求解矩形条带装箱问题的动态匹配启发式算法

A Dynamic-Fit Heuristic Algorithm for the Rectangular Strip Packing Problem

矩形条带装箱问题(RSPP)是指将一组矩形装入在一个宽度固定高度不限的矩形容器中,以期获得最小装箱高度.RSPP理论上属于NP难问题,在新闻组版、布料下料以及金属切割等工业领域中有着广泛的应用.为解决该问题,采用了一种混合算法,即将一种新的启发式算法——动态匹配算法——与遗传算法结合起来.混合算法中,动态匹配算法能根据4类启发式规则动态选择与装填区域相匹配的下一个待装矩形,同时将装箱后所需容器高度用遗传算法的进化策略进行优化.对2组标准测试问题的计算结果表明,相对于文献中的已有算法,提出的算法更加有效.

Given a set of small rectangular pieces of different sizes and a rectangular container of fixed width and infinite length, the rectangular strip packing problem （RSPP） consists of orthogonally placing all the pieces within the container, without overlapping, such that the overall length of the packing is minimized. RSPP belongs to NP-hard problem in theory and has many industrial applications such as the composition of news, the cutting of clothing and the cutting of metal, etc. To solve the rectangular strip packing problem, a hybrid algorithm, which combines a novel heuristic algorithm--dynamic-fit heuristic algorithm （DFHA）, with the genetic algorithm, is adopted. The DFHA algorithm can dynamically select the better-fit rectangle for packing, according to the width-fit first （WFF） rule, the height-fit first （HFF） rule, the placeable first （PF） rule, and the biggest- rectangle first （BRF） rule, and the evolutionary capability of genetic algorithm is used to optimize the height of the packing which is calculated by DFHA. The hybrid algorithm is tested on two sets of benchmark problems taken from the previous literature. The first set includes 21 instances and the other one includes 13 instances. The computational results show that the hybrid algorithm is more effective than the existing algorithms from the previous literature.