矩形件排样问题的遗传算法求解

本文研究了求解矩形件正交排样优化问题的遗传算法。同时，将矩形件正交排样问题转化为一个排列问题，提出了求一个排列所对应的排样图的下台阶算法（改进的ＢＬ算法）将下台阶算法与遗传算法相结合，用于矩形件排样问题的求解，给出了该算法的实现。用该算法对文献中的两个算例进行了求解，结果表明该算法获得了比ＢＬ算法更好的解，是一种较为行之有效的方法。     

基于遗传算法的大规模矩形件优化排样

大规模矩形件优化排样是一个典型的组合优化问题，属于NP-hard问题．实际工程中对一个排样方案一般有满足“一刀切”的工艺要求，“一刀切”要求增加了对排样的约束．提出的优化算法，将矩形匹配分割算法作为遗传算法染色体的解码器实现一个排样方案，用遗传算法进行排样方案的全局搜索．算例比较表明，该算法可以求得满足“一刀切”约束的最优解．     

遗传算法在矩形件优化排样中的应用

遗传算法是一种全局优化的数值计算方法。与传统优化算法相比,它对函数的要求不高,一般不会陷入局部最优解,更适应于求解大规模离散化问题。该文将遗传算法应用于工程问题的一个典型离散优化问题矩形件优化排样。通过该算法可以找出高效率的排样加工方法。设计结果能广泛应用于各零件的排样加工实例。     

基于改进遗传算法的矩形件优化排样

论文利用遗传算法结合剩余矩形排样法求解矩形件正交排样问题。通过对排样问题已知解信息进行统计分析,并根据分析结果改进原遗传算法判断个体好坏的标准,对父代种群进行了优劣分类,针对不同的分类采用不同的遗传操作,构造出一种改进遗传算法。通过实例验证,该算法得到了排样问题的最优解,说明了其有效性。     

矩形件优化排样的混合启发式方法

提出一种启发式递归与遗传算法相结合的混合启发式算法求解矩形件优化排样问题。首先给出一种启发式递归算法,利用该算法逐个从待排矩形件中生成局部利用率高的条料,直到所有待排矩形件均生成条料;利用遗传算法全局搜索能力强的特点,对这些条料序进行搜索重组,使其所用的板材数最少;最后再次利用遗传算法,对条料生成之前的矩形件种类序进行全局最优搜索,使总的板材利用率达到了最大。对两个典型实际算例进行计算,并与相关文献比较,结果表明了该算法的有效性。     

矩形件优化排样问题的混合遗传算法求解

利用遗传算法结合剩余矩形排样法求解矩形件正交排样问题。通过遗传算法将矩形件正交排样问题转化为一个排列问题,并引入剩余矩形排样算法来惟一确定每一个排列所对应的排样图(即排样方案),两者结合用于求解矩形件排样问题。最后用此混合遗传算法对文献[1]中的两个算例进行了验证,表明了其有效性。     

矩形件优化排样问题的混合遗传算法求解

利用遗传算法结合剩余矩形排样法求解矩形件正交排样问题。通过遗传算法将矩形件正交排样问题转化为一个排列问题，并引人剩余矩形排样算法来惟一确定每一个排列所对应的排样图（即排样方案），两者结合用于求解矩形件排样问题。最后用此混合遗传算法对文献[1]中的两个算例进行了验证，表明了其有效性。     

矩形件排样优化的一种近似算法

本文对理论上属于ＮＰ－完备问题的二维矩形件优化排样问题，构造了一个效率高、速度快、可令人满意的一种近似算法，该算法的主要思想是在排样过程中根据一种局部最优原则不断地动态产生一些较小的矩形，然后对这些小矩形区域排样，同时也消去一些已排过的矩形区域，直至所有的矩形件被排完，根据本文算法我们开发了一个矩形件排样系统。     

基于改进最低水平线方法与遗传算法的矩形件排样优化算法

传统的最低水平线方法用于矩形件排样时可能产生较多未被利用的空白区域,造成不必要的材料浪费。针对此缺陷,在搜索过程中引入启发式判断,实现空白区域的填充处理,提高板材利用率。在应用遗传算法优化矩形件排样顺序时,在进化过程中采用分阶段设置遗传算子的方法,改善算法的搜索性能与效果。通过改进最低水平线方法与基于分阶段遗传算子的遗传算法相结合,共同求解矩形件排样问题。排样测试数据表明,所提出的矩形件排样优化算法能够有效改善排样效果,提高材料利用率。     

一种改进的矩形件优化排样近似算法

分析了传统矩形件优化排样近似算法的主要缺陷，并在此基础上提出了一个改进算法，运用该算法获得了比原算法更好的优化排样结果。     

A genetic algorithm for the two-dimensional knapsack problem with rectangular pieces

Given a set of rectangular pieces and a rectangular container, the two-dimensional knapsack problem (2D-KP) consists of orthogonally packing a subset of the pieces within the container such that the sum of the values of the packed pieces is maximized. If the value of a piece is given by its area, the objective is to maximize the covered area of the container. A genetic algorithm (GA) is proposed addressing the guillotine case of the 2D-KP as well as the non-guillotine case. Moreover, an orientation constraint may optionally be taken into account and the given piece set may be constrained or unconstrained. The GA is subjected to an extensive test using well-known benchmark instances. Compared with recently published methods, the GA yields competitive results.     

矩形件优化排样的一种启发式算法

对大规模矩形件正交排样问题,提出了一种快速高效的启发式排放算法。对当前的可排放位置（水平线）,用贪婪算法从未排矩形件中选择可排放于该水平线的最优矩形件组合块;根据各个排放位置与其对应的矩形件组合块的匹配程度,选择最优的可排放位置（最优水平线）优先排放。在排放时,为了便于后续排放,先将待排放位置对应的矩形件组合块从低到高进行排序,再排放。对E.Hopper提供的规模最大的一类实例进行计算,排样率都在99%以上,平均排样率达到了99.38%,平均计算时间只用了1.12秒。与相关文献最好结果进行了比较,结果表明该文算法解决大规模的矩形件排样具有高效性。     

A recursive branch-and-bound algorithm for the rectangular guillotine strip packing problem

A heuristic recursive algorithm for the two-dimensional rectangular strip packing problem is presented. It is based on a recursive structure combined with branch-and-bound techniques. Several lengths are tried to determine the minimal plate length to hold all the items. Initially the plate is taken as a block. For the current block considered, the algorithm selects an item, puts it at the bottom-left corner of the block, and divides the unoccupied region into two smaller blocks with an orthogonal cut. The dividing cut is vertical if the block width is equal to the plate width; otherwise it is horizontal. Both lower and upper bounds are used to prune unpromising branches. The computational results on a class of benchmark problems indicate that the algorithm performs better than several recently published algorithms.     

一种高效的矩形套裁排样的带填充排样算法

提出一种带填充排样算法,实现矩形毛坯套裁排样。该算法首先用水平剪切线将板材分层,每层的宽度和板材宽度相同,高度和层最左端的主毛坯高度相同;通过调用两个递归过程确定最优排样方式,第一个过程确定每层左端的主毛坯,第二个过程确定层右端区域的毛坯排列方式。采用分支定界技术缩小搜索空间。实验计算结果说明所述算法比文献中最近报道的几种算法都有效。     

An exact strip packing algorithm based on canonical forms

Given a set of rectangles and a rectangular container with a fixed width, called a strip, the two-dimensional strip packing problem (2SP) requires all the given rectangles to be placed orthogonally without overlap within the strip so as to minimize the height of the strip. 2SP and its variants have many applications in steel and textile industries, including an indirect application in scheduling problems. However, 2SP is known to be NP-hard.     

Extended local search algorithm based on nonlinear programming for two-dimensional irregular strip packing problem

This paper presents an extended local search algorithm (ELS) for the irregular strip packing problem. It adopts two neighborhoods, swapping two given polygons in a placement and placing one polygon into a new position. The local search algorithm is used to minimize the overlap on the basis of the neighborhoods mentioned above and the unconstrained nonlinear programming model is adopted to further minimize the overlap during the search process. Moreover, the tabu search algorithm is used to avoid local minima, and a compact algorithm is presented to improve the result. The results of standard test instances indicate that when compared with other existing algorithms, the presented algorithm does not only show some signs of competitive power but also updates several best known results.     

二维离线非旋转装箱问题的一个混合算法

针对二维离线非旋转装箱问题,在凹角和适应值的思想的基础上,提出了一个改进型的Best-Fit启发式算法,并结合基于自然数编码的遗传算法构建了混合算法。同时在遗传迭代过程中,引入二维装箱问题的下界思想作为迭代的终止条件之一,减少了遗传算法无效迭代次数,另外根据问题自身特点,有效地降低了染色体长度,提高了整体的计算速度。在36个标准测试案例的测试基础上与一些经典的算法进行了比较,实验结果表明该算法在工业生产可接受的时间内与其他经典的算法相比能够获得更为满意的结果。     

A least wasted first heuristic algorithm for the rectangular packing problem

The rectangular packing problem is to pack a number of rectangles into a single large rectangular sheet so as to maximize the total area covered by the rectangles packed. The paper first presents a least wasted first strategy which evaluates the positions used by the rectangles. Then a random local search is introduced to improve the results and a least wasted first heuristic algorithm (LWF) is further developed to find a desirable solution. Twenty-one rectangular-packing instances are tested by the algorithm developed, the experimental results show that the presented algorithm can achieve an optimal solution within reasonable time and is fairly efficient for dealing the rectangular packing problem. LWF still performs well when it is extended to solve zero-waste and non-zero-waste strip packing instances.     

基于模拟退火算法的布局问题研究

在传统模拟退火算法的基础上,对布局问题的优化算法进行了研究,采用回火策略,改进一般模拟退火算法寻优的效果;结合布局问题的具体特点,采用Sequence Pair来描述布局问题的解结构,综合构成了一种新的求解布局问题的模拟退火算法.通过算例验证,该算法优于传统优化算法和普通启发式搜索算法,并且对增量布局也能够取得较好的效果.