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

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.