Presolve strongly affects mixed-integer programming (MIP) performance, yet learning-based methods only optimize parameter configurations and cannot express 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 distribution by up to several-fold. We recast presolve planning as autoregressive sequence generation over a unified atomic action space, moving the decision object to action sequences; we call this framework ORDO---Operation-level Round-aware Dynamic Ordering for MIP Presolve. Its payoff is cross-domain generalization: on multiple unseen domains it attains end-to-end zero-shot speedup---to our knowledge 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 facility, added by modifying the SCIP source, that injects sequences along the native path and records which actions actually execute and in which round.
Figures & tables
Figure 1: The four-stage pipeline of the method in this paper. Corpus construction and sequence modelling are each performed once offline; the online part performs only per-instance decoding and sequence racing; the measurement layer takes the solver-internal time of the isomorphic default strategy as the denominator and reports the SGM ratio and the per-instance win rate.
Figure 2: Structure and conditioning of the sequence generation model. Instance features are fed as the initial state concatenated with the historical action tokens, and causal self-attention (rotary position embedding, RoPE, applied to Q/K ) autoregressively predicts the next item; round boundaries and the terminator share one output space with the actions, so that "in what order and at which round to execute" is given by the same distribution.
Figure 3: The deployment form and measurement protocol of concurrent racing. Pool = np + content× K + fallback× K = 2K+1 paths launched together; the first to finish wins and the others are withdrawn (SIGKILL); the numerator is the solver-internal time of the winner, and the denominator is the internal clock of the replica of the isomorphic default strategy selected as the first to finish, so the speedup shown in the figure is the ratio reading with which that instance enters SGM.
Department of Data Science and Artificial Intelligence, Monash University, Melbourne, Australia · The Graduate University for Advanced Studies, SOKENDAI, Kanagawa, Japan