Mixed-Integer Linear Programming (MILP) is a fundamental problem class in operations research and combinatorial optimization, with broad applications to industrial decision-making. Owing to their NP-hardness, however, modern solvers may struggle to find high-quality solutions for challenging MILP instances within practical time limits.
arXiv:2608. 19953v1 Announce Type: new Abstract: Mixed-Integer Linear Programming (MILP) is a fundamental problem class in operations research and combinatorial optimization, with broad applications to industrial decision-making.
arXiv:2508. 20330v5 Announce Type: replace Abstract: Combinatorial optimization problems are ubiquitous in science and engineering.
arXiv:2605. 09382v2 Announce Type: replace Abstract: The Linear Assignment Problem is a fundamental combinatorial optimization task where classical exact solvers ensure optimality but suffer from an $\mathcal{O}(N^{3})$ bottleneck, while recent neural approximations struggle with scalability and exactness.
arXiv:2604. 23053v2 Announce Type: replace Abstract: Mixed Binary Quadratic Programs (MBQPs) are an important and complex set of problems in combinatorial optimization.
arXiv:2602. 14772v2 Announce Type: replace Abstract: The Winner Determination Problem (WDP) in combinatorial auctions is NP-hard, and no existing method reliably predicts which instances will defeat fast greedy heuristics.
arXiv:2607. 18252v1 Announce Type: new Abstract: Machine learning methods have shown that data-driven policies can accelerate mixed-integer linear programming (MILP) solvers, but many such approaches remain difficult to inspect, adapt, and deploy because the learned policy is represented as an external predictor or other opaque model.
arXiv:2605. 25246v3 Announce Type: replace Abstract: Large language models (LLMs) are increasingly used for optimization modeling and solver-code generation, yet practical operations research and optimization problems often require a harder capability: designing scalable algorithms that exploit problem structure and outperform direct formulation-and-solve baselines.
arXiv:2606. 00002v1 Announce Type: new Abstract: Mixed-Integer Linear Programming (MILP) decision engines routinely output nominally optimal plans for high-stakes industrial systems.
arXiv:2606. 04816v1 Announce Type: new Abstract: Large language models (LLMs) increasingly translate natural-language optimization problems into executable solver code.
arXiv:2606. 25832v1 Announce Type: new Abstract: Achieving strong optimization generalization across diverse optimization problems while requiring limited training resources remains a challenging problem for optimization-oriented large language models (LLMs).
arXiv:2606. 15197v1 Announce Type: cross Abstract: Optimization modeling is inherently hierarchical, requiring a precise sequence of symbolic commitments.
arXiv:2607. 13373v1 Announce Type: cross Abstract: Column generation (CG) is central to many large-scale optimization algorithms, including branch-price-and-cut methods for vehicle routing problems, but unstable dual solutions can substantially slow its convergence.