A general optimization solver based on OP-to-MaxSAT reduction

Expensive optimization tasks are ubiquitous in real-world applications, demanding highly specialized solvers. While LLM-driven automated solver generation shows promise, current paradigms face three critical issues when tackling expensive optimization: factual hallucinations due to deficient domain knowledge, the frequent dismantling of previously established locally optimal structures during refinement, and the prohibitive evaluation costs alongside restricted generalization caused by executing on training instances. To address these issues, we introduce AutoSG, a fully automated workflow directly translating natural language prompts into executable customized solvers. AutoSG features three core innovations: a retrieval-augmented solver generation module strictly grounding code in verified literature; a one-step self-refinement operator introducing task-specific improvements while preserving critical structural components; and an instance-free Elo-based LLM-as-a-Judge evaluation mechanism rapidly establishing global rankings. Extensive evaluations across diverse expensive optimization tasks confirm AutoSG significantly outperforms human-designed state-of-the-art frameworks and existing LLM-generated solvers.

Discrete optimization is ubiquitous in science and engineering. The vast array of existing discrete optimization problems, coupled with the continuous emergence of new ones, necessitates off-the-shelf optimizers capable of generating high-quality solutions for a large variety of optimization problems. This article introduces MEGO, a novel general-purpose neural optimizer for binary optimization under the black-box setting, intended for broad applicability across diverse binary optimization problem classes with minimal problem-specific customization. MEGO comprises a mixture-of-experts trained without domain knowledge. When presented with a new problem instance to solve, it employs a routing policy to dynamically activate the most relevant expert models to generate high-quality solutions. The strong generalization capability of MEGO is demonstrated on six problem classes from different disciplines, including classic problems and real-world applications. Trained solely on classic problems, MEGO effectively generalizes to unseen and complex real-world problem classes, significantly outperforming widely-used general-purpose optimizers in both solution quality and efficiency. Furthermore, MEGO provides a computational approach for quantifying similarity between optimization problems and classifying them, which is fundamentally different from the conventional analysis-based problem classification.

Achieving strong optimization generalization across diverse optimization problems while requiring limited training resources remains a challenging problem for optimization-oriented large language models (LLMs). Existing approaches typically rely on large-scale supervised datasets, costly reasoning annotations, and expensive intermediate step verification, resulting in substantial training overhead. To address these challenges, we propose MiniOpt, a reinforcement learning framework that learns to solve optimization problems through an "reasoning-to-model-and-solve" paradigm. MiniOpt decomposes optimization reasoning into structured optimization modeling and executable solver generation. Building upon this paradigm, we introduce OptReward, a reward function with hierarchical score structure that jointly evaluates formulation and solution, enabling effective policy learning without expert demonstrations. We further develop an optimization-oriented policy optimization strategy that improves exploration efficiency and stabilizes reinforcement learning for compact models. Extensive experiments show that MiniOpt-3B exhibits strong optimization generalization across various optimization types, problem scenarios, and task domains. For models with fewer than 10B parameters, MiniOpt series achieves the highest average solving accuracy (SA). For models with more than 10B parameters, MiniOpt still shows competitive performance. These results suggest that optimization-oriented reward design and reinforcement learning provide an effective pathway for developing compact optimization-specialized language models with strong optimization generalization capabilities. The code is available at https://github.com/Hsiang-1/MiniOpt.