基于动作空间求解二维矩形Packing问题的高效算法

摘要

对于二维矩形Packing这一典型的NP难度问题,在黄文奇等人提出的拟人型穴度算法的基础上,通过定义动作空间来简化对不同放入动作的评价,使穴度的计算时间明显缩短,从而使算法能够快速地得到空间利用率较高的布局图案.实验测试了Hopper和Turton提出的21个著名的二维矩形Packing问题的实例.改进的算法对其中的每一个实例都得到了空间利用率为100％的最优布局,且在普通PC机上的平均计算时间未超过7分钟.实验结果表明,基于动作空间对拟人型穴度算法所进行的改进是明显而有效的.%This paper addresses a typical NP-hard problem, the two-dimensional (2D) rectangular packing problem. The study makes improvements on a quasi-human approach, a caving degree algorithm proposed by Huang Wen-Qi, et al., by defining the conception of action space such that the calculation of the caving degree is simplified. Therefore, the evaluation on different placements is reduced considerably, and good layouts could be obtained quickly. The experiments tested 21 famous instances of the 2D rectangular packing problem provided by Hopper and Turton. The improved algorithm achieved optimal layout with a space utilization of 100% for each instance, and the average computing time on a personal computer was within seven minutes. Computational results show that the improvement strategies on the quasi-human caving degree approach are evident and effective.