Given a list of items and a sequence of variable-sized bins arriving one by one, it is NP-hard to pack the items into the bin list with a goal to minimize the total size of bins from the earliest one to the last used....Given a list of items and a sequence of variable-sized bins arriving one by one, it is NP-hard to pack the items into the bin list with a goal to minimize the total size of bins from the earliest one to the last used. In this paper a set of approximation algorithms is presented for cases in which the ability to preview at most k（〉=2） arriving bins is given. With the essential assumption that all bin sizes are not less than the largest item size, analytical results show the asymptotic worst case ratios of all k-bounded space and offiine algorithms are 2. Based on experiments by applying algorithms to instances in which item sizes and bin sizes are drawn independently from the continuous uniform distribution respectively in the interval [0,u] and [u,l ], averagecase experimental results show that, with fixed k, algorithms with the Best Fit packing（closing） rule are statistically better than those with the First Fit packing（closing） rule.展开更多
A version of the k-bounded space on-line bin packing problem, where a fixed collection of bin sizes is allowed, is considered. By packing large items into appropriate bins and closing appropriate bins, we can derive a...A version of the k-bounded space on-line bin packing problem, where a fixed collection of bin sizes is allowed, is considered. By packing large items into appropriate bins and closing appropriate bins, we can derive an algorithm with worst-case performance bound 1.7 for k≥3.展开更多
The online 3D packing problem has received increasing attention in recent years due to its practical value. However, the problem itself possesses some peculiar properties, such as sequential decision-making and the la...The online 3D packing problem has received increasing attention in recent years due to its practical value. However, the problem itself possesses some peculiar properties, such as sequential decision-making and the large size of the state space, which have made the use of reinforcement learning with Markov decision processes a popular approach for solving this problem. In this paper, we focus on the problem of high variance in value estimation caused by reward uncertainty in the presence of highly uncertain dynamics. To address this, proposed a solution based on auxiliary tasks and intrinsic rewards for the online 3D bin packing problem, guided by a binary-valued network, to assist the agent in learning the policy within the framework of actor-critic deep reinforcement learning. Specifically, the maintenance of two-valued networks and the utilization of multi-valued network estimates are employed to replace the original value estimates, aiming to provide better guidance for the learning of policy networks. Experimentally, it has been demonstrated that our model can achieve more robust learning and outperform previous works in terms of performance.展开更多
物流作为现代经济的重要组成部分,在国民经济和社会发展中发挥着重要作用.物流中的三维装箱问题(Three-dimensional bin packing problem,3D-BPP)是提高物流运作效率必须解决的关键难题之一.深度强化学习(Deep rein-forcement learning,...物流作为现代经济的重要组成部分,在国民经济和社会发展中发挥着重要作用.物流中的三维装箱问题(Three-dimensional bin packing problem,3D-BPP)是提高物流运作效率必须解决的关键难题之一.深度强化学习(Deep rein-forcement learning,DRL)具有强大的学习与决策能力,基于DRL的三维装箱方法(Three-dimensional bin packing method based on DRL,DRL-3DBP)已成为智能物流领域的研究热点之一.现有DRL-3DBP面对大尺寸容器3D-BPP时难以达成动作空间、计算复杂性与探索能力之间的平衡.为此,提出一种四向协同装箱(Four directional cooperative packing,FDCP)方法:两阶段策略网络接收旋转后的容器状态,生成4个方向的装箱策略;根据由4个策略采样而得的动作更新对应的4个状态,选取其中价值最大的对应动作为装箱动作.FDCP在压缩动作空间、减小计算复杂性的同时,鼓励智能体对4个方向合理装箱位置的探索.实验结果表明,FDCP在100×100大尺寸容器以及20、30、50箱子数量的装箱问题上实现了1.2%~2.9%的空间利用率提升.展开更多
目的针对冷链运输中的生鲜打包及装载优化问题,提出一种允许货物以体积恒定为前提进行尺寸变化的包装装载方案,以最大化集装箱的空间利用率。方法基于上述问题,构建非线性混合整数规划模型,为了方便CPLEX或LINGO等求解器对该非线性混合...目的针对冷链运输中的生鲜打包及装载优化问题,提出一种允许货物以体积恒定为前提进行尺寸变化的包装装载方案,以最大化集装箱的空间利用率。方法基于上述问题,构建非线性混合整数规划模型,为了方便CPLEX或LINGO等求解器对该非线性混合整数规划模型进行求解,采用一种分段线性化方法,将该非线性模型进行线性化处理。由于所研究问题具有NP-hard属性,无论是CPLEX还是LINGO都无法有效求解大规模算例,因此设计一种有效结合遗传算法与深度、底部、左部方向优先装载(Deepest bottom left with fill,DBLF)的算法。结果大小规模算例实验验证结果表明,混合遗传算法能够在合理时间内获得最优解或近似最优解。结论所提出的可变尺寸包装方案有效提高了装载率,有益于客户和物流公司。展开更多
文摘Given a list of items and a sequence of variable-sized bins arriving one by one, it is NP-hard to pack the items into the bin list with a goal to minimize the total size of bins from the earliest one to the last used. In this paper a set of approximation algorithms is presented for cases in which the ability to preview at most k（〉=2） arriving bins is given. With the essential assumption that all bin sizes are not less than the largest item size, analytical results show the asymptotic worst case ratios of all k-bounded space and offiine algorithms are 2. Based on experiments by applying algorithms to instances in which item sizes and bin sizes are drawn independently from the continuous uniform distribution respectively in the interval [0,u] and [u,l ], averagecase experimental results show that, with fixed k, algorithms with the Best Fit packing（closing） rule are statistically better than those with the First Fit packing（closing） rule.
文摘A version of the k-bounded space on-line bin packing problem, where a fixed collection of bin sizes is allowed, is considered. By packing large items into appropriate bins and closing appropriate bins, we can derive an algorithm with worst-case performance bound 1.7 for k≥3.
文摘The online 3D packing problem has received increasing attention in recent years due to its practical value. However, the problem itself possesses some peculiar properties, such as sequential decision-making and the large size of the state space, which have made the use of reinforcement learning with Markov decision processes a popular approach for solving this problem. In this paper, we focus on the problem of high variance in value estimation caused by reward uncertainty in the presence of highly uncertain dynamics. To address this, proposed a solution based on auxiliary tasks and intrinsic rewards for the online 3D bin packing problem, guided by a binary-valued network, to assist the agent in learning the policy within the framework of actor-critic deep reinforcement learning. Specifically, the maintenance of two-valued networks and the utilization of multi-valued network estimates are employed to replace the original value estimates, aiming to provide better guidance for the learning of policy networks. Experimentally, it has been demonstrated that our model can achieve more robust learning and outperform previous works in terms of performance.
文摘物流作为现代经济的重要组成部分,在国民经济和社会发展中发挥着重要作用.物流中的三维装箱问题(Three-dimensional bin packing problem,3D-BPP)是提高物流运作效率必须解决的关键难题之一.深度强化学习(Deep rein-forcement learning,DRL)具有强大的学习与决策能力,基于DRL的三维装箱方法(Three-dimensional bin packing method based on DRL,DRL-3DBP)已成为智能物流领域的研究热点之一.现有DRL-3DBP面对大尺寸容器3D-BPP时难以达成动作空间、计算复杂性与探索能力之间的平衡.为此,提出一种四向协同装箱(Four directional cooperative packing,FDCP)方法:两阶段策略网络接收旋转后的容器状态,生成4个方向的装箱策略;根据由4个策略采样而得的动作更新对应的4个状态,选取其中价值最大的对应动作为装箱动作.FDCP在压缩动作空间、减小计算复杂性的同时,鼓励智能体对4个方向合理装箱位置的探索.实验结果表明,FDCP在100×100大尺寸容器以及20、30、50箱子数量的装箱问题上实现了1.2%~2.9%的空间利用率提升.
文摘目的针对冷链运输中的生鲜打包及装载优化问题,提出一种允许货物以体积恒定为前提进行尺寸变化的包装装载方案,以最大化集装箱的空间利用率。方法基于上述问题,构建非线性混合整数规划模型,为了方便CPLEX或LINGO等求解器对该非线性混合整数规划模型进行求解,采用一种分段线性化方法,将该非线性模型进行线性化处理。由于所研究问题具有NP-hard属性,无论是CPLEX还是LINGO都无法有效求解大规模算例,因此设计一种有效结合遗传算法与深度、底部、左部方向优先装载(Deepest bottom left with fill,DBLF)的算法。结果大小规模算例实验验证结果表明,混合遗传算法能够在合理时间内获得最优解或近似最优解。结论所提出的可变尺寸包装方案有效提高了装载率,有益于客户和物流公司。
