We picked this challenge to put everything we've studied on combinatorial optimization into practice. We started sketching it as a CLP model, then considered ILP, but the geometry (rectilinear polygons, rotations, variable ceiling) blew up the formulation. So we pivoted to what actually fit the budget: a greedy constructive phase plus local search with LNS + Simulated Annealing over a bitmap state. Each iteration ended up being a 2D convolution — clean, fast, and surprisingly elegant.
Simulated Appealing Optimizer
Warehouse shelf placement optimizer: a greedy strip-packer builds an initial layout, then LNS+Simulated Annealing on bitmaps uses FFT convolutions to find sparse regions and refill them optimally.
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