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Mixed integer convex and nonlinear programs, MICP and MINLP, are expressivebut require long solving times. Recent work that combines learning methods onsolver heuristics has shown potential to overcome this issue allowing forapplications on larger scale practical problems. Gathering sufficient trainingdata to employ these methods still present a challenge since getting data fromtraditional solvers are slow and newer learning approaches still require largeamounts of data. In order to scale up and make these hybrid learning approachesmore manageable we propose ReDUCE, a method that exploits structure withinsmall to medium size datasets. We also introduce the bookshelf organizationproblem as an MINLP as a way to measure performance of solvers with ReDUCE.Results show that existing algorithms with ReDUCE can solve this problem withina few seconds, a significant improvement over the original formulation. ReDUCEis demonstrated as a high level planner for a robotic arm for the bookshelfproblem.

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