Optimization Modeling via Semantic Anchored Alignment

2025-09-28

AI Summary

Existing LLM-based optimization modeling approaches are solver-driven, relying on single-shot code generation and limited error feedback, which hinders detection of logical correctness and often yields syntactically valid but semantically incorrect models. Method: We propose SAC-Opt, the first framework featuring semantic anchoring alignment—a mechanism that explicitly establishes fine-grained anchors between natural language descriptions and mathematical semantic structures (e.g., variables, constraints, objectives), enabling iterative, localized corrections without additional training and optimizing for semantic consistency rather than solver output. Contribution/Results: SAC-Opt significantly improves logical fidelity: it achieves an average modeling accuracy gain of 7.8% across seven public benchmarks, and a 21.9% improvement on ComplexLP—demonstrating high-fidelity translation from natural language to executable optimization code.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Learning to Search
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Large language models for search
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Large language models (LLMs) have opened new paradigms in optimization modeling by enabling the generation of executable solver code from natural language descriptions. Despite this promise, existing approaches typically remain solver-driven: they rely on single-pass forward generation and apply limited post-hoc fixes based on solver error messages, leaving undetected semantic errors that silently produce syntactically correct but logically flawed models. To address this challenge, we propose SAC-Opt, a backward-guided correction framework that grounds optimization modeling in problem semantics rather than solver feedback. At each step, SAC-Opt aligns the original semantic anchors with those reconstructed from the generated code and selectively corrects only the mismatched components, driving convergence toward a semantically faithful model. This anchor-driven correction enables fine-grained refinement of constraint and objective logic, enhancing both fidelity and robustness without requiring additional training or supervision. Empirical results on seven public datasets demonstrate that SAC-Opt improves average modeling accuracy by 7.8%, with gains of up to 21.9% on the ComplexLP dataset. These findings highlight the importance of semantic-anchored correction in LLM-based optimization workflows to ensure faithful translation from problem intent to solver-executable code.

Problem

• Addressing semantic errors in LLM-generated optimization code
• Ensuring logical fidelity between natural language and solver models
• Correcting mismatched components through semantic anchor alignment

Innovation

• Backward correction framework grounds modeling in semantics
• Aligns original semantic anchors with reconstructed code anchors
• Selectively corrects mismatched components for semantic fidelity