排列组合问题中的有序无序与排序

在排列组合问题中有一类问题是讨论把m个元素放在n个位置有多少种不同方法,这类问题在汉字编码、信号输出、股票投资、桥牌比赛、彩票中奖等实际问题中都有应用.解决这类问题关键是正确区分具体问题中的元素是有序、无序或者需要排序.我们先看下面一个简单的例子.     

有理数的排序问题

有理数的排序问题融知识性和趣味性于一体，处理方法灵活多变．本文通过一些不同形式的例题，介绍解答此类问题的思考方法．     

数学应用问题解决图式理论的实证研究与认知分析

利用有暗示与无暗示试题开展数学应用问题解决图式理论实验，探索模式识别在数学应用问题解决中的认知特征。     

两类单机成组排序的问题

讨论了单机成组排序问题的加权总完工时间和最大延迟时间的极小化问题.并分别给出了算法.对于单杌成组排序误工总数问题,通过构造函数,利用动态规划方法给出其算法.     

一个动力学模型的稳定性分析

对一个描述教育经济学过程的非线性常微分方程组进行了讨论,分析了其稳态的稳定性及其在参数空间的分布,讨论该模型的一些动力学性质.     

圆内一类线段长度的排序问题

[数学问题351]问题 P为三角形ABC内的一点,直线4P分别交边BC和三角形ABC的外接圆于点M和N,当点P为三角形ABC的内心,重心,约尔刚点（M为内切圆切点）,奈格尔点（M为旁切圆切点）,外心和垂心时,分别记线段MN的长为l_1,l_G.l_K,l_O,l_H.     

一个排序问题的解决

问题 一天内的不同时刻,经理把文件交给秘书打印,每次都将一份文件放在秘书文件堆的上面,秘书有时间就将文件堆最上面的那份取来打印,每次取一份．若有n份文件,且经理是按1,2,…,n的顺序依次交来,问：秘书打印完这n份文件的可能顺序有多少种？     

排序法解题漫谈

如果一个数学问题 ,涉及到一批可以比较大小的对象 (如实数、线段、角、面积等等 ) ,它们之间事前并未规定顺序 ,在解题时 ,若能按照某种顺序关系 (如实数的大小、线段的长短等 )把它们依次排列起来 ,对问题的解决常常是有益的 .这种通过把所讨论的对象依某种顺序排列起来以达到解题目的的方法 ,我们称之为排序法 ,本文举列说明排序法在解题方面的应用 .1　解方程 (组 )例 1　求方程 ω!=x!+y!+z!的所有正整数解 .解　不妨设 x≤ y≤ z,显然有 w≥ z+1.所以有 (z+1) !≤w!=x!+y!+z!≤ 3z!,即 z+1≤ 3,z≤ 2 ,只能 x=y=z=2 ,w=3.例 2　已知方…     

用排序不等式巧解物理题

在新课程改革中,数学的教学分为文科数学和理科数学,必修数学和选修数学.在数学选修4-5中加入了排序不等式的新内容,经研究发现,排序不等式可以非常巧妙地解决某类物理问题,并能很大程度地做到把抽象的数学理论与形象的物理情景完美结合.高中数学选修4-5第3讲第3节中提到的排序     

Algorithms for semi on-line multiprocessor scheduling problems

In the classical multiprocessor scheduling problems, it is assumed that the problems are considered in off-line or on-line environment. But in practice, problems are often not really off-line or on-line but somehow in between. This means that, with respect to the on-line problem, some further information about the tasks is available, which allows the improvement of the performance of the best possible algorithms. Problems of this class are called semi on-line ones. The authors studied two semi on-line multiprocessor scheduling problems, in which, the total processing time of all tasks is known in advance, or all processing times lie in a given interval. They proposed approximation algorithms for minimizing the makespan and analyzed their performance guarantee. The algorithms improve the known results for 3 or more processor cases in the literature. Project supported by the National Natural Science Foundation of China (Nos. 19701028 and 19971078) and National 973 Research Project of China.     

组成于平行机和批处理机的二阶段混合流水作业问题

A hybrid two-stage flowshop scheduling problem was considered which involves m identical parallel machines at Stage 1 and a burn-in processor M at Stage 2, and the makespan was taken as the minimization objective. This scheduling problem is NP-hard in general. We divide it into eight subcases. Except for the following two subcases： （1） b≥ an, max{m, B} 〈 n; （2） a1 ≤ b ≤ an, m ≤ B 〈 n, for all other subcases, their NP-hardness was proved or pointed out, corresponding approximation algorithms were conducted and their worst-case performances were estimated. In all these approximation algorithms, the Multifit and PTAS algorithms were respectively used, as the jobs were scheduled in m identical parallel machines.     

A hybrid two-stage fexible flowshop scheduling problem with m identical parallel machines and a burn-in processor separately

A hybrid two-stage flowshop scheduling problem was considered which involves m identical parallel machines at Stage 1 and a burn-in processor M at Stage 2,and the makespan was taken as the minimization objective.This scheduling prob- lem is NP-hard in general.We divide it into eight subcases.Except for the following two subcases:(1)b≥a_n,max{m,B}＜n; (2)a_1≤b≤a_n,m≤B≤n,for all other subcases,their NP-hardness was proved or pointed out,corresponding approxima- tion algorithms were conducted and their worst-case performances were estimated.In aU these approximation algorithms,the Multifit and PTAS algorithms were respectively used,as the jobs were scheduled in m identical parallel machines.     

最小化最大延误无等待流水车间调度问题的禁忌搜索算法(英文)

为求解最小化最大延误无等待流水车间调度问题,提出了3个基于任务块交换的邻域,其中块交换邻域的规模为O(n4),块对换和简化块交换邻域的规模为O(n3).所提邻域的规模均大于现有邻域,因此可提高局部搜索算法的解质量.给出了3个邻域的加速性质,使一个相邻解的评估时间为常量,邻域的评估时间与其规模成正比.同基于支配规则的加速方法相比,所提出的加速性质适用于任何机器数.在禁忌搜索中比较了3个邻域,以及块对换和简化块交换邻域的并集.标准实例集上的计算结果表明:3个基于O(n3)邻域的禁忌搜索算法均好于现有算法;在所有的测试算法中,采用邻域并集的禁忌搜索算法的性能最好.     

Scheduling problems on tardiness penalty and earliness award with simply linear processing time

In this paper, a single-machine scheduling model with a given common due date and simple linear processing times was considered. The objective is the total weighted tardiness penalty and earliness award. Some polynomial time solvable cases for this problem are given. A dynamic programming algorithm was provided and a branch and bound algorithm for general case of the problem was provided based on a rapid method for estimating the lower bound.     

Online algorithms for scheduling with machine activation cost on two uniform machines

INTRODUCTION In this paper we investigate the uniform ma-chines scheduling problem with machine activationcost. This problem has application in garment pro-duction of international trade and is motivated by thefollowing scenario. Import-export company is com-pared to scheduler in this model, and orders are jobs,which arrive one by one. And garment factories canbe regarded as machines. Since jobs should be fin-ished on time, scheduler will choose a reasonablenumber of machines to make the…     

一类基于人工免疫系统与极值优化的混合算法求解流水作业调度问题

The permutation flowshop scheduling problem (PFSP) is one of the most well-known and well-studied production scheduling problems with strong industrial background. This paper presents a new hybrid optimization algorithm which combines the strong global search ability of artificial immune system (AIS) with a strong local search ability of extremal optimization (EO) algorithm. The proposed algorithm is applied to a set of benchmark problems with a makespan criterion. Performance of the algorithm is evaluated. Comparison results indicate that this new method is an effective and competitive approach to the PFSP.     

Sensitivity analysis for generalized parametric implicit quasi-variational inequalities

1IntroductionandpreliminariesaRecently,Noor[1],Agarwal,ChoandHuang[2]studiedthesensitivityofthesolutionsforsomevariationalinequalitiesonaparameterinHibertspaces.Inthispaper,theauthorstudiesaclassofgeneralizedparametricimplicitquasivariationalinequalities,provesanewexistencetheoremofthesolutionsandanalyzesthesensitivityofsolutions.LetHbearealHilbertspacewithanorm||?||andaninnerproduct??,??.LetKbeanonemptyclosedconvexsubsetofH,PKtheprojectionofHontoKandManopensubsetofHinwhichtheparameterλ…     

Genetic algorithm for scheduling reentrant jobs on parallel machines with a remote server

This paper considers a reentrant scheduling problem on parallel primary machines with a remote server machine, which is required to carry out the setup operation. In this problem, each job has three operations. The first and last operations are performed by the same primary machine, implying the reentrance, and the second operation is processed on the single server machine. The order of jobs is predetermined in our context. The challenge is to assign jobs to the primary machines to minimize the makespan. We develop a genetic algorithm（GA） to solve this problem. Based on a simple strategy of assigning jobs in batches on the parallel primary machines, the standardized random key vector representation is employed to split the jobs into batches. Comparisons among the proposed algorithm, the branch and bound（BB） algorithm and the heuristic algorithm, coordinated scheduling（CS）, which is only one heuristic algorithm to solve this problem in the literature, are made on the benchmark data. The computational experiments show that the proposed genetic algorithm outperforms the heuristic CS and the maximum relative improvement rate in the makespan is 1.66%.     

对变分问题的灵密度分析

考虑变分问题的灵密度分析,利用扰动法推出边界值问题和流动方程,以此来获得偏导数（灵敏性）的目标函数的所有参数。主要考虑参数系变分问题的灵密度分析,当参数产生改变时,它相应的最优解是如何随之而改变的,为了问题简单,开始考虑有限维参数的变分问题,最后定理4给出灵密度分析的一个固定公式,这个结果利于直接通过原始的目标函数关于参数P分析灵密度。