Application of hybrid classical-quantum annealing technology to the 3D Bin-Packing Problem

TL;DR

This paper explores hybrid classical-quantum annealing for 3D bin-packing, developing a new MIP model with support constraints and comparing quantum and classical solvers' performance on complex optimization tasks.

Contribution

It introduces a novel mixed-integer programming model with fewer variables and a support constraint formulation, and evaluates quantum versus classical solvers for the problem.

Findings

Quantum solver shows competitive optimality gaps.

Hybrid approach improves volume utilization.

Classical solver performs better on larger instances.

Abstract

In this paper, we study the use of hybrid classical-quantum annealing technology to solve a critical business optimization problem that is a form of multiproduct multi-bin packing in three dimensions with support constraints and case orientations along all three axes. We developed an exact mathematical model based on mixed-integer programming (MIP) to solve the problem, using fewer variables than previously existing models. Furthermore, to ensure the stability of the cases within bins, the model employs a novel formulation to represent the support constraints. We then compared and analyzed the solution performance of the classical solver Gurobi and D-Wave's constrained quadratic model (CQM) solver on the MIP model, both with and without support constraints. Results from the computational studies offer valuable insights into how the hybrid classical-quantum solver compares against widely used purely classical solvers on computationally hard problems, such as the problem of interest. This comparison examines aspects such as the optimality gap and volume utilization across different computational time limits.