  The bin packing is a well-known NP-Hard problem in the domain of artificial
intelligence, posing significant challenges in finding efficient solutions.
Conversely, recent advancements in quantum technologies have shown promising
potential for achieving substantial computational speedup, particularly in
certain problem classes, such as combinatorial optimization. In this study, we
introduce QAL-BP, a novel Quadratic Unconstrained Binary Optimization (QUBO)
formulation designed specifically for bin packing and suitable for quantum
computation. QAL-BP utilizes the Augmented Lagrangian method to incorporate the
bin packing constraints into the objective function while also facilitating an
analytical estimation of heuristic, but empirically robust, penalty
multipliers. This approach leads to a more versatile and generalizable model
that eliminates the need for empirically calculating instance-dependent
Lagrangian coefficients, a requirement commonly encountered in alternative QUBO
formulations for similar problems. To assess the effectiveness of our proposed
approach, we conduct experiments on a set of bin packing instances using a real
Quantum Annealing device. Additionally, we compare the results with those
obtained from two different classical solvers, namely simulated annealing and
Gurobi. The experimental findings not only confirm the correctness of the
proposed formulation but also demonstrate the potential of quantum computation
in effectively solving the bin packing problem, particularly as more reliable
quantum technology becomes available.
