Large language models (LLMs) have been widely adopted in mathematical optimization in scientific scenarios for their extensive knowledge and advanced reasoning capabilities. Existing methods mainly focus on utilizing LLMs to solve optimization problems in a prompt-based manner, which takes observational feedback as additional textual descriptions. However, due to LLM’s **high sensitivity to the prompts** and **tendency to get lost in lengthy prompts**, these methods struggle to effectively utilize the observational feedback from each optimization step, which severely hinders the applications for real-world scenarios. To address these challenges, we propose a conceptually simple and general bi-level optimization method, namely **G**eneral **S**cientific **O**ptimizers (GSO).Specifically, GSO first utilizes inner-level simulators as experimental platforms to evaluate the current solution and provide observational feedback. Then, LLMs serve as knowledgeable and versatile scientists, generating new solutions by refining potential errors from the feedback as the outer-level optimization.Finally, simulations together with the expert knowledge in LLMs are jointly updated with bi-level interactions via model editing.Extensive experiments show that GSO consistently outperforms existing state-of-the-art methods using *six* different LLM backbone on *seven* different tasks, demonstrating the effectiveness and a wide range of applications.

Knowledge graphs (KGs) play a pivotal role in knowledge-intensive tasks across specialized domains, where the acquisition of precise and dependable knowledge is crucial. However, existing KG construction methods heavily rely on human intervention to attain qualified KGs, which severely hinders the practical applicability in real-world scenarios. To address this challenge, we propose a general KG construction framework, named **SAC-KG**, to exploit large language models (LLMs) as **S**killed **A**utomatic **C**onstructors for domain **K**nowledge **G**raph. SAC-KG effectively involves LLMs as domain experts to generate specialized and precise multi-level KGs. Specifically, SAC-KG consists of three components: Generator, Verifier, and Pruner. For a given entity, Generator produces its relations and tails from raw domain corpora, to construct a specialized single-level KG. Verifier and Pruner then work together to ensure precision by correcting generation errors and determining whether newly produced tails require further iteration for the next-level KG. Experiments demonstrate that SAC-KG automatically constructs a domain KG at the scale of over one million nodes and achieves a precision of 89.32%, leading to a superior performance with over 20% increase in precision rate compared to existing state-of-the-art methods for the KG construction task.