constraint-based model distillation

Mixed-integer linear programming (MILP) solvers often suffer from high computational overhead due to problem complexity and redundant constraints. Method: This paper proposes a constraint reduction-based model simplification method that precisely identifies and converts critical tight inequality constraints into equalities—thereby reducing problem size while preserving feasibility. We introduce the first systematic investigation of constraint reduction for MILP simplification, designing a multimodal representation learning framework that jointly encodes instance-level features (e.g., coefficient matrix, variable bounds) and abstraction-level features (e.g., constraint graph structure). Tight-constraint labels derived from optimal solutions and heuristic filtering further enable efficient identification of pivotal constraints. Contribution/Results: Experiments demonstrate that our approach achieves, on average, a 17.47% reduction in solving time and improves feasible solution rate by over 50%, outperforming state-of-the-art methods while maintaining solution quality.

Streamlining constraints in Constraint Optimization Problems (COPs) rely heavily on manual, problem-specific design, suffering from poor generalizability and scalability. Method: We propose the first LLM-based approach for automatically generating MiniZinc streamlining constraints. Our method integrates prompt engineering, lightweight empirical feedback loops, and test-driven iterative validation to dynamically identify high-performing constraint combinations—mitigating memorization bias and ensuring offline runtime independence and cross-problem generalizability. Contribution/Results: Evaluated on seven representative COP classes, our generated constraints significantly reduce search space size and outperform both human-crafted and systematically constructed baselines in solving speed. Ablation studies—including on adversarial “confused” and “camouflaged” benchmarks—demonstrate robustness and transferability. This work pioneers the use of LLMs for creative, data-efficient streamlining constraint synthesis and establishes a verifiable, reproducible empirical optimization paradigm grounded in rigorous testing and feedback.

This paper addresses the trade-off in modeling disjunctive constraints in mixed-integer programming (MIP): the big-M formulation yields weak relaxations, while the convex-hull formulation is computationally expensive. We propose the *P*-split method—a novel reformulation paradigm situated between these extremes—by performing dimensional lifting and piecewise convex-hull construction over additively separable convex functions. Crucially, *P*-split establishes the first hierarchical family of formulations whose relaxation strength monotonically improves with the split parameter *P*, enabling progressive convergence from the big-M relaxation to the convex hull. The method unifies modeling for both convex and nonconvex disjunctive terms, extending beyond classical applicability limits. Evaluated on 344 benchmark instances—including K-means clustering, semi-supervised clustering, P_ball problems, and ReLU neural network optimization—*P*-split achieves node counts comparable to the convex hull while reducing solution time by an order of magnitude, significantly outperforming big-M.

This paper investigates the parameterized complexity of “almost satisfying all constraints” for finite Boolean constraint languages Γ, formalized as Min SAT(Γ) (minimize the number k of unsatisfied constraints) and its weighted variant Weighted Min SAT(Γ) (ensure total violation weight ≤ W). Employing a novel synthesis of directed flow augmentation, algebraic classification of constraint languages, weight-sensitive kernelization, and structural analysis of graph cuts, we establish, for the first time, a unified complexity dichotomy for both unweighted and weighted cases. For every Γ, we completely characterize fixed-parameter tractability: either (i) Weighted Min SAT(Γ) is FPT while Min SAT(Γ) is W[1]-hard, (ii) both are W[1]-hard, or (iii) Weighted Min SAT(Γ) is FPT (implying Min SAT(Γ) is also FPT). Our framework overcomes prior limitations in modeling implication constraints (u → v), and systematically generalizes and unifies landmark results including Almost 2-SAT, ℓ-Chain SAT, and Coupled Min-Cut.

This work addresses the lack of systematic methodologies in model optimization, which often relies on heuristic choices and struggles to accommodate diverse deployment constraints. It formalizes model compression and acceleration as a constraint-aware multi-objective engineering decision problem, establishing a unified and actionable framework grounded in five key dimensions: data availability, latency, memory footprint, accuracy tolerance, and retraining budget. By integrating techniques such as quantization, pruning, knowledge distillation, parameter-efficient fine-tuning (PEFT), and inference optimization, the study proposes tailored optimization pipelines for four representative industrial scenarios, delivering a reproducible and quantifiable guide for technology selection.

This study addresses a central challenge in behavioral economics: extracting boundedly rational models that are both descriptively accurate and welfare-relevant from computationally complex and imperfectly rational choice behavior. The authors introduce techniques from constraint programming and combinatorial optimization to jointly analyze two prominent classes of bounded rationality models—“consideration set” and “limited attention” frameworks—and propose selection criteria that substantially reduce predictive ambiguity. Using real-world human choice data, the analysis reveals that limited attention models exhibit superior explanatory power and greater inclusiveness. Moreover, combining both model classes accounts for nearly all observed choices and significantly narrows welfare-relevant prediction intervals, thereby enhancing the practical applicability of these models for policy and welfare analysis.

This work addresses the challenges of using large language models (LLMs) to generate solvers for combinatorial optimization problems, where directly optimizing search strategies often introduces errors or degrades performance. The authors construct CP-SynC-XL, a benchmark comprising 100 problem types and 4,577 instances, to systematically evaluate three modeling paradigms: native Python, Python with OR-Tools, and MiniZinc with OR-Tools. Their analysis reveals a “heuristic trap”: compelling LLMs to generate optimized search logic yields only marginal speedups (1.03–1.12×) while significantly compromising correctness. Among the paradigms, Python+OR-Tools demonstrates superior performance. Based on these findings, the study proposes a “reformulate carefully, optimize sparingly” principle, advocating that LLMs should focus on formalizing variables, constraints, and objectives rather than synthesizing search strategies, thereby enhancing solver reliability.

This work addresses the inefficiency of traditional finite-domain propagation methods that handle difference constraints $x - y \leq d$ individually. It presents the first global propagator for difference constraints equipped with an explanation mechanism, unifying all such constraints into a single model and enforcing bounds consistency via shortest-path algorithms. The propagator is seamlessly integrated into a lazy clause generation (LCG) solving framework, overcoming the limitations of constraint-by-constraint propagation. For the first time in constraint programming, this approach enables synergistic global reasoning over difference constraints and conflict explanation. Experimental results demonstrate that the proposed method significantly outperforms standard propagation strategies in terms of solving efficiency.

This work investigates how to effectively transfer the performance of large models to compact ones in combinatorial optimization tasks through knowledge distillation. To this end, the authors propose a novel distillation framework based on algorithmic alignment, which explicitly aligns the architecture of graph neural networks with dynamic programming algorithms. For the first time, they establish theoretical guarantees for this distillation process: under the assumption that the teacher model admits a linear representation, and by leveraging decision tree complexity analysis, they prove that distillation can be performed efficiently with respect to the decision tree complexity of the dynamic programming transition function. By integrating graph neural networks, dynamic programming, and learning theory, this study introduces a new paradigm and provides rigorous theoretical foundations for model compression in combinatorial optimization.