CG4AI is a column generation framework that trains AI models while enforcing linear constraints on their outputs. It constructs a convex combination of models, using a master linear program to set mixture weights and a pricing subproblem to generate new models guided by dual variables, focusing on the most violated constraints. The method is applied to MNIST digit classification—demonstrating constraint learning, adversarial robustness, error correction, and output relabeling—and to multi‑commodity flow routing, achieving feasible predictors with higher accuracy than single‑model baselines.
By Youcef Magnouche, Abderrahmane Driouch, S\'ebastien Martin, Pierre Bauguion
arXiv:2609.26275v1 Announce Type: new
Abstract: The vehicle routing problems with real-world constraints (we consider vehicles capacity limits, time windows constrains, pickup-and-delivery multi-depo...
By Andrew Soroka, Alex Meshcheryakov
arXiv:2606. 04816v1 Announce Type: new Abstract: Large language models (LLMs) increasingly translate natural-language optimization problems into executable solver code.
By Xizi Luo, Changhong He, Dongdong Geng, Chenggong Shi, Yu Mei
arXiv:2606. 01987v1 Announce Type: cross Abstract: We show that the Vehicle Routing Problem (VRP) can be reformulated as a Graph Edit Distance (GED) maximization problem.
By Adel Dabah
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.
By Guanlin Li, Chengrui Gao, Chenguang Wang, Haopu Shang, Zherong Zhang, Ke Xue, Jixiang Lu, Weiyong Yang, Chao Qian
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:2503. 03137v3 Announce Type: replace Abstract: Constructive neural combinatorial optimization (NCO) offers a promising paradigm for solving vehicle routing problems (VRPs) by directly learning to construct approximate optimal solutions, thereby reducing reliance on expert knowledge for algorithm design.
By Changliang Zhou, Xi Lin, Zhenkun Wang, Qingfu Zhang
StoSignSGD is a new sign‑based optimization algorithm that injects structural stochasticity into the sign operator, ensuring unbiased updates. It resolves the divergence issues of traditional SignSGD on non‑smooth objectives, achieving optimal convergence rates in convex settings and improved complexity bounds in non‑convex, non‑smooth problems. Empirical results show that StoSignSGD is stable and efficient across large language model training, outperforming AdamW and SignSGD in low‑precision regimes (FP8 and FP4) and delivering speedups and accuracy gains on models ranging from OLMo2‑370M to 7B LLMs.
By Dingzhi Yu, Rui Pan, Yuxing Liu, Difan Zou, Tong Zhang
The paper presents a method for reducing the size of Quadratic Unconstrained Binary Optimization (QUBO) models used to solve the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) on quantum annealers. It introduces adaptive penalty calibration to improve constraint satisfaction and replaces hand‑tuned merge heuristics with a graph neural network (GNN) that consistently achieves higher feasibility across Solomon benchmark families. Experiments on simulated annealing and a D‑Wave Advantage2 processor show significant reductions in constraint violations and improved feasibility rates, with the QUBO size remaining 5–6 times smaller.
By Youssef Kamel Rezk, Pawe{\l} Gora
arXiv:2607. 18632v1 Announce Type: new Abstract: Automated Algorithm Selection (AS) aims to improve problem-solving performance by selecting, for each problem instance, the most suitable algorithm from a predefined portfolio.
By Zhaoxuan Li, Jiale Yang, Yifei Lu, Mustafa Misir
arXiv:2608. 09042v1 Announce Type: new Abstract: Large traveling salesman problem (TSP) instances require a solver to allocate limited computation while preserving the validity of its outputs.
By Yancheng Song, Yongzhi Qi, Wei Qi, Zuo-Jun Max Shen
Large traveling salesman problem (TSP) instances require a solver to allocate limited computation while preserving the validity of its outputs. Existing neural--operations-research (OR) hybrids predict guidance without requiring learned transitions to satisfy constraints discovered during search.