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

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 reformulations 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.