EquivaMap: Leveraging LLMs for Automatic Equivalence Checking of Optimization Formulations

• URL: http://arxiv.org/abs/2502.14760v1
• Date: Thu, 20 Feb 2025 17:35:32 GMT
• Title: EquivaMap: Leveraging LLMs for Automatic Equivalence Checking of Optimization Formulations
• Authors: Haotian Zhai, Connor Lawless, Ellen Vitercik, Liu Leqi,
• Abstract summary: We introduce quasi-Karp equivalence, a formal criterion for determining when two optimization formulations are equivalent. We propose EquivaMap, a framework that leverages large language models to automatically discover such mappings.
• Score: 12.962019992859531
• License:
• Abstract: A fundamental problem in combinatorial optimization is identifying equivalent formulations, which can lead to more efficient solution strategies and deeper insights into a problem's computational complexity. The need to automatically identify equivalence between problem formulations has grown as optimization copilots--systems that generate problem formulations from natural language descriptions--have proliferated. However, existing approaches to checking formulation equivalence lack grounding, relying on simple heuristics which are insufficient for rigorous validation. Inspired by Karp reductions, in this work we introduce quasi-Karp equivalence, a formal criterion for determining when two optimization formulations are equivalent based on the existence of a mapping between their decision variables. We propose EquivaMap, a framework that leverages large language models to automatically discover such mappings, enabling scalable and reliable equivalence verification. To evaluate our approach, we construct the first open-source dataset of equivalent optimization formulations, generated by applying transformations such as adding slack variables or valid inequalities to existing formulations. Empirically, EquivaMap significantly outperforms existing methods, achieving substantial improvements in correctly identifying formulation equivalence.

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