LLM for Large-Scale Optimization Model Auto-Formulation: A Lightweight Few-Shot Learning Approach

Large-scale optimization is a key backbone of modern business decision-making. However, building these models is often labor-intensive and time-consuming. We address this by proposing LEAN-LLM-OPT, a LightwEight AgeNtic workflow construction framework for LLM-assisted large-scale OPTimization auto-formulation. LEAN-LLM-OPT takes as input a problem description together with associated datasets and orchestrates a team of LLM agents to produce an optimization formulation. Specifically, upon receiving a query, two upstream LLM agents dynamically construct a workflow that specifies, step-by-step, how optimization models for similar problems can be formulated. A downstream LLM agent then follows this workflow to generate the final output. Leveraging LLMs' text-processing capabilities and common modeling practices, the workflow decomposes the modeling task into a sequence of structured sub-tasks and offloads mechanical data-handling operations to auxiliary tools. This design alleviates the downstream agent's burden related to planning and data handling, allowing it to focus on the most challenging components that cannot be readily standardized. Extensive simulations show that LEAN-LLM-OPT, instantiated with GPT-4.1 and the open source gpt-oss-20B, achieves strong performance on large-scale optimization modeling tasks and is competitive with state-of-the-art approaches. In addition, in a Singapore Airlines choice-based revenue management use case, LEAN-LLM-OPT demonstrates practical value by achieving leading performance across a range of scenarios. Along the way, we introduce Large-Scale-OR and Air-NRM, the first comprehensive benchmarks for large-scale optimization auto-formulation. The code and data of this work is available at https://github.com/CoraLiang01/lean-llm-opt.

Enhancing binary classification: A new stacking method via leveraging computational geometry

Stacking, a potent ensemble learning method, leverages a meta-model to harness the strengths of multiple base models, thereby enhancing prediction accuracy. Traditional stacking techniques typically utilize established learning models, such as logistic regression, as the meta-model. This paper introduces a novel approach that integrates computational geometry techniques, specifically solving the maximum weighted rectangle problem, to develop a new meta-model for binary classification. Our method is evaluated on multiple open datasets, with statistical analysis showing its stability and demonstrating improvements in accuracy compared to current state-of-the-art stacking methods with out-of-fold predictions. This new stacking method also boasts two significant advantages: enhanced interpretability and the elimination of hyperparameter tuning for the meta-model, thus increasing its practicality. These merits make our method highly applicable not only in stacking ensemble learning but also in various real-world applications, such as hospital health evaluation scoring and bank credit scoring systems, offering a fresh evaluation perspective.