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.

翻译：装箱问题是人工智能领域中著名的NP难问题，在寻找高效解方面具有显著挑战。相反，量子技术的最新进展展现出在特定问题类别（如组合优化）中实现大幅计算加速的潜力。本研究提出QAL-BP——一种专为装箱问题设计、适用于量子计算的新型二次无约束二元优化（QUBO）形式。QAL-BP采用增广拉格朗日方法将装箱约束纳入目标函数，同时通过启发式但经验稳健的惩罚乘子分析估计简化计算。该方法构建了一个更具通用性和可扩展性的模型，无需像其他同类问题的QUBO形式那样依赖经验计算实例相关的拉格朗日系数。为评估所提方法的有效性，我们使用真实量子退火设备对一组装箱实例进行实验。此外，我们将实验结果与两种经典求解器（模拟退火和Gurobi）获得的结果进行比较。实验结果不仅验证了所提形式的正确性，还揭示了量子计算在有效解决装箱问题方面的潜力——尤其是随着更可靠的量子技术的出现。