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一个著名的NP难问题，在寻找高效解方面面临重大挑战。相反，量子技术的最新进展已显示出在特定问题类别（如组合优化）中实现显著计算加速的巨大潜力。在本研究中，我们提出QAL-BP，一种专为装箱问题设计且适用于量子计算的新型二次无约束二元优化（QUBO）形式。QAL-BP利用增广拉格朗日方法将装箱约束融入目标函数中，同时促进了对启发式但经验稳健的惩罚乘数的解析估计。该方法生成一个更具通用性和可推广性的模型，消除了经验计算实例依赖的拉格朗日系数的需求，而这一需求在类似问题的替代QUBO形式中经常遇到。为评估我们提出方法的有效性，我们在实际量子退火设备上对一组装箱实例进行了实验。此外，我们将结果与两种不同经典求解器（即模拟退火和Gurobi）获得的结果进行比较。实验结果不仅确认了所提形式化的正确性，还展示了量子计算在有效解决装箱问题方面的潜力，特别是随着更可靠的量子技术的出现。