Evaluating Data-driven Performances of Mixed Integer Bilinear Formulations for Book Placement Planning

TL;DR

This paper compares data-driven reformulations of mixed integer bilinear programs for book placement, showing that data-driven methods significantly improve solving speed and provide guidance for selecting suitable approaches.

Contribution

It evaluates and compares various data-driven reformulations of MIBLPs in a book placement problem, highlighting their advantages over traditional methods.

Findings

Data-driven methods accelerate MIBLP solving times.

Success rate and cost are improved with data-driven reformulations.

Guidelines for choosing reformulations are provided.

Abstract

Mixed integer bilinear programs (MIBLPs) offer tools to resolve robotics motion planning problems with orthogonal rotation matrices or static moment balance, but require long solving times. Recent work utilizing data-driven methods has shown potential to overcome this issue allowing for applications on larger scale problems. To solve mixed-integer bilinear programs online with data-driven methods, several re-formulations exist including mathematical programming with complementary constraints (MPCC), and mixed-integer programming (MIP). In this work, we compare the data-driven performances of various MIBLP reformulations using a book placement problem that has discrete configuration switches and bilinear constraints. The success rate, cost, and solving time are compared along with non-data-driven methods. Our results demonstrate the advantage of using data-driven methods to accelerate the solving speed of MIBLPs, and provide references for users to choose the suitable re-formulation.