带拒绝箱覆盖问题的局内算法

作为对装箱覆盖问题的推广,提出带拒绝的装箱覆盖问题.设有许多等长的一维箱子,给定一个物品集,每个物品有两个参数:长度和费用.物品可以放入箱子也可被拒绝放入箱子,每个物品只准放入一只箱子中,每只箱子中的物品容量总和至少为箱子容量,一旦箱子中的物品长度达到要求则需启用新箱.如果物品被放入箱中,则产生费用.该问题是一个新的组合优化问题,在内部互联网信息管理等问题中有着广泛的应用背景.给出一个求解该问题的局内近似算法C-FF,分析其最坏情况渐近性能比为1/2,并给出了相应的实验结果.     

On Lazy Bin Covering and Packing problems

In this paper, we study two interesting variants of the classical bin packing problem, called Lazy Bin Covering (LBC) and Cardinality Constrained Maximum Resource Bin Packing (CCMRBP) problems. For the offline LBC problem, we first prove the approximation ratio of the First-Fit-Decreasing and First-Fit-Increasing algorithms, then present an APTAS. For the online LBC problem, we give a competitive analysis for the algorithms of Next-Fit, Worst-Fit, First-Fit, and a modified HARMONIC_M algorithm. The CCMRBP problem is a generalization of the Maximum Resource Bin Packing (MRBP) problem Boyar et al. (2006) [1]. For this problem, we prove that its offline version is no harder to approximate than the offline MRBP problem.     

Improved Approximation Algorithms for Maximum Resource Bin Packing and Lazy Bin Covering Problems

In this paper, we study two variants of the bin packing and covering problems called Maximum Resource Bin Packing (MRBP) and Lazy Bin Covering (LBC) problems, and present new approximation algorithms for them. For the offline MRBP problem, the previous best known approximation ratio is frac65frac{6}{5} (=1.2) achieved by the classical First-Fit-Increasing (FFI) algorithm (Boyar et al. in Theor. Comput. Sci. 362(1–3):127–139, 2006). In this paper, we give a new FFI-type algorithm with an approximation ratio of frac8071frac{80}{71} (≈1.12676). For the offline LBC problem, it has been shown in Lin et al. (COCOON, pp. 340–349, 2006) that the classical First-Fit-Decreasing (FFD) algorithm achieves an approximation ratio of frac7160frac{71}{60} (≈1.18333). In this paper, we present a new FFD-type algorithm with an approximation ratio of frac1715frac{17}{15} (≈1.13333). Our algorithms are based on a pattern-based technique and a number of other observations. They run in near linear time (i.e., O(nlog n)), and therefore are practical.     

带约束的一维装箱问题近似算法的研究

作为经典装箱问题的扩展,有色装箱问题在多处理器实时调度的过程中有很强的应用背景。论文提出了有色装箱问题的新算法-SCPF算法,按颜色分类,将相同颜色的物品分成一类。放置时按照相同颜色的物品首先放置的原则,将物品进行装箱。实验证明,该算法与文献犤3犦中的KC-A算法相比具有更好的装箱效果,使用的箱子数更少。并从理论上论证了该算法的性能比KC-A算法更好。     

受启动空间约束的装箱问题

提出了一种带有启动空间的约束装箱问题(start-up bin packing problem,简称SBPP),即不同类型的物品放入同一箱子中需要一个启动空间.该问题在工作分配、任务调度和日常生活中的包装等问题中有着广泛的应用背景.给出了一个求解SBPP的线性脱线算法C-NF,其最坏情况渐近性能比为2,与启动空间的大小无关.对该算法的平均性能进行了实验分析.另外,还分析了SBPP的在线特性,指出大量的经典在线装箱算法应用于SBPP都不存在确定的最坏情况渐近性能比,也给出了一种具有确定的最坏情况渐近性能比的在线算法.     

一类受限机器人的学习控制

本文给出了一类受限机器人的一个学习控制方案，学习控制器的设计是基于受限机器人的奇异模型，在存在未知的有界干扰的情况下，对末端操纵器受线性、无摩擦约束面约束的机器人，本文给出的控制方案实现了机器人运动的完全跟踪，保证了力跟踪误差是有界的，并且界的大小是可调节的。     

一类约束非线性系统的自适应模糊容错控制

针对一类输出受限的非线性系统,提出了一种自适应模糊容错控制方案。在考虑可能发生的执行器故障的情况下,采用非线性映射的方法处理系统受约束的输出变量,从而将约束量的初值选取区间扩大为整个约束空间;用有界的参考信号代换未知函数的自变量,再用模糊逼近器处理这些未知函数,并结合自适应技术处理代换误差和逼近误差,从而使得闭环系统为全局一致最终有界,系统输出可以有效跟踪参考信号。仿真结果进一步验证了本文方法的有效性。     

平面双连杆受限柔性机器人臂的动力学建模*

对一类平面双连杆受限柔性机器人臂的动力学建模问题进行研究，利用Ｄ’Ａｌｅｍｂｅｒｔ－Ｌａｇｒａｎｇｅ原理得到了一组描述该机器人系统运动性态的动力学方程。与已有的动力学模型相比，本文所建立的运动方程和振动方程具有模型准确、结构简单等特点，且具有与传统无约束刚性机器人类似的模型形式，因而有可能直接或间接利用现有的关于刚性机器人运动控制等方面的成果来研究复杂的受限柔性机器人的控制问题。     

Genetic Algorithms for Solving a Class of Constrained Nonlinear Integer Programs

We consider a class of constrained nonlinear integer programs, which arise in manufacturing batch-sizing problems with multiple raw materials. In this paper, we investigate the use of genetic algorithms (GAs) for solving these models. Both binary and real coded genetic algorithms with six different penalty functions are developed. The real coded genetic algorithm works well for all six penalty functions compared to binary coding. A new method to calculate the penalty coefficient is also discussed. Numerical examples are provided and computational experiences are discussed.     

一类有约束的分段线性系统双模预测控制

研究分段线性（PL）系统预测控制问题,提出了PL系统双模预测控制,并证明了该方法的稳定性.该方法使用混合逻辑动态系统来建模PL系统,利用PL系统状态反馈控制来确定PL系统的受控不变集,并结合双模预测控制方法获得PL系统双模预测控制.该方法解决了系数矩阵的选择问题,不需要满足最终状态等式约束.一个分段线性系统的实例证明了该方法是可行的.     

Selfish Bin Packing

Following recent interest in the study of computer science problems in a game theoretic setting, we consider the well known bin packing problem where the items are controlled by selfish agents. Each agent is charged with a cost according to the fraction of the used bin space its item requires. That is, the cost of the bin is split among the agents, proportionally to their sizes. Thus, the selfish agents prefer their items to be packed in a bin that is as full as possible. The social goal is to minimize the number of the bins used. The social cost in this case is therefore the number of bins used in the packing.     

Bin stretching revisited

We study three on-line models of bin stretching on two machines. For the case where the machines are identical and the jobs arrive sorted by non-increasing sizes, we show a tight bound of 10/9 on the competitive ratio. For two related machines, we show a preemptive algorithm with competitive ratio 1 for any speed ratio, and two new non-preemptive algorithms. We prove that the upper bound on the competitive ratio achieved by the non-preemptive algorithms is optimal for almost any speed ratio, and close to optimal for all other speed ratios. Received: 14 February 2002 / 18 November 2002 Research supported in part by the Israel Science Foundation, (grant No. 250/01-1).     

Fair versus Unrestricted Bin Packing

Abstract. We consider the on-line Dual Bin Packing problem where we have n unit size bins and a sequence of items. The goal is to maximize the number of items that are packed in the bins by an on-line algorithm. We investigate unrestricted algorithms that have the power of performing admission control on the items, i.e., rejecting items while there is enough space to pack them, versus fair algorithms that reject an item only when there is not enough space to pack it. We show that by performing admission control on the items, we get better performance compared with the performance achieved on the fair version of the problem. Our main result shows that with an unfair variant of First-Fit, we can pack approximately two-thirds of the items for sequences for which an optimal off-line algorithm can pack all the items. This is in contrast to standard First-Fit where we show an asymptotically tight hardness result: if the number of bins can be chosen arbitrarily large, the fraction of the items packed by First-Fit comes arbitrarily close to five-eighths.     

Bin Packing with Rejection Revisited

We consider the following generalization of bin packing. Each item has a size in (0,1] associated with it, as well as a rejection cost, that an algorithm must pay if it chooses not to pack this item. The cost of an algorithm is the sum of all rejection costs of rejected items plus the number of unit sized bins used for packing all other items. We first study the offline version of the problem and design an APTAS for it. This is a non-trivial generalization of the APTAS given by Fernandez de la Vega and Lueker for the standard bin packing problem. We further give an approximation algorithm of an absolute approximation ratio 3/2, where this value is best possible unless P=NP.     

多约束的箱子大小可变的装箱问题

作为经典装箱问题的扩展,带有约束条件的装箱问题有着很强的应用背景。从钢铁公司板坯入库引发的装箱问题中,物品除了重量这一参数,还引入了特性和种类等参数。将板坯入库归结为多约束的箱子大小可变的装箱问题后,建立了数学模型,将经典装箱算法进行了推广,构建了新的启发式算法A,它对输入物品按特性进行预处理,再进行装箱。理论分析了NFD,FFD,算法A的最坏情况的性能,并对这三种算法进行了数值模拟,得出在相关特性均匀分布下,算法A的性能最好。     

Covering a string

We consider the problem of finding the repetitive structures of a given stringx. The periodu of the stringx grasps the repetitiveness ofx, sincex is a prefix of a string constructed by concatenations ofu. We generalize the concept of repetitiveness as follows: A stringw covers a stringx if there is a superstring ofx which is constructed by concatenations and superpositions ofw. A substringw ofx is called aseed ofx ifw coversx. We present anO(n logn)-time algorithm for finding all the seeds of a given string of lengthn.Partially supported by SERC Grants GR/F 00898 and GR/J 17844, NATO Grant CRG 900293, ESPRIT BRA Grant 7131 for ALCOMII, and MRC Grant G 9115730.Partially supported by MRC Grant G 9115730 and S.N.U. Posco Research Fund 94-15-1112.     

覆盖Value集

覆盖粗糙集和Vague集都是处理不确定性问题的数学工具,它们分别是粗糙集和模糊集的扩展。已有的覆盖粗糙集模型在求上、下近似时,可能将一些实际上并非肯定属于给定集合的元素纳入到下近似中,而一些可能属于给定集合的元素却没有纳入到上近似中,这就会改变一些元素与给定集合的关系。通过深入分析论域中的元素与其相关覆盖元之间的关系,建立了覆盖Vague集。该覆盖Vague集能够从一种新的角度反映出论域中各元素与给定集合之间的从属程度。进一步研究了覆盖Vague集与覆盖粗糙集中一些重要概念之间的关系。最后讨论了当覆盖退化为划分时覆盖Vague集的特性。