ReDUCE: Reformulation of Mixed Integer Programs using Data from Unsupervised Clusters for Learning Efficient Strategies

TL;DR

ReDUCE is a novel method that leverages data from unsupervised clusters to reformulate mixed integer programs, significantly reducing solving times and enabling efficient application to complex problems like the bookshelf organization and robotic planning.

Contribution

The paper introduces ReDUCE, a new approach that exploits structure in small datasets to improve solver efficiency for MICP and MINLP problems, facilitating scalable hybrid learning methods.

Findings

ReDUCE enables solving the bookshelf problem in seconds, a major speedup.

ReDUCE improves solver performance for MINLPs in practical applications.

Demonstrated as a high-level planner for robotic arm tasks.

Abstract

Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines learning methods on solver heuristics has shown potential to overcome this issue allowing for applications on larger scale practical problems. Gathering sufficient training data to employ these methods still present a challenge since getting data from traditional solvers are slow and newer learning approaches still require large amounts of data. In order to scale up and make these hybrid learning approaches more manageable we propose ReDUCE, a method that exploits structure within small to medium size datasets. We also introduce the bookshelf organization problem as an MINLP as a way to measure performance of solvers with ReDUCE. Results show that existing algorithms with ReDUCE can solve this problem within a few seconds, a significant improvement over the original formulation. ReDUCE is demonstrated as a high level planner for a robotic arm for the bookshelf problem.