optimization solver integration

This work addresses the interoperability challenges arising from inconsistent interfaces among numerical solvers by proposing and implementing MaRDI—a standardized, open interface tailored for nonlinear optimization. Designed with a modular architecture, MaRDI establishes a generic solver adapter layer that enables seamless integration of diverse optimizers and embeds naturally within physics-informed neural network (PINN) training pipelines. Its efficacy is demonstrated through application to the viscous Burgers equation, where it substantially reduces the development overhead and benchmarking costs associated with solver-specific bindings. By abstracting low-level implementation details, MaRDI allows researchers to focus on core algorithmic innovation while significantly enhancing the efficiency and reproducibility of cross-solver experimentation.

This work addresses the lack of scalable, general-purpose tools for polynomial-time reductions among NP-hard optimization problems, which hinders flexible integration with quantum hardware, commercial solvers, or heuristic algorithms. The authors propose a "constraint engineering" framework that leverages AI-powered coding agents to automatically construct a comprehensive reduction library. Built in Rust, the system features type safety, multi-layer verification, and a fully automated pipeline for implementation, review, and integration, enabling composable, transitive reduction graphs. Within three months, the team developed over 170,000 lines of code, covering more than 100 NP-hard problems and 200 reduction rules. Once a new solver is registered, it immediately becomes available across the entire connected component of the reduction graph, significantly enhancing reusability and interoperability.

针对自然语言描述的优化问题中数值信息不完整的问题，SAILOR系统通过与用户互动提问来补充缺失值，并更新模型以求解。

This study addresses the heavy reliance of scientific software optimization on domain experts, which impedes large-scale data processing. To overcome this limitation, this work proposes a framework in which large language model (LLM) agents autonomously optimize mature scientific software. Within this paradigm, human involvement is restricted to defining objectives and verification mechanisms, while automated acceleration is achieved through algorithmic restructuring and low-level code optimization. The contributions demonstrate that, for verifiable problems, artificial intelligence can attain automated optimization surpassing manual efforts, thereby reshaping human–machine collaboration paradigms. Empirically, the proposed approach yields up to two orders of magnitude speedup in tasks such as t-SNE and discovers novel graph counting algorithms.

Many optimization problems in manufacturing, logistics, and healthcare remain reliant on manual heuristics due to the high modeling barrier for Mixed-Integer Linear Programming (MILP). Method: This paper proposes the first end-to-end MILP automation framework driven by natural language descriptions. It introduces a modular large language model (LLM) architecture integrating natural language understanding, program synthesis, code debugging, solution quality verification, and feedback-driven iterative refinement. Additionally, it establishes NLP4LP—the first long-horizon, complex LP benchmark dataset derived from natural language problem specifications. Contribution/Results: Experiments demonstrate that our framework achieves an accuracy gain of +12.3% over state-of-the-art methods on easy instances and +8.7% on hard instances—including those in NLP4LP—significantly advancing automated modeling and efficient solving of large-scale real-world optimization problems.

This study addresses the limitation of existing numerical solvers that rely on execution-feedback-driven trial-and-error optimization, which hinders root-cause identification of performance bottlenecks. We propose ADSD, a framework adhering to a "diagnosis-first" paradigm that pioneers the integration of automated diagnosis with skill discovery. By employing AI agents to analyze failure mechanisms and encapsulate reusable numerical skills, ADSD transforms blind code editing into a structured knowledge accumulation process encompassing diagnosis, discovery, and implementation. Experimental results demonstrate that this approach significantly enhances solution accuracy and robustness across four major domains, including power flow equations. Notably, it achieves a 71-fold error reduction on the GOC-500 benchmark while exhibiting strong cross-scenario generalization capabilities.

This work addresses the lack of interoperability among nonlinear optimization solvers in scientific computing, which typically necessitates extensive code refactoring and revalidation when switching solvers or invoking them across programming languages. To overcome this limitation, the authors propose a universal interface framework tailored for nonlinear optimization problems. The framework employs a modular architecture that integrates multi-language bindings and an automated data marshaling mechanism, enabling plug-and-play solver integration and seamless cross-language invocation. By abstracting solver-specific implementation details, the framework substantially reduces the development and verification overhead associated with solver substitution and cross-language collaboration, thereby significantly enhancing the iteration efficiency of scientific computing workflows.

Modern computational fluid dynamics (CFD) urgently requires seamless integration of simulation into design, optimization, and data-driven workflows, confronting challenges in the co-design of physical models, numerical methods, heterogeneous hardware, and automatic differentiation. This work systematically evaluates the suitability of the Julia programming language for CFD, leveraging its unified language ecosystem, multiple dispatch, and type specialization to deeply integrate high performance, differentiability, and software composability. Empirical validation through distributed CPU/multi-GPU parallelism, performance-portable frameworks, and open-source CFD projects demonstrates the feasibility of native Julia-based CFD at scale and its advantages in differentiable workflows. Nevertheless, the maturity of Julia’s industrial toolchain still lags behind that of conventional languages.

This study addresses the limitation of existing globally unified testing frameworks, which achieve average optimality yet remain suboptimal for individual instances and struggle to adapt to specific task cases. To overcome this, we propose the first adaptive framework that recycles information from global optimization experiences. Methodologically, our approach repurposes global optimization artifacts to generate structured manuals and trains an editor to craft instance-aware patches for each case, thereby enabling dynamic framework generation and optimization. We evaluate the proposed method across seven benchmarks encompassing interactive agents, software engineering, and long-horizon terminal tasks. Experimental results demonstrate that our approach consistently outperforms existing baselines, establishing a robust solution for instance-level adaptation in complex testing environments.

研究提出ANVIL编译器架构，通过语言模型生成LaTeX公式再由确定性编译器转换为代码，以解决优化问题自然语言描述转代码的准确性问题。