of possibilities, under rules that pull against each other, where making one thing better makes another worse. Nice to have: - Any exposure to space planning or architectural software. Your approach: What approach would you recommend for a task like this — how would you generate candidate arrangements, how would you decide which one is best, and how would you make sure the few we show are genuinely different from each other? Please let us know your hourly rate and your availability per week.