cutting-set optimization

Configuring Mixed-Integer Linear Programming (MILP) solver parameters—particularly for cutting-plane separation—is challenging due to high-dimensional, problem-dependent search spaces; existing machine learning approaches suffer from poor generalization, heavy reliance on large-scale labeled data, and difficulty integrating into solver pipelines. Method: We propose the first LLM-driven zero-shot cutting-plane separator configuration framework. It leverages large language models to jointly parse natural-language problem descriptions and LaTeX-based MILP formulations, augmented by literature-informed prompt engineering and semantic modeling of separators—requiring no custom interfaces or extensive retraining. A lightweight, performance-driven clustering ensemble strategy ensures both robustness and real-time responsiveness. Results: On benchmark combinatorial optimization instances and real-world datasets, our method matches state-of-the-art performance while reducing training data requirements by over 90% and generating configurations in under one second.

This work presents the first experimental study that simultaneously approximates solutions to both the Max-Cut problem and the Weighted Fractional Cut Cover problem. Building upon a primal-dual framework, the approach integrates semidefinite programming (SDP) relaxation with randomized hyperplane rounding, while replacing conventional theoretical algorithms with a linear programming (LP) solver to substantially enhance empirical performance. Using only ⌈128 ln m⌉ random samples, the method consistently achieves an approximation ratio close to the Goemans–Williamson bound of 0.878 for the vast majority of instances, demonstrating robustness and reproducibility. Notably, the LP-based variant frequently outperforms theoretical expectations, thereby validating the efficacy and practicality of the proposed hybrid strategy.

Cut selection in mixed-integer programming (MIP) relies heavily on hand-crafted heuristics, while existing learning-based approaches optimize only at the single-node level, ignoring inter-node dependencies across the branch-and-cut search tree. Method: We propose a global, cooperative cut selection framework that models the entire search tree as a bipartite graph to capture structural dependencies among nodes; integrates graph neural networks (GNNs) for topology-aware feature extraction with deep reinforcement learning for policy optimization; and seamlessly embeds the learned policy into the Branch-and-Cut framework. Contribution/Results: This is the first method to perform cut selection at the full-search-tree level, transcending local node-centric limitations. Evaluated on synthetic and large-scale real-world MIP instances, it reduces average solving time by 27.4% and accelerates optimal gap convergence by 2.1×, significantly outperforming both classical heuristics and single-node learning methods.

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 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 addresses the limitation of existing exact solvers for large-scale Maximum k-Cut problems (k > 2), which stems from the absence of effective preprocessing techniques. The paper introduces, for the first time, optimality-preserving data reduction rules tailored to this problem, leveraging structured cutset identification and graph decomposition strategies to partition the input graph into independently solvable connected components. A novel proof framework based on weighted graph superposition is developed to underpin these reductions. By engineering an integration of established MaxCut preprocessing methods into a unified system, the authors present the first efficient preprocessing pipeline specifically designed for k > 2. Experimental results demonstrate that the proposed approach substantially reduces instance sizes, significantly accelerates exact solvers when integrated, and enables solving more instances to optimality than previously possible.

This study addresses the unclear practical efficacy of automatically generated polynomial symmetry-breaking constraints in integer linear programming across different solvers. The authors systematically evaluate the performance of mainstream mathematical programming and SMT solvers when handling such constraints, comparing three strategies: native quadratic handling, internal reformulation, and explicit linearization. Their experiments reveal that the effectiveness of symmetry breaking is highly solver-dependent, advocating for a solver-aware evaluation paradigm. The findings indicate that compact families of quadratic symmetry-breaking constraints generally enhance solver performance, whereas excessive linearization, overly large breaking sets, or inappropriate reformulations often lead to model bloating or search degradation, thereby diminishing or even reversing potential benefits.

This work addresses the lack of formal guarantees regarding semantic preservation during problem reformulation and solver correctness in constraint programming. It presents the first end-to-end verified framework implemented in the Lean theorem prover, enabling formal proofs of parameterized equivalence, equisatisfiability, and symmetry-breaking correctness for entire families of problems. The approach combines general, parameterized proofs with instance-level certificate checking, thereby eliminating the need to trust external solvers. Verified certificates are produced via backend transformations, and a single high-level proof suffices for arbitrarily large instances. This methodology achieves dramatic search-space reductions—up to a factor of twenty million—and enables full verification of the largest instances in just a few minutes.

This work addresses the lack of machine-verifiable formalizations of line search methods in nonlinear optimization, which has hindered algorithmic reliability. Within the Lean 4 theorem prover, it presents the first systematic formalization of several classical line search criteria—including Armijo, Goldstein, Wolfe, and their nonmonotone variants—alongside rigorous definitions of gradient descent, descent directions, and backtracking step-size selection. The study fully verifies the Zoutendijk convergence theorem within this framework, thereby establishing a comprehensive formal foundation for line search theory. This contribution significantly enhances the verifiability and trustworthiness of nonlinear optimization algorithms through mechanized mathematical reasoning.