Imperfect Is Perfect: Learned Column Prefilling for Branch-Price-and-Cut

Key points

• Because the columns need not be optimal, producing them becomes a learning task: a neural edge scorer guides a constructive generator that builds the pool in seconds.1
• With prefill and center in place, exact pricing dominates root pricing time, so we rebuild bucket-graph labeling around its dominance test for the GPU and certify on the CPU.1
• Inside RouteOpt, the state-of-the-art exact solver for capacitated vehicle routing, the pipeline reaches the same certified root bound in 13.2% of vanilla RouteOpt's root pricing time over 95 instances with 300 to 1000 customers, prefill alone in 26.1%, and 17.5 times faster in the best case.1
• In an exact branch-price-and-cut solver for unrelated parallel machine scheduling, prefill with smoothing and the learned center certifies all 25 benchmark instances, 12 times faster than the solver's own column generation, which certifies 20 of them.1

Sources (1)

• [1]Imperfect Is Perfect: Learned Column Prefilling for Branch-Price-and-Cut
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 14, 10:38 PM

  Column generation folklore warns that initial columns hurt: a warm start may bias the dual and slow the root of branch-price-and-cut.

  Because the columns need not be optimal, producing them becomes a learning task: a neural edge scorer guides a constructive generator that builds the pool in seconds.

Extractive summary: sentences quoted from the sources.