We study certain extremal problems in combinatorial geometry that ask about configurations of points in an $n \times n$ grid that satisfy strict, global geometric constraints. Classical exact solvers suffer from combinatorial explosion for these types of problems, and standard reinforcement learning and transformer-based models struggle with the sparse reward "validity cliff" and quadratic token-consumption limits.
arXiv:2606. 09278v1 Announce Type: cross Abstract: Large Language Models frequently hallucinate in precision-critical domains such as technical diagramming and mechanical design, where outputs must satisfy strict geometric constraints.
By Rafael Cabral, Pang Zixi, Ziyi Shou, Shen Xin
arXiv:2607. 05359v1 Announce Type: new Abstract: Planning under uncertainty in continuous domains is essential for autonomous systems, yet computationally demanding.
By Idan Lev-Yehudi, Vadim Indelman
arXiv:2609.38863v1 Announce Type: cross
Abstract: The two-dimensional irregular knapsack problem in a fixed circular container is an important combinatorial optimization problem for maximizing materi...
By Zhongman Du, Huiming Zhang, Linlin Yang, Sheng Xu, Baochang Zhang
arXiv:2609. 29881v1 Announce Type: cross Abstract: Choosing Shellsort gaps is a well-known open problem.
By Bo Liu
Planning under uncertainty in continuous domains is essential for autonomous systems, yet computationally demanding. Tree-based search methods such as Monte Carlo Tree Search (MCTS) remain popular, but their branching structure can require sampling budgets that grow exponentially with lookahead depth in the worst case.
arXiv:2607. 23602v1 Announce Type: cross Abstract: Controllers based on sampling and latent world models assign a predicted terminal cost to each candidate action sequence, choose the minimum, execute its first action block, and replan.
By Liangyu Li, Qingwen Liu, Mingqing Liu
GeoPAR is a geometry-guided parallel autoregressive reinforcement learning framework designed for large-scale multi-agent combinatorial optimization. It introduces a projection-window sparse geometry mechanism, sparse edge-biased attention, and cache-guided conflict-aware assignment to better model local geometric structures and reduce duplicate task selections. Experiments on heterogeneous vehicle routing and multi-depot pickup-and-delivery problems demonstrate improved zero-shot generalization, fewer rollout steps, and efficient inference.
By Wenjian Wu, Zesheng Jia, Jiaying Tang, Benyuan Yang, Jin Wang
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
arXiv:2609.37356v1 Announce Type: new
Abstract: Generating optimization instances that are both feasible and computationally challenging is crucial for benchmarking solvers and training learning-base...
By Jitin Singla, Parikshit Pareek, Pratik Jawanpuria, Parag Singla
arXiv:2607. 27169v1 Announce Type: new Abstract: Solving a continuous algebraic constraint system requires two decisions: which values satisfy the constraints, and which structural augmentation renders an unsolvable system solvable.
By Quang Bui, Sparsh Roy, Akash Gundimeda, Davin Yin
arXiv:2607. 23785v1 Announce Type: cross Abstract: The Simple Temporal Problem (STP) is a core framework for quantitative temporal constraints.
By Johannes K. Fichte, Johanna Groven, Peter Jonsson, Victor Lagerkvist, Jorke M. de Vlas