EquivaMap: Leveraging LLMs for Automatic Equivalence Checking of Optimization Formulations

Haotian Zhai, Connor Lawless, Ellen Vitercik, Liu Leqi

Keywords: Combinatorial Optimization, Large Language Models, Mixed Integer Linear Programming, AI for OR

Abstract:

A fundamental problem in combinatorial optimization is
identifying equivalent formulations. Despite the growing need for automated equivalence checks---driven, for example, by *optimization copilots*, which generate problem formulations from natural language descriptions---current approaches rely on simple heuristics that fail to reliably check formulation equivalence.
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 for scalable, reliable equivalence checking, with a verification stage that ensures mapped solutions preserve feasibility and optimality without additional solver calls. To evaluate our approach,
we construct *EquivaFormulation*, 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.

Submission Number: 42