Scalable Learned Large Neighborhood Search via Fixed-Canvas Segmentation

Large neighborhood search improves an incumbent by releasing selected variables and repairing the resulting subproblem under a time limit. FOVEA casts variable selection as dense semantic segmentation on a fixed $128\times 128$ canvas. A small U-Net reads twelve semantic channels and predicts cell scores, which are decoded into a variable set subject to a fixed variable budget. Family-specific layouts connect the search state to the canvas, while one set of network weights serves four problem families. The FP32 network input occupies $786$ kB across instance sizes. Our analysis bounds constraint coupling for spatially coherent regions, gives a rank certificate for rounds with zero possible improvement, and bounds the coupling advantage attainable on an expander family. On the tested families and hardware, FOVEA trails the strongest graph encoder at $10^4$ variables and overtakes it near $1.5\times 10^4$; the cost model provides an approximate crossover estimate. At larger sizes, where the graph-encoder baselines exceed device memory, FOVEA reduces the primal integral by $12$ to $16\%$ relative to the best runnable baselines. On the expander family, FOVEA performs comparably to random selection, with a coupling advantage close to one.