Imperfect Is Perfect: Learned Column Prefilling for Branch-Price-and-Cut
Column generation folklore warns that initial columns hurt: a warm start may bias the dual and slow the root of branch-price-and-cut. We show the opposite once the columns are imperfect in the right way. Preloading the support of the optimal root LP, the best columns one could know in advance, fails to finish on half of our hardest instances; a pool of ordinary routes that need not belong to any optimal solution, held outside the master and priced at the current smoothed dual, speeds the root up. 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. A second network predicts th...
| Authors | Haoran Liu, Yu Yang |
|---|---|
| Primary category | cs.LG |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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