arXiv subjects

Wim P. M. Nuijten

Publications and source records attributed to Wim P. M. Nuijten.

4 recordsLinked to original sources

arXiv2026

Learning to Optimize through Solver-Grounded Self-Play

Optimization modeling is central to many decision-making scenarios, but traditionally requires extensive domain expertise. While Large Language Models (LLMs) have shown promise in automating this process, current training paradigms mainly rely on human-annotated or teacher-generated datasets. This dependence introduces a Generalization Ceiling, where models overfit to narrow data distributions, and Capability Anchoring, where models' reasoning is bounded by annotator proficiency and teacher model capability. In response, we propose OPT-Zero, the first fully self-play training framework for optimization modeling that requires zero external training data. OPT-Zero employs a single LLM in a dual-role closed loop: a Proposer that synthesizes increasingly challenging optimization problems alongside their mathematical formulations and solving code, and a Solver that attempts to resolve the problems given only natural-language problem descriptions. Grounded in execution feedback from external optimization solvers, we alternately train both roles using reinforcement learning. This process fosters an auto-curriculum in which the Proposer and Solver co-evolve: generating harder valid problems by the Proposer seamlessly enhances the structural reasoning ability of the Solver. Extensive results indicate that with zero curated data, OPT-Zero matches state-of-the-art data-dependent methods while exhibiting substantially stronger generalizability, establishing self-play training as a highly scalable paradigm for advancing LLM reasoning in modeling and solving optimization problems.

cs.LG↗

arXiv2026

Towards Solving Polynomial-Objective Integer Programming with Hypergraph Neural Networks

Complex real-world optimization problems often involve both discrete decisions and nonlinear relationships between variables. Many such problems can be modeled as polynomial-objective integer programs, encompassing cases with quadratic and higher-degree variable interactions. Nonlinearity makes them more challenging than their linear counterparts. In this paper, we propose a hypergraph neural network (HNN) based method to solve polynomial-objective integer programming (POIP). Besides presenting a high-degree-term-aware hypergraph representation to capture both high-degree information and variable-constraint interdependencies, we also propose a hypergraph neural network, which integrates convolution between variables and high-degree terms alongside convolution between variables and constraints, to predict solution values. Finally, a search process initialized from the predicted solutions is performed to further refine the results. Comprehensive experiments across a range of benchmarks demonstrate that our method consistently outperforms both existing learning-based approaches and state-of-the-art solvers, delivering superior solution quality with favorable efficiency. Note that our experiments involve both polynomial objectives and constraints, demonstrating our HNN's versatility for general POIP problems and highlighting its advancement over the existing literature.

cs.NE↗

arXiv2025

Revisiting Expected Possession Value in Football: Introducing a Benchmark, U-Net Architecture, and Reward and Risk for Passes

This paper introduces the first Expected Possession Value (EPV) benchmark and a new and improved EPV model for football. Through the introduction of the OJN-Pass-EPV benchmark, we present a novel method to quantitatively assess the quality of EPV models by using pairs of game states with given relative EPVs. Next, we attempt to replicate the results of Fernández et al. (2021) using a dataset containing Dutch Eredivisie and World Cup matches. Following our failure to do so, we propose a new architecture based on U-net-type convolutional neural networks, achieving good results in model loss and Expected Calibration Error. Finally, we present an improved pass model that incorporates ball height and contains a new dual-component pass value model that analyzes reward and risk. The resulting EPV model correctly identifies the higher value state in 78% of the game state pairs in the OJN-Pass-EPV benchmark, demonstrating its ability to accurately assess goal-scoring potential. Our findings can help assess the quality of EPV models, improve EPV predictions, help assess potential reward and risk of passing decisions, and improve player and team performance.

cs.CV↗

arXiv2024

Neural Combinatorial Optimization for Stochastic Flexible Job Shop Scheduling Problems

Neural combinatorial optimization (NCO) has gained significant attention due to the potential of deep learning to efficiently solve combinatorial optimization problems. NCO has been widely applied to job shop scheduling problems (JSPs) with the current focus predominantly on deterministic problems. In this paper, we propose a novel attention-based scenario processing module (SPM) to extend NCO methods for solving stochastic JSPs. Our approach explicitly incorporates stochastic information by an attention mechanism that captures the embedding of sampled scenarios (i.e., an approximation of stochasticity). Fed with the embedding, the base neural network is intervened by the attended scenarios, which accordingly learns an effective policy under stochasticity. We also propose a training paradigm that works harmoniously with either the expected makespan or Value-at-Risk objective. Results demonstrate that our approach outperforms existing learning and non-learning methods for the flexible JSP problem with stochastic processing times on a variety of instances. In addition, our approach holds significant generalizability to varied numbers of scenarios and disparate distributions.

cs.AI↗