矩形装箱问题的协同决策模型
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摘要
随着工业技术的发展,装箱问题逐渐受到现代学者青睐,越来越多的装箱算法呈现在我们的眼前。由于应用场景抑或设计角度的不同,这些装箱算法往往只适用于某一类装箱实例。也就是说,对于任意一个装箱算法,我们总是能够找到一个它不能很好解决的特例。为了避免这种情况的发生,阎春平教授提出了基于Internet的优化方法。该方法允许同时运行多个装箱算法,而后从所有结果中选出最好的那个作为最终结果。这种方法虽然能够在一定程度上实现各个装箱算法之间的互补,但是由于缺乏彼此之间的交流与沟通,而无法实现更深层次上的优势互补。
为了最大程度上地实现各个装箱算法之间的优势互补,本文在同一个容器格局、统一的评价标准的基础上提出了矩形装箱问题的协同决策模型。该模型由两种基本决策模式构成：1)共同决策；2)并行决策。前者允许参与决策的装箱算法之间进行充分的交流,并从中选出当前排放场景下最优秀的装箱算法来执行排放工作；后者允许参与决策的装箱算法互不影响地同时执行排放工作。这两种决策模式各有利弊：一个能够最大限度的提高排放方案的空间利用率；一个能够最大限度地缩短决策时间。权衡利弊,我们将这两种决策模式有机地结合起来,并称为协同决策,以期在提高排放结果空间利用率的同时减少决策时间。
理论分析表明,协同决策模型下,容器格局的规模总是不超过装箱实例中矩形块的数目,而且时间复杂度不超过参与决策的具有最大时间复杂度的装箱算法的复杂度。
实验表明,在协同决策模型下,容器格局的规模都远小于装箱实例中矩形块的数目,而且随着装箱实例中矩形块数目的增加,这个差距将逐渐增大。以Hopper and Turton benchmark(2001)为例,协同决策时容器格局的规模最大不超过50。从空间利用率的角度来说,在中间排放场景数目较少时,层排放算法与平面排放算法之间的协同决策往往能够取得较高的空间利用率；而随着中间排放场景数目的增加,平面排放算法之间协同决策的优势逐渐明显。考虑到决策时间的问题,我们通常取中间排放场景的数目为装箱实例中矩形块个数的三分之一。此时平面排放算法之间的协同决策不比其它任何装箱算法之间的协同决策所得结果差。
With the development of industrial technology, packing problem is gradually favored by the modern scholars and more and more packing algorithms present in our eyes. Due to different application scenario or design view, these packing algorithms are only applicable to one class of packing instances. That is to say, for an arbitrary packing algorithm, we can always find one instance and this algorithm can not solve it well. To avoid this case, Prof. Chunping Yan put forward one optimization method based on Internet, which allows multiple packing algorithms run at the same time, and then choose the best from all the solutions as the final solution. Although this method can achieve complementarity between each packing algorithm in some extent, but because of the lack of communication between each other, they are unable to be realized more deeply complementary advantages.
To maximize complementary advantages between each packing algorithm, one cooperative decision model for rectangle packing problem is proposed based on one uniform container scenario and evaluation criterion. This model consists of two basic decision patterns:1) codetermination;2) parallel decision. The former allows all the involved packing algorithms to choose the most suitable one under current packing scenario for execution between their communications; the latter allows all the involved packing algorithms execute parallel. These two decision patterns cut both ways:one can raise the space utilization and one can shorten the decision time. Therefore, these two decisions are combined, called cooperative decision, in order to raise space utilization and meanwhile shorten the decision time.
Theoretical analysis indicates, with cooperative decision, the size of container scenario is never more than the number of rectangles in each packing instance, and time complexity is never more than the worst one of all involed packing algorithms.
Experiments indicates, with cooperative decision, the size of container scenario is faraway less than the number of rectangles in each packing instance, and their difference is increased with the increasing number of rectangles in each packing instance. For example, the size of container scenario with cooperative decision is not more than50for each packing instance in Hopper and Turton benchmark (2001). Generally, the cooperative decision between level packing algorithms and plane packing algorithms holds much higher space utilization, and the advantage of the cooperative decision among plane packing algorithms gradually clear. Taking the decision time into account, the number of intermediate packing scenarios is always set one third of the number of rectangles in the packing instance. In this case, the cooperative decision among plane packing algorithms is not worse than the cooperative among any packing algorithms.
为了最大程度上地实现各个装箱算法之间的优势互补,本文在同一个容器格局、统一的评价标准的基础上提出了矩形装箱问题的协同决策模型。该模型由两种基本决策模式构成：1)共同决策；2)并行决策。前者允许参与决策的装箱算法之间进行充分的交流,并从中选出当前排放场景下最优秀的装箱算法来执行排放工作；后者允许参与决策的装箱算法互不影响地同时执行排放工作。这两种决策模式各有利弊：一个能够最大限度的提高排放方案的空间利用率；一个能够最大限度地缩短决策时间。权衡利弊,我们将这两种决策模式有机地结合起来,并称为协同决策,以期在提高排放结果空间利用率的同时减少决策时间。
理论分析表明,协同决策模型下,容器格局的规模总是不超过装箱实例中矩形块的数目,而且时间复杂度不超过参与决策的具有最大时间复杂度的装箱算法的复杂度。
实验表明,在协同决策模型下,容器格局的规模都远小于装箱实例中矩形块的数目,而且随着装箱实例中矩形块数目的增加,这个差距将逐渐增大。以Hopper and Turton benchmark(2001)为例,协同决策时容器格局的规模最大不超过50。从空间利用率的角度来说,在中间排放场景数目较少时,层排放算法与平面排放算法之间的协同决策往往能够取得较高的空间利用率；而随着中间排放场景数目的增加,平面排放算法之间协同决策的优势逐渐明显。考虑到决策时间的问题,我们通常取中间排放场景的数目为装箱实例中矩形块个数的三分之一。此时平面排放算法之间的协同决策不比其它任何装箱算法之间的协同决策所得结果差。
With the development of industrial technology, packing problem is gradually favored by the modern scholars and more and more packing algorithms present in our eyes. Due to different application scenario or design view, these packing algorithms are only applicable to one class of packing instances. That is to say, for an arbitrary packing algorithm, we can always find one instance and this algorithm can not solve it well. To avoid this case, Prof. Chunping Yan put forward one optimization method based on Internet, which allows multiple packing algorithms run at the same time, and then choose the best from all the solutions as the final solution. Although this method can achieve complementarity between each packing algorithm in some extent, but because of the lack of communication between each other, they are unable to be realized more deeply complementary advantages.
To maximize complementary advantages between each packing algorithm, one cooperative decision model for rectangle packing problem is proposed based on one uniform container scenario and evaluation criterion. This model consists of two basic decision patterns:1) codetermination;2) parallel decision. The former allows all the involved packing algorithms to choose the most suitable one under current packing scenario for execution between their communications; the latter allows all the involved packing algorithms execute parallel. These two decision patterns cut both ways:one can raise the space utilization and one can shorten the decision time. Therefore, these two decisions are combined, called cooperative decision, in order to raise space utilization and meanwhile shorten the decision time.
Theoretical analysis indicates, with cooperative decision, the size of container scenario is never more than the number of rectangles in each packing instance, and time complexity is never more than the worst one of all involed packing algorithms.
Experiments indicates, with cooperative decision, the size of container scenario is faraway less than the number of rectangles in each packing instance, and their difference is increased with the increasing number of rectangles in each packing instance. For example, the size of container scenario with cooperative decision is not more than50for each packing instance in Hopper and Turton benchmark (2001). Generally, the cooperative decision between level packing algorithms and plane packing algorithms holds much higher space utilization, and the advantage of the cooperative decision among plane packing algorithms gradually clear. Taking the decision time into account, the number of intermediate packing scenarios is always set one third of the number of rectangles in the packing instance. In this case, the cooperative decision among plane packing algorithms is not worse than the cooperative among any packing algorithms.
引文
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