ORDO: Operation-level Round-aware Dynamic Ordering for MIP Presolve

Presolve strongly affects mixed-integer programming (MIP) performance, yet learning-based methods only optimize parameter configurations and cannot ex- press the non-commutative temporal dependencies among actions, whose default order is nearly unique on most domains, yet functionally necessary: artificially shuffling the order of the same sequence inflates the tail of the solve-time distribu- tion by up to several-fold. We recast presolve planning as autoregressive sequence generation over a unified atomic action space, moving the decision object to ac- tion sequences; we call this framework ORDO—Operation-level Round-aware Dy- namic Ordering for MIP Presolve. Its payoff is cross-domain generalization: on multiple unseen domains it attains end-to-end zero-shot speedup—to our knowl- edge the first for presolve action sequences—varying by domain and not explained by corpus richness, the strongest domain reaching the largest speedup once racing is added. Deployment uses sequence racing, in which candidate sequences run concurrently and the winner is kept, enabled by an execution-and-observation fa- cility, added by modifying the SCIP source, that injects sequences along the native path and records which actions actually execute and in which round.