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 Pool = np + content× K + fallback× K = 2K+1 paths launched together; the first to finish wins and the others are withdrawn (SIGKILL); the numerator is the solver-internal time of the winner, and the denominator is the internal clock of the replica of the isomorphic default strategy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.
Optimization problems are central to decision-making in manufacturing, logistics, scheduling, and other industrial settings. Translating complicated descriptions of these problems into solver-ready formulations requires specialized operations research (OR) expertise, making it hard to scale. We present AutoOR, a scalable synthetic data generation and reinforcement learning pipeline that trains LLMs to autoformalize optimization problems specified in natural language across linear, mixed-integer, and non-linear categories. AutoOR generates verified training data from standard optimization forms and uses solver execution feedback as the reward signal for RL post-training. AutoOR applied to an 8B model achieves state-of-the-art or competitive results across six established OR benchmarks, matching significantly larger frontier models. For a non-linear problem class involving physical dynamics, where frontier models score near 0%, we introduce a curriculum RL strategy that bootstraps from limited initial training data to make this class tractable for post-training. We believe that methods such as AutoOR can significantly accelerate industrial decision-making with AI.
Sumeet Ramesh Motwani, Chuan Du, Aleksander Petrov +4
Column generation and branch-and-price (B&P) are leading mathematical optimization methods for large-scale exact optimization, iterating between solving a master problem and a pricing problem. Due to the difficulty of discrete optimization, high-performance column generation often relies on a custom pricing algorithm built specifically to exploit the problem's structure. This bespoke nature of the pricing solver makes column generation a problem-specific method and hinders the use of generic implementations across a wide range of problems. We show that domain-independent dynamic programming (DIDP), a model-based paradigm for dynamic programming, can be used as a generic pricing solver. We develop new modeling features and a solving algorithm for DIDP to achieve better performance in typical pricing problems. We demonstrate that in four problem classes, our implementations of B&P, with pricing by DIDP, empirically outperform an existing automated B&P solver and B&P with pricing by mixed-integer programming or constraint programming.
Ryo Kuroiwa, Edward Lam
Department of Data Science and Artificial Intelligence, Monash University, Melbourne, Australia · The Graduate University for Advanced Studies, SOKENDAI, Kanagawa, Japan
Mixed-integer programming (MIP) research is both mathematically sophisticated and engineering-intensive: testing an algorithmic hypothesis within a branch-and-cut solver requires substantial implementation, debugging, tuning, and large-scale benchmarking. We propose an agentic MIP research framework that shortens this feedback loop by embedding LLM agents into a solver-aware harness for generating, verifying, and evaluating plugins for the open-source solver SCIP. Propagation methods play a central role in accelerating MIP solving by exploiting global constraints. We instantiate our framework on the semantic lifting of MIP formulations into global constraints and the automatic construction of propagation-only SCIP constraint handlers. On the MIPLIB 2017 benchmark set, the framework successfully recovers global constraint structures from constraint programming and generates executable constraint detectors and propagation-only constraint handlers. Furthermore, the framework naturally extends to in-context learning within a sandboxed environment, enabling agents not only to tune and debug generated constraint handlers on real instances, but also to explore global constraint patterns in MIP problems and discover novel propagation strategies not yet implemented in SCIP. This framework allows us to systematically distinguish meaningful algorithmic improvements from low-value or overly costly candidates: the novel propagation methods successfully solved five additional instances within the explored benchmark. Overall, this framework demonstrates that LLM agents can autonomously navigate the complex MIP research loop, paving the way for a more automated solver development process.
Liding Xu, Yugeng Zhou, Sebastian Pokutta
Zuse Institute Berlin, Berlin, Germany. · Independent Researcher. · Zuse Institute Berlin +1