Code Retrieval for MILP Instance Generation

TL;DR

This paper introduces a novel approach to generate MILP instances efficiently by reformulating the task as code generation, utilizing a similarity metric and retrieval method to produce high-quality, diverse instances for improved solver training.

Contribution

It presents a new MILP code generation framework and a similarity metric, enabling flexible, interpretable, and scalable instance generation for learning-based MILP solvers.

Findings

MILP-Retrieval outperforms baselines in code and instance generation

The MILP-EmbedSim metric accurately measures instance similarity

The approach offers a new perspective on scalable MILP instance generation

Abstract

Mixed-Integer Linear Programming (MILP) is widely used in fields such as scheduling, logistics, and planning. Enhancing the performance of MILP solvers, particularly learning-based solvers, requires substantial amounts of high-quality data. However, existing methods for MILP instance generation typically necessitate training a separate model for each problem class and are computationally intensive when generating new instances. To address these limitations, we reformulate the MILP Instance Generation task as MILP Code Generation task, enabling efficient, flexible, and interpretable instance generation through code. Since MILP instances generated from code can vary significantly in scale, we introduce MILP-EmbedSim, a new similarity metric that accurately measures the similarity between instances of varying sizes within the same problem class. Leveraging this metric, we propose MILP-Retrieval, a pipeline that retrieves generation code from library to produce MILP instances highly similar to target instance. MILP-Retrieval outperforms baselines in both MILP Code Generation and Instance Generation tasks, provides a novel perspective on MILP instance generation and opens new possibilities for learning-based solvers.