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
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
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
As FlexRay communication protocol is extensively used in distributed real-time applications on vehicles, signal scheduling in Flex Ray network becomes a critical issue to ensure the safe and efficient operation of tim...As FlexRay communication protocol is extensively used in distributed real-time applications on vehicles, signal scheduling in Flex Ray network becomes a critical issue to ensure the safe and efficient operation of time-critical applications. In this study, we propose a rectangle bin packing optimization approach to schedule communication signals with timing constraints into the FlexRay static segment at minimum bandwidth cost. The proposed approach, which is based on integer linear programming(ILP), supports both the slot assignment mechanisms provided by the latest version of the FlexRay specification, namely, the single sender slot multiplexing, and multiple sender slot multiplexing mechanisms. Extensive experiments on a synthetic and an automotive X-by-wire system case study demonstrate that the proposed approach has a well optimized performance.展开更多
In 1985, Johnson and Garey[4] devised an algorithm which they call MFFD. Compared with other modifications of the famous FFD algorithm, theirs is apparently simpler in practical applications and substantially improves...In 1985, Johnson and Garey[4] devised an algorithm which they call MFFD. Compared with other modifications of the famous FFD algorithm, theirs is apparently simpler in practical applications and substantially improves the worst case behavior of FFD. In fact, they proved that the inequality MFFD(L) OPT(L)+ holds for all the lists L. Their proof requires 40 pages.In this paper we give a proof for the inequality MFFD(L) OPT(L)+1, L. The proof is much simpler than theirs.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
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。
基金supported by the Program for Changjiang Scholars and Innovative Research Team in the University of Ministry of Education of China(No.IRT1017)
文摘As FlexRay communication protocol is extensively used in distributed real-time applications on vehicles, signal scheduling in Flex Ray network becomes a critical issue to ensure the safe and efficient operation of time-critical applications. In this study, we propose a rectangle bin packing optimization approach to schedule communication signals with timing constraints into the FlexRay static segment at minimum bandwidth cost. The proposed approach, which is based on integer linear programming(ILP), supports both the slot assignment mechanisms provided by the latest version of the FlexRay specification, namely, the single sender slot multiplexing, and multiple sender slot multiplexing mechanisms. Extensive experiments on a synthetic and an automotive X-by-wire system case study demonstrate that the proposed approach has a well optimized performance.
文摘In 1985, Johnson and Garey[4] devised an algorithm which they call MFFD. Compared with other modifications of the famous FFD algorithm, theirs is apparently simpler in practical applications and substantially improves the worst case behavior of FFD. In fact, they proved that the inequality MFFD(L) OPT(L)+ holds for all the lists L. Their proof requires 40 pages.In this paper we give a proof for the inequality MFFD(L) OPT(L)+1, L. The proof is much simpler than theirs.
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.
