Lecture Integer Programming and Index Funds
课程名称最优化方法(双语)
课程名称：最优化方法（双语）课程编码：7121101课程学分：3学分课程学时：48学时适用专业：信息与计算科学《最优化方法》(双语)Optimization Method (Bilingual)教学大纲1．课程性质与任务（1）本课程是信息与计算科学专业学生的专业选修课。
最优化方法是从众多可能方案中选择出最佳者，从而达到最优目标的科学。
作为一门新兴的应用数学分支，最优化方法在近二、三十年来随着计算机的应用而迅猛发展，已经应用于国民经济各个部门和科学技术的各个领域中。
（2）通过本课程的学习，使学生掌握数学规划，主要指线性规划、整数规划、运输问题、目标规划、非线性规划的基本理论和方法，为在该领域的深入学习和研究打下良好的基础。
培养学生分析和解决实际问题的能力，使学生通过最优化方法的学习，能够将实际问题抽象为数学的问题，分析和解释最优结果，并将结果应用到实际中去。
2．课程教学基本内容及要求本课程主要介绍线性规划、整数规划、运输问题、目标规划、非线性规划的基本理论和方法。
通过对最优化方法的教学活动，对学生的要求按了解、理解、掌握三个层面给出，具体要求如下：(1)引言掌握最优化模型及分类。
掌握凸集和凸函数、凸规划的基本概念，理解其性质。
(2)线性规划的基本性质掌握线性规划的标准型，掌握图解法。
(3)单纯形方法掌握单纯形方法的原理、单纯形表、两阶段法和大M法。
了解退化情形和修正单纯形方法。
(4)对偶原理及灵敏度分析理解线性规划的对偶理论，掌握对偶单纯形算法。
(5)运输问题掌握运输问题的数学模型、掌握表上作业法。
(6)整数规划掌握典型整数规划的数学模型，掌握割平面法、分枝定界法，了解0-1规划的隐数法。
(7)无约束问题掌握一维搜索的概念，掌握非线性规划的模型建立，以及凸集、凸函数，最优性条件等基本概念，掌握最速下降法、牛顿法。
理解直接搜索法，可行方向法等最优化方法。
(8)有约束问题掌握非线性规划的模型建立，以及最优性条件等基本概念。
基于整数线性规划和混合整数线性规划的投资组合优化
1引言线性规划是用来寻求变量处于线性关系时的有效方法，在项目选择、投资组合优化、季节收益预测等问题中有多种应用。
整数规划与线性规划非常相似，但它要求所有或部分变量是整数。
某些情况下，整数规划更可取，如二元变量的管理决策。
部分决策变量为整数的模型，称为混合整数规划。
本文将会研究整数线性规划在投资组合优化中的应用。
模型A ，即整数线性规划（ILP ）模型可以看作NP 完全问题中的0-1背包问题，通过模型A 找出可选入投资组合的股票。
另一个模型是混合整数线性规划（MILP ），这里使用的是有限资产平均绝对偏差（LAMAD ）模型的演变来确定投资所选股票的确切数量，分配最合适的权重，以达到风险最小化、回报最大化的效果。
本文采用3种算法求解：分支剪界算法、动态规划算法和贪心算法。
分支剪界算法用CPLEX 12.6实现，动态规划算法和贪心算法在Eclipse 标准4.4平台上，用Java 语言实现，所采用的股票信息和数据由NASDAQ 和yahoo finance 网站获取。
2算法介绍以下介绍的算法都可以归属于启发法的范畴。
启发法是指不以找到问题的最佳或最确切的解决方案为目标的技术，而是找到一个足够可信的解决方案的方法。
直觉判断、刻板印象和常识都属于这个“范畴”。
它非常适用于在计算或搜索过于详尽和不实际的情况下，通过心理捷径来加快得到满意解决方案的过程，以减轻作出决策的认知负担。
它有常见的几种策略：第一种是将问题的目标状态进行切分，然后通过实现子目标逐渐实现总的目的；第二种是从最终目标状态逆向去寻找达到这个状态的途径；第三种是逐步收缩初始状态和目标状态的距离的方法。
元启发式是指导搜索过程的策略或上层方法论，元启发式的目标是有效地探索搜索空间，以找到最接近的最优解。
启发式依赖于问题，用于确定特定问题的“足够好”的解决方案，而元启发式就像一种设计模式，可以应用于更广泛的问题。
启发式方法特别适用于混合整数规划，因为混合整数规划太大而无法求解最优，而线性规划较为松弛，可以在合理的时间内求解。
programming and problem solving with c++ 中文版
《Programming and Problem Solving with C++》（中文版《C++程序设计教程》）是一本由美国作家Bjarne Stroustrup所著的教材。
以下是这本书的主要内容：
1.程序设计的基本元素：数据类型、控制结构和变量等基本概念，以及如何
使用它们来编写程序。
2.函数和程序结构：介绍如何使用函数来组织程序，包括函数的定义、声明
和调用，以及如何处理函数参数和返回值。
3.面向对象编程：介绍如何使用类和对象来组织程序，包括类的定义、对象
的创建和使用，以及如何使用继承和多态等面向对象编程技术。
4.泛型编程：介绍如何使用模板来编写泛型程序，包括模板函数的定义和使
用，以及如何使用标准模板库(STL)中的容器和算法等。
5.异常处理：介绍如何使用异常处理技术来处理程序中的错误和异常情况，
包括异常的抛出、捕获和处理。
6.文件和流：介绍如何使用文件和流来读写数据，包括文件的打开、读取、
写入和关闭等操作。
7.高级主题：介绍一些高级主题，包括多线程编程、网络编程和并发编程等。
总的来说，这本书是一本全面介绍C++编程语言的教材，适合初学者和有一定经验的程序员阅读。
整数规划和动态规划lecture_IP1
(整数规划和动态规划) Xiaoling Sun
School of Management, Fudan University Email: xls@
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Lecture 1: Introduction
Train scheduling Airline crew scheduling Highway pavement maintenance and rehabilitation Production planing Electricity generation planning Telecommunications Cutting problem
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How Hard is Integer Programming?
First thought (a bit naive):
Total enumeration: For Stone Problem and 0-1 Knapsack Problem. To list all the feasible points, a super computer with speed 108 (Yi) basic operations per second needs: n = 30, 230 ≈ 109 , 10 seconds. n = 60, 260 ≈ 1018 , 360 years n = 100, 2100 ≈ 1030 , 4 × 1014 years ...
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Deep thoughts
Most of the integer programs are NP-complete or NP-hard, which means the problem is “as difficult as a combinatorial problem can be”, if we knew an efficient algorithm for one problem, we would be able to convert it to an efficient algorithm to solve any other combinatorial problem. Solving the linear programming relaxation results in a lower bound on the optimal solution to the IP. Rounding to a feasible integer solution may be difficult or impossible. The optimal solution to the LP relaxation can be arbitrarily far away from the optimal solution to the MIP (except totally unimodular case). Solving general integer programs can be much more difficult than solving linear programs or convex optimization problems. This is more than just an empirical statement. There is a whole theory surrounding it (you will learn some soon)
数学建模应用中整数线性规划问题的常用解法初探
数学建模应用中整数线性规划问题的常用解法初探作者：***来源：《现代职业教育》2021年第07期[摘要] 在数学建模应用中，整数线性规划问题是一种常见的运筹学问题，其常用的解法有分支定界法、割平面法、蒙特卡罗法等。
试图从数学建模实践的角度，淡化理论证明，仅对这几种典型方法的原理、优缺点、应用范围等作一个简要的分析比较，以供读者在实际的数学建模过程中灵活应用。
[关键词] 整数线性规划;分支定界法;割平面法;蒙特卡罗法[中图分类号] O151.2 [文献标志码] A [文章编号] 2096-0603（2021）07-0178-02一、整数线性规划问题规划问题是运筹学的一个重要分支，从表达形式上看，可以分为线性规划（linear programming，LP）和非線性规划（non-linear programming，NLP）;从变量的可行域要求来看，也可以分为整数规划（integer programming，IP）和非整数规划（non-integerprogramming，NIP），若既有表达式上的线性特征，又有变量的取整要求，这样的规划问题我们一般称之为整数线性规划（integer linear programming，ILP）问题[1]。
整数线性规划问题的传统解法是先求解与之对应的松弛问题（即先不考虑变量的整数约束而形成的新的线性规划问题），若刚好得到整数解，则求解过程结束;否则，再通过适当方法（切割平面或分支定界）生成一个或多个新的松弛问题（最初松弛问题加上新的切割或分支条件），重复以上步骤直至求得最优解。
一般而言，整数线性规划问题的求解难度要比普通线性规划问题大，其根本原因在于自变量取值增加了离散特性，但在工程上，离散特性恰好可以被计算机利用。
蒙特卡罗算法是一类随机方法的统称。
这类方法的基本思路是，可以通过随机采样进行计算而得到近似结果，随着采样的增多，得到正确结果的概率将逐渐加大，经过一定的步骤之后，就会尽可能趋近最佳结果。
常用数学软件介绍Maple、Mathematica、Matlab、_MathCAD、_SAS、SPSS、LINDO、LINGO
世界上应用最广泛的专业统计软件。在国际学术界有 条不成文的规定，即在国际学术交流中，凡是用SPSS软 件完成的计算和统计分析，可以不必说明算法 。
和SAS相同，SPSS也由多个模块构成，在最新的11版 中，SPSS一共由十个模块组成，其中SPSS Base为基本 模块，其余九个模块分别用于完成某一方面的统计分析 功能，他们均需要挂接在Base上运行。除此之外， SPSS 11完全版还包括SPSS Smart Viewer和SPSS Report Writer两个软件，他们并未整合进来，但功能 上完全是SPSS的辅助软件。 SPSS最突出的特点就是操作界面极为友好，输出结果 美观漂亮（从国外的角度看），他使用Windows的窗口 方式展示各种管理和分析数据方法的功能，使用对话框 展示出各种功能选择项。 是非专业统计人员的首选统计软件。
Matlab的功能和特点
1．功能强大
(1) 运算功能强大
Matlab的数值运算要素不是单个数据，而是矩阵， 每个元素都可看作复数，运算包括加、减、乘、除、 函数运算等； 通过Matlab的符号工具箱，可以解决在数学、应用
科学和工程计算领域中常常遇到的符号计算问题。
(2) 功能丰富的工具箱
Matlab主要由主程序和功能各异的各种工具箱组成，其
主要特点是使用操作简单，输入格式与人们习惯的 数学书写格式很近似，采用所见即所得界面。 对于数值精度要求很严格的情形，或者是对于计算 方法有特殊要求的情况，MathCAD不适合。
四种软件的比较
如果同时要求计算精度、符号计算和编程的话，最好同
时使用Maple和Mathematica ，它们在符号处理方面各具
2. Quadratic Integer Program
U.C.Berkeley Handout N7 CS294:PCP and Hardness of Approximation February13,2006 Professor Luca Trevisan Scribe:Robert KrauthgamerNotes for Lecture7This lecture is based on the Goemans-Williamson paper[4],and Vazirani’s book[13].Outline1.Max-Cut–problem definiton:Given an undirected graph G=(V,E),find a partition of the vertex set V=S∪¯S that maximizes the number of cut-edges(edges with an endpoint in S and an endpoint in¯S).Examples:A clique,a bipartite graph,an odd cycle.The problem is NP-hard[7].Can be approximated within factor1/2[11].Exercise1:Show that local search(iteratively move to the other side a vertex if more than half of its neighbors are in the same side,while possible)yields1/2-approximation.Exercise2:Show that by randomly assigning vertices to either S or¯S the expected number of cut-edges is at least|E|/2.2.Quadratic Integer Program:Max(i,j)∈E 1−x i x j2s.t.x i∈{+1,−1},∀i∈VRelaxing the variables to be in[−1,1]does not give a linear program.Replacing x S∈{0,1} with x S≥0.3.Semidefinite programming relaxation:A relaxation to a vector program can be obtained by assuming x i is a unit-length vector inEuclidean space of large dimension m(instead of one dimension):Max(i,j)∈E 1−v i·v j2s.t. v i 2=1,∀i∈VThe above vector program is equivalent to the following semidefinite program by letting y ij=v i·v j:Max(i,j)∈E 1−y ij2s.t.y ii=1,∀i∈VY=(y ij)is symmetric positive semidefinite.4.Relaxation provides an upper bound:Lemma1:The SDP above can be solved in polynomial time within any desired accuracy.Lemma2:SDP≥OPT.Importance of upper bound:Proving ALG≥ρ·SDP will imply ALG≥ρ·OPT.Example:For a3-cycle,OPT=2while SDP=9/4by3vectors in the plane120degrees apart of each other.5.Hyperplane-cut rounding[4]:Algorithm:Let{v i}be an optimal SDP solution in R m.Choosen at random a vector r from the unit sphere S m,and set x i=sgn(r·v i),i.e.S={i∈V:r·v i≥0}.Geometric view:Choose a random hyperplane going through the origin(whose normal is r).It partitions the vectors(vertices)into two sides,forming a partition of V.Observations:(1)The rounding is invariant to rotation(just like the vector program).(2)Choosing a random vector from S m can be done by choosing m iid Gaussians X1,...,X mand letting r be a unit-length vector in the direction(X1,...,X m).In fact,the same holds wrt to any orthogonal basis of R m.Theorem3:The cut producted by this algorithm has expected size at least0.878·SDP.6.Claim:For every i,j∈V,Pr[exactly one of i,j falls into S]=αij/π,whereαij∈[0,π]isthe angle between v i and v j.Proof of claim:By the rotation invariance of r and of the SDP solution,we may assume that v i and v j are nonzero in all but thefirst two coordinates.Consequently,v i and v j lie in a two-dimensional plane,and for the event we are interested in,we may assume that X3=...=X m=0,i.e.r is chosen uniformly from the unit circle in that ing a two-dimensional picture,it is easy to verify that the probability the normal to r separates v i from v j is exactlyαij/π.7.Proof of Theorem:By the claim,for every i,j∈V,E[1−x i x j2]=αij/π.By elementary calculus,the RHS is atleast0.878·(1−cosαij2)=0.8781−v i·v j2.Summing over all edges,we have by linearity of expectation,E[ALG]≥0.878·SDP. Exercise3:Suppose that SDP=c|E|for some1/2<c<1.Show there exist c in this range, for which this rounding achieves a better approximation factor.ments:1.The above rounding can be derandomized.2.One can add additional constraints like the triangle inequality:(v i−v k)2≤(v i−v j)2+(v j−v k)2,∀i,j,k∈V,but they did not lead to an improved approximation factor for Max-Cut.3.The integrality ratio of the SDP above is exactly what the randomized rounding gives(even with triangle inequality),i.e.ρGW=minα∈[0,π]α/π(1−cosα)/2≈0.878.A5-cycle gives abound slightly worse than0.878,but an exact bound requires considerable more work,see Delorme-Poljak[1,2],Feige-Schechtman[3]and Khot-Vishnoi[9].4.If the Unique Games conjecture is true,than it is NP-hard to achieve approximation factorbetter thanρGW≈0.878[8,10].Otherweise,the hardness of approximation factor currently known is a bigger(worse)constant[12,5].5.A similar rounding procedure works for other problems like Max-DICUT and MAX-2SAT.Two main differences:(1)There is an additional vector v0used to“distinguish”the two sides.(2)The triangle inequalities are useful to improve the approximation ratio.6.The SDP rounding above motivated a more involved SDP rounding procedure for coloring3-colorable graph[6].References[1]Charles Delorme and Svatopluk binatorial properties and complexity of a max-cutapproximation.European Journal of Combinatorics,14(4):313–333,1993.3[2]Charles Delorme and Svatopluk placian eigenvalues and the maximum cut problem.Mathematical Programming,62(1-3):557–574,1993.3[3]Uriel Feige and Gideon Schechtman.On the optimality of the random hyperplane roundingtechnique for MAX CUT.Random Structures and Algorithms,20(3):403–440,2002.3[4]M.X.Goemans and D.P.Williamson.Improved approximation algorithms for maximum cutand satisfiability problems using semidefinite programming.Journal of the ACM,42(6):1115–1145,1995.Preliminary version in Proc.of STOC’94.1,2[5]Johan H˚astad.Some optimal inapproximability results.Journal of the ACM,48(4):798–859,2001.3[6]D.Karger,R.Motwani,and M.Sudan.Approximate graph coloring by semidefinite program-ming.In Proceedings of the35th IEEE Symposium on Foundations of Computer Science,pages 2–13,1994.3[7]R.M.Karp.Reducibility among combinatorial problems.In ler and J.W.Thatcher,editors,Complexity of Computer Computations,pages85–103.Plenum Press,1972.1[8]Subhash Khot,Guy Kindler,Elchanan Mossel,and Ryan O’Donnell.Optimal inapproxima-bility results for MAX-CUT and other two-variable CSPs?In Proceedings of the45th IEEE Symposium on Foundations of Computer Science,pages146–154,2004.3[9]Subhash Khot and Nisheeth Vishnoi.The unique games conjecture,integrality gap for cutproblems and the embeddability of negative type metrics into 1.In Proceedings of the46th IEEE Symposium on Foundations of Computer Science,pages53–63,2005.3[10]Elchanan Mossel,Ryan O’Donnell,and Krzysztof Oleszkiewicz.Noise stability of functionswith low influences:invariance and optimality.In Proceedings of the46th IEEE Symposium on Foundations of Computer Science,pages21–30,2005.3[11]S.Sahni and T.Gonzalez.P-complete approximation problems.Journal of the ACM,23:555–565,1976.1[12]L.Trevisan,G.B.Sorkin,M.Sudan,and D.P.Williamson.Gadgets,approximation,and linearprogramming.SIAM Journal on Computing,29(6):2074–2097,2000.3[13]Vijay Vazirani.Approximation Algorithms.Springer,2001.1。
05-Integer Program
5 3 8
1 1
0 1
最优解 x* = (1，0，1)T，z*= 8 若计算过程中不断改进过滤条件(如在检查了(0，0， 1)后将过滤条件改进为 3x1-2x2 + 5x3 5)，可减少计算量。
点 (x1,x2,x3) (0，0，0) (0，0，1) 0 5 条 ① -1 ② 1 件 ③ 0 ④ 1 满足条件? z值
5
点 (x1,x2,x3) (0，1，0) (0，1，1) 3 8
条 ① 0 ② 2
件 ③ 1 ④ 1
满足条件?
z值
8
再将过滤条件改进为 3x1-2x2 + 5x3 8
点 (x1,x2,x3) (1，0，0) (1，0，1) (1，1，0) (1，1，1) 2 3 1 6 条 ① ② 件 ③ ④ 满足条件? z值
7
2. 相互排斥的约束条件 ① 二者择一 如例1中体积约束： 车运 船运
引入0-1变量y ，令 体积约束为：
5x1 + 4x2 24
7x1 + 3x2 45
5x1 + 4x2 24 + yM
7x1 + 3x2 45 + (1-y)M
y = 0或1
其中M为充分大的数。
② 多者择一 有m个互相排斥的约束条件：
西南航空公司机组人员安排
西雅图 SEA
旧金山 SFO
丹佛 DEN
芝加哥 ORD
洛杉矶 LAX
周建勤
jqzhou@
18
西南航空公司机组人员安排
航班 可行的航班次序 1 2 1 1 2 2 3 2 4 3 3 4 2 2 4 3 5 2 4 2 4 2 4 3 4 3 3 4 3 4 5 1 1 2 6 7 8 1 1 3 2 5 9 10 11 1 1 3 5 12
integer programming 教材
integer programming教材【释义】integer programming整数规划：一种数学优化或可行性问题，其中一些或全部变量被限制为整数。
【短语】1Mixed Integer Programming数混合整数规划;混合整数编程;混合整数规划问题;规划方法2zero-one integer programming数零一整数规划3integer programming algorithm整数规划算法;翻译4Pure Integer Programming纯整数规划;规划问题5All Integer Programming整数规划60-1integer programming整数规划;规划7Mixed integer programming model混合整数规划模型;规划模式8integer programming problem整数规划问题【例句】1Scheduling;Open shop;Mixed integer programming.排程；开放型工厂；混整数规划。
2The scheduling is formalized as a integer programming problem.该描述将调度问题形式化为整数规划问题。
3It is to understand the basis for other integer programming problem.它是理解其它整数规划问题的基础。
4The problem of bounded nonlinear mixed integer programming is studied.对一有界约束非线性混合整数规划问题进行了研究。
5The number of the most optimal solutions of this integer programming is determined.给出了一类整数规划问题有唯一最优解的充要条件。
第三章整数线性规划
割平面法
IP LP xl*
Yes xI* = xl*
判别是否整数解
No 加入割平面条件 用对偶单纯型方法继续求解
§3.3 分枝定界方法
分枝定界方法的基本思想 分枝定界方法的实现——例题
1 分枝定界方法的基本思想
如果松弛问题(P0)无解，则(P)无解；
如果(P0)的解为整数向量，则也是(P)的解；
min -(x1 x2 ) s.t.-4x1 2 x2 1 (P1 ) 4x1 2 x2 11 x1 1 x1 , x2 0, Integer
P2
约束 x1 1, x1 2 (它们将x1=3/2排除在外)，得到两个子问题：
min -(x1 x2 ) s.t.-4x1 2 x2 1 (P2 ) 4x1 2 x2 11 x1 2 x1 , x2 0, Integer
运筹 帷幄之中
决胜 千里之外
运 筹 学
主讲教师
赵玉英
62338357(O) yuyingzhao@
北京林业大学理学院
第3章 整数线性规划
整数线性规划问题 Gomory割平面方法(1958) 分枝定界方法(Land doig and Dakin 1960’s) 0-1规划
3
(3/2,10/3)
3
x1
3 整数线性规划问题的求解
思路2：由于纯整数线性规划的可行集合就是一些离散 的格点，可否用穷举的方法寻找最优解？ 当格点个数较少时，这种方法可以； 对一般的ILP问题，穷举方法无能为力。
3 整数线性规划问题的求解
目前，常用的求解整数规划的方法有： 割平面法和分枝定界法； 对于特别的0－1规划问题采用隐枚举法和匈牙利法。
数学建模各题型的算法
数学建模各题型的算法数学建模的题型很多，对应的算法也有多种。
以下是数学建模常见题型以及相应的算法：1. 线性规划（Linear Programming）：常用的线性规划算法包括单纯形法（Simplex Algorithm）、内点法（Interior Point Method）等。
2. 整数规划（Integer Programming）：常用的整数规划算法包括分支定界法（Branch and Bound）、动态规划法（Dynamic Programming）、割平面法（Cutting Plane Method）等。
3. 非线性规划（Nonlinear Programming）：常用的非线性规划算法包括梯度下降法（Gradient Descent）、牛顿法（Newton's Method）、拟牛顿法（Quasi-Newton Method）、遗传算法（Genetic Algorithm）等。
4. 图论（Graph Theory）：常用的图论算法包括最短路径算法（Dijkstra Algorithm、Floyd-Warshall Algorithm）、最小生成树算法（Prim Algorithm、Kruskal Algorithm）、最大流算法（Ford-Fulkerson Algorithm、Edmonds-Karp Algorithm）等。
5. 动态规划（Dynamic Programming）：动态规划算法用于求解具有重叠子问题性质的最优化问题，常用的算法有钢条切割问题、背包问题、旅行商问题等。
6. 模拟退火算法（Simulated Annealing）：模拟退火算法是一种全局优化算法，常用于求解复杂的组合优化问题，如旅行商问题、装箱问题等。
7. 神经网络（Neural Network）：神经网络算法常用于函数拟合、分类、聚类等问题，其中包括前馈神经网络（Feedforward Neural Network）、卷积神经网络（Convolutional Neural Network）、循环神经网络（Recurrent Neural Network）等。
嵌入式系统论文英文
2. Prove that the static I-Cache locking problem for ACET reduction is an NP-Hard problem, and propose a fully locking algorithm and a partially locking algorithm.
Received: 27 August 2010 / Revised: 31 August 2011 / Accepted: 21 November 2011 © Springer Science+Business Media, LLC 2011
Abstract Cache is effective in bridging the gap between processor and memory speed. It is also a source of unpredictability because of its dynamic and adaptive behavior. A lot of modern processors provide cache locking capability which locks instructions or data of a program into cache so that a more precise estimation of execution time can be obtained. The selection of instructions or data to be locked in cache has dramatic influence on the system performance. For real-time systems, cache locking is mostly utilized to improve the Worst-Case Execution Time (WCET). However, Average-Case Execution Time (ACET) is also an important criterion for some embedded systems, especially for soft real-time embedded systems, such as image processing systems. This paper aims to utilize instruction cache (I-Cache) locking technique to guarantee a minimized estimable ACET for embedded systems by exploring the probability profile information. A Probability Execution Flow Tree (PEFT) is introduced to model an embedded application with runtime profile information. The static I-Cache locking problem is proved to be NP-Hard and two kinds of locking, fully locking and partially locking, are proposed to find the instructions to be locked. Dynamic I-Cache locking can further improve the ACET. For dynamic I-Cache locking, an algorithm that leverages the application’s branching information is proposed. All the algorithms are executed during the compilation time and the results are applied during the runtime. Experimental
integer programming 教材
integer programming 教材整洁美观、通顺流畅的文字，这是每一位写作者都力求追求的目标。
下面是关于integer programming（整数规划）的教材。
整数规划教材第一章：整数规划导论1.1 整数规划的背景和应用领域整数规划作为线性规划的一种扩展形式，在现实生活和工业领域中具有广泛的应用，如物流优化、供应链管理、排产问题等。
1.2 整数规划的基本概念和特点整数规划是在决策变量中引入整数要求的线性规划问题。
与线性规划相比，整数规划的求解更加困难，但也具有更高的实用性和准确性。
第二章：整数规划的数学建模2.1 整数规划模型的建立步骤整数规划的数学建模是解决实际问题的关键步骤。
本节介绍整数规划建模的具体步骤，包括确定决策变量、建立目标函数和约束条件等。
2.2 整数规划的常见模型介绍了整数规划中常见的模型，如整数线性规划、混合整数规划、整数非线性规划等，并以实际案例进行详细说明和分析。
第三章：整数规划的求解方法3.1 精确求解方法介绍了整数规划精确求解方法，如分支定界法、割平面法等，并比较其优缺点和适用范围。
3.2 启发式求解方法介绍了整数规划启发式求解方法，如遗传算法、模拟退火算法等，并以实际案例进行了具体应用和分析。
第四章：整数规划的应用案例4.1 物流优化问题通过实际案例，介绍了整数规划在物流优化中的应用，如配送路径优化、仓库选址等问题。
4.2 生产排产问题以实例为基础，介绍了整数规划在生产排产问题中的应用，如工序调度、资源优化等。
第五章：整数规划的软件工具5.1 整数规划求解软件的选择介绍了目前常用的整数规划求解软件，并对其特点和适用范围进行了分析和比较。
5.2 整数规划求解软件的使用以具体案例为基础，讲解了整数规划求解软件的使用方法，包括数据输入、模型建立和结果分析等。
总结：整数规划作为一种重要的决策分析工具，在实际应用中发挥着广泛的作用。
通过本教材的学习，读者可以熟悉整数规划的基本概念和特点，掌握整数规划的建模方法和求解技巧，实现实际问题的优化和决策。
关于大学生上课玩手机的英语作文
关于大学生上课玩手机的英语作文College Students Playing on Their Phones During ClassHi there! My name is Amy and I'm 8 years old. Today I want to tell you about something I've noticed when I visit my big brother Tom at his college. He's a sophomore studying engineering and I love going to see him on campus. It's such a big place with lots of buildings and so many people walking around. It's fun to explore and imagine what it will be like when I go to college too someday.One thing I've noticed though, is that a lot of the college students seem to be looking at their phones during class instead of paying attention to the teacher. At first, I didn't really understand why they would do that. Don't they know they're supposed to be listening and taking notes? That's what we always have to do in elementary school. If I played on my phone during Mrs. Robinson's math class, she would take it away for sure!I asked Tom about it once after I saw a bunch of students typing away on their phones when the professor was giving a lecture. He said, "Yeah, a lot of people do that in college. Theyget bored or distracted easily." I was surprised to hear that. Don't they care about learning? Don't they want to get good grades?Tom tried to explain it to me. He said in college, the classes are much bigger with sometimes over a hundred students. It can be hard to stay focussed, especially in those huge lecture halls. He also said the material is a lot more challenging than what we learn in elementary school. Things like advanced calculus, engineering physics, computer programming - it can be really dense and dry material. After an hour or two of intense lectures, a lot of students just zone out and go on their phones to take a little mental break.That made a bit more sense to me, but I still think it seems kind of rude to be playing games or browsing social media when the professor is trying to teach. When I said that to Tom, he agreed but said a lot of students also use their phones or laptops to actually take notes, look up supplemental information, or work on assignments for that class during the lecture. As long as they aren't being a distraction, some professors are okay with students multi-tasking like that.I can kind of understand that, I guess. Typing notes is probably faster than writing them out by hand. And if you need to look something up related to what the teacher is saying, itcould be helpful to have a phone or laptop right there. Though I still think playing games during class seems pretty disrespectful!Tom said it's really up to each individual student to decide how much they'll allow themselves to get distracted. The students who can stay focussed and motivated tend to do better. But he admitted it is a struggle with all the apps, social media, videos, and games just a tap away on your phone these days. It makes it very easy to go down a rabbit hole of distractions, especially for some of the more boring material.I still think college students shouldn't play on their phones so much during class. They are paying a lot of money for their education and they should get the most out of it. Sure, maybe take a break to send a quick message once in a while. But they shouldn't be scrolling through TikTok videos or playing mobile games when they're supposed to be learning!Maybe professors need to make their classes more engaging and interactive if students are getting bored and distracted that easily. Or maybe colleges should have stricter rules about phone and laptop use during lectures. I don't know - it seems like a complicated issue with no simple solution.All I know is that when I go to college one day, you can bet I'll be paying close attention and taking good notes - not zoningout on my phone! I'll study hard, participate in class, and make sure I take full advantage of all my educational opportunities. Today's students are lucky to have such easy access to so much information and knowledge. They should appreciate it more!Well, that's just my two cents as an elementary schooler looking at this phone usage issue. Let me know if you have any other questions! I'll do my best to explain things in a way that makes sense. Thanks for reading my essay!。
(最新整理)clpex,GLPK,lpsolve,yalmip简介与教程
clpex,GLPK,lpsolve,yalmip简介与教程编辑整理：尊敬的读者朋友们：这里是精品文档编辑中心，本文档内容是由我和我的同事精心编辑整理后发布的，发布之前我们对文中内容进行仔细校对，但是难免会有疏漏的地方，但是任然希望（clpex,GLPK,lpsolve,yalmip 简介与教程）的内容能够给您的工作和学习带来便利。
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最近建立了一个网络流模型，是一个混合整数线性规划问题(模型中既有连续变量，又有整型变量).当要求解此模型的时候，发现matlab优化工具箱竟没有自带的可以求解这类问题的算法（只有bintprog求解器，但是只能求解不含连续变量的二值线性规划问题)。
于是在网上找了一些解决问题的途径，下面说说几种可能的解决方案. cplex 首先想到的是IBM公司大名鼎鼎的cplex。
cplex是IBM公司一款高性能的数学规划问题求解器，可以快速、稳定地求解线性规划、混合整数规划、二次规划等一系列规划问题。
CPLEX 的速度非常快,可以解决现实世界中许多大规模的问题,它能够处理有数百万个约束（constraint）和变量 (variable）的问题，而且一直刷新数学规划的最高性能记录。
他的标准版本是一个windows下的IDE应用软件，但是开发人员能通过组件库从其他程序语言调用 CPLEX 算法。
随标准版本一起发布的文件中包含一个名为matlab文件夹,将此文件夹添加到matlab的搜索路径下就可以在matlab下调用cplex高效地求解数学规划问题。
cplex IDE主界面（是不是很熟悉的界面？没错，cplex也是基于eclipse插件机制开发的。
）： bin目录下有matlab插件所必须的.mexw32文件和函数库API（。
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• Select a small portion from index. E.g., q out of n.
经济与管理学院
School of Economics & Management, UCAS
经济与管理学院
School of Economics & Management, UCAS
Lecture 5: EXCEL for Integer Programming
• Integer variables are assigned as "int" • Binary variables are assigned as "bin" (0 or 1) • Other constraints are the same as in Linear Programming. • Uncheck the box "ingore integral constraints" • Number of variables should be less than 200.
经济与管理学院
School of Economics & Management, UCAS
Lecture 5: Tracking S&P 500
• Select 6 stocks from S&P 500 for illustration. • XOM, MSFT, APPL, PG, JPM, GE • Choose 3 out of 6 stocks to track these 6 stocks. • Data ranges from 1995 to 2013. • Data from 1995 to 2006 is used to construct index fund; the rest is used for validation.
Lecture 5: Models for Index Funds • A Large-Scale Deterministic Model
– cluster similar assets into groups – select one representative asset from each group • Let ij represents the similarity between asset
经济与管理学院
School of Economics & Management, UCAS
Lecture 5: Support for Index Funds
• Market Efficiency
– Theoretically, price reflects all information available in the market.
经济与管理学院
School of Economics & Management, UCAS
Lecture 5: Integer Programming and Index Funds
• Index Funds • Integer Programming (IP) - Theory and Algorithms • EXCEL and MATLAB for IP • Revisit portfolio optimization with VaR & CVaR
经济与管理学院
School of Economics & Management, UCAS
Lecture 5: Issues in Index Funds
• Strategies for forming index funds involve choosing a broad market index as a proxy for an entire market, e.g. the Standard and Poor list of 500 stocks (S & P 500). • A pure indexing is to purchase all the stocks in the index, with the same weights as in index.
i=1
where Vi is the market value of asset i. wj is the total market value of the assets \represented" by the stock j in the fund. The fraction of the index fund to be invested in asset j is proportional to wj , i.e. wj Pn f =1 wf
65 60 55 50 45 40 35 30 25 0 200 400 600 800 1000 1200 1400 1600 Whole index Fund index
经济与管理学院
School of Economics & Management, UCAS
Lecture 5: Value at Risk
The variables yj describe which assets j are in the index fund (yj = 1 if j is selected in the fund, 0 otherwise). For each stock i = 1; :::; n, the variable xij indicates which stock j in the index fund is most similar to i (xij = 1 if j is the most similar asset in the index fund, 0 otherwise).
Lecture 5: Why Index Funds
• Passive management of portfolios
– "buy and hold": selected assets on the basis of some fundamental criteria, then no active selling or buying of these stocks afterwards. – "indexing": choose a portfolio that mirrors the movements of a broad market population or a market index.
• Passive management of portfolios
– avoids any forecasting techniques and rather relies on diversification to achieve a desired performance.
经济与管理学院
School of Economics & Management, UCAS
(1)
µ
¶
µ
¶
µ ¶ ¡0:1 = 0:3
经济与管理学院
School of Economics & Management, UCAS
Optimization of Value at Risk
min s.t. ° (¡r (s) )T w · ° + M ¢ ys ; s = 1; :::; S PS y · b ² ¢ S c s s =1 Pn i=1 wi = 1 ys 2 f0; 1g; s = 1; :::; S:
• Emperical Performance
– Fund managers underperformed major indexes. – Lucky top performing funds in short term
• Transaction Cost
– Active managed funds incur transaction costs
经济与管理学院
School of Economics & Management, UCAS
Optimization of Value at Risk – Example
0:1 0 (2) r = ; r = ; r(3) ¡0:2 0:1 µ ¶ 0:5 If w = , then 0:5 ¡(r(1) )T w = 0:05; ¡(r(2) )T w = ¡0:05; ¡(r(3) )T w = ¡0:10 µ ¶ 0:8 If w = , then 0:2 ¡(r(1) )T w = ¡0:04; ¡(r(2) )T w = ¡0:02; ¡(r(3) )T w = 0:02
经济与管理学院
School of Economics & Management, UCAS
Lecture 5: Correlation of total returns
Correl XOM MSFT AAPL PG JPM GE XOM 1 0.5727 0.8432 0.8970 0.7416 0.6908 MSFT 0.5727 1 0.3408 0.6090 0.8306 0.8610 AAPL 0.8432 0.3408 1 0.6790 0.5527 0.4299 PG 0.8970 0.6090 0.6790 1 0.7007 0.5791 JPM 0.7416 0.8306 0.5527 0.7007 1 0.8408 GE 0.6908 0.8610 0.4299 0.5791 0.8408 1
经济与管理学院
School of Economics & Management, UCAS