@inproceedings{zeng-etal-2026-milp,
title = "{MILP}-Solve-Free Selection of {LLM}-Generated {MILP} Programs via Multi-Signal Structural-Semantic Consistency",
author = "Zeng, Shuli and
Liu, Guozhu and
Chen, Yinghao and
Xie, Wantong and
Liu, Ji and
Tang, Shaojie and
Wu, Feng and
Zhang, Sijia and
Li, Xiang-Yang",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.2336/",
pages = "53068--53084",
ISBN = "979-8-89176-459-0",
abstract = "Large language models make natural-language-to-MILP modeling increasingly plausible, but reliably selecting among multiple generated programs remains challenging: structurally similar errors can create false majorities, while solving every candidate integer program is costly. We propose Structural-Semantic Consistency (SSC), a best-of-$K$ selector combining structural consistency, static quality, text alignment, and two diagnostics obtained from continuous LP relaxations. Notably, SSC does not require solving any candidate integer programs during selection. Across seven benchmarks and 618 fixed candidate pools, SSC obtains 55.7{\%} accuracy, compared with a random baseline of 51.5{\%}, 53.7{\%} for a zero-shot listwise LLM judge, and 55.3{\%} for a leave-one-benchmark-out learned ranker. The symbolic fusion reaches 53.6{\%}, with LP diagnostics adding 2.1 percentage points. These results establish multi-signal weak verification as a competitive and interpretable baseline for candidate selection."
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<abstract>Large language models make natural-language-to-MILP modeling increasingly plausible, but reliably selecting among multiple generated programs remains challenging: structurally similar errors can create false majorities, while solving every candidate integer program is costly. We propose Structural-Semantic Consistency (SSC), a best-of-K selector combining structural consistency, static quality, text alignment, and two diagnostics obtained from continuous LP relaxations. Notably, SSC does not require solving any candidate integer programs during selection. Across seven benchmarks and 618 fixed candidate pools, SSC obtains 55.7% accuracy, compared with a random baseline of 51.5%, 53.7% for a zero-shot listwise LLM judge, and 55.3% for a leave-one-benchmark-out learned ranker. The symbolic fusion reaches 53.6%, with LP diagnostics adding 2.1 percentage points. These results establish multi-signal weak verification as a competitive and interpretable baseline for candidate selection.</abstract>
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%0 Conference Proceedings
%T MILP-Solve-Free Selection of LLM-Generated MILP Programs via Multi-Signal Structural-Semantic Consistency
%A Zeng, Shuli
%A Liu, Guozhu
%A Chen, Yinghao
%A Xie, Wantong
%A Liu, Ji
%A Tang, Shaojie
%A Wu, Feng
%A Zhang, Sijia
%A Li, Xiang-Yang
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F zeng-etal-2026-milp
%X Large language models make natural-language-to-MILP modeling increasingly plausible, but reliably selecting among multiple generated programs remains challenging: structurally similar errors can create false majorities, while solving every candidate integer program is costly. We propose Structural-Semantic Consistency (SSC), a best-of-K selector combining structural consistency, static quality, text alignment, and two diagnostics obtained from continuous LP relaxations. Notably, SSC does not require solving any candidate integer programs during selection. Across seven benchmarks and 618 fixed candidate pools, SSC obtains 55.7% accuracy, compared with a random baseline of 51.5%, 53.7% for a zero-shot listwise LLM judge, and 55.3% for a leave-one-benchmark-out learned ranker. The symbolic fusion reaches 53.6%, with LP diagnostics adding 2.1 percentage points. These results establish multi-signal weak verification as a competitive and interpretable baseline for candidate selection.
%U https://aclanthology.org/2026.emnlp-main.2336/
%P 53068-53084
Markdown (Informal)
[MILP-Solve-Free Selection of LLM-Generated MILP Programs via Multi-Signal Structural-Semantic Consistency](https://aclanthology.org/2026.emnlp-main.2336/) (Zeng et al., EMNLP 2026)
ACL
- Shuli Zeng, Guozhu Liu, Yinghao Chen, Wantong Xie, Ji Liu, Shaojie Tang, Feng Wu, Sijia Zhang, and Xiang-Yang Li. 2026. MILP-Solve-Free Selection of LLM-Generated MILP Programs via Multi-Signal Structural-Semantic Consistency. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 53068–53084, Budapest, Hungary. Association for Computational Linguistics.