AlphaOPT: Formulating Optimization Programs with Self-Improving LLM
  Experience Library
Authors: name: Minwei Kong, name: Ao Qu, name: Xiaotong Guo, name: Wenbin Ouyang, name: Chonghe Jiang, name: Han Zheng, name: Yining Ma, name: Dingyi Zhuang, name: Yuhan Tang, name: Junyi Li, name: Hai Wang, name: Cathy Wu, name: Jinhua Zhao

Optimization modeling enables critical decisions across industries but
remains difficult to automate: informal language must be mapped to precise
mathematical formulations and executable solver code. Prior LLM approaches
either rely on brittle prompting or costly retraining with limited
generalization. We present AlphaOPT, a self-improving experience library that
enables an LLM to learn from limited demonstrations (even answers alone,
without gold-standard programs) and solver feedback - without annotated
reasoning traces or parameter updates. AlphaOPT operates in a continual
two-phase cycle: (i) a Library Learning phase that reflects on failed attempts,
extracting solver-verified, structured insights as {taxonomy, condition,
explanation, example}; and (ii) a Library Evolution phase that diagnoses
retrieval misalignments and refines the applicability conditions of stored
insights, improving transfer across tasks. This design (1) learns efficiently
from limited demonstrations without curated rationales, (2) expands continually
without costly retraining by updating the library rather than model weights,
and (3) makes knowledge explicit and interpretable for human inspection and
intervention. Experiments show that AlphaOPT steadily improves with more data
(65% to 72% from 100 to 300 training items) and surpasses the strongest
baseline by 7.7% on the out-of-distribution OptiBench dataset when trained only
on answers. Code and data are available at:
https://github.com/Minw913/AlphaOPT.