Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines data-driven methods on solver heuristics has shown potential to overcome this issue allowing for applications on larger scale practical problems. To solve mixed-integer bilinear programs online with data-driven methods, several formulations exist including mathematical programming with complementary constraints (MPCC), mixed-integer programming (MIP). In this work, we benchmark the performances of those data-driven schemes on a bookshelf organization problem that has discrete mode switch and collision avoidance constraints. The success rate, optimal cost and solving time are compared along with non-data-driven methods. Our proposed methods are demonstrated as a high level planner for a robotic arm for the bookshelf problem.