cplex中文教程
Cplex安装简介
Cplex安装简介
最近实验室不少同志来询问Cplex的安装及使用。
虽然有官方的安装说明，但是事无巨细地看起来也麻烦，这里就安装过程写一个简单的说明文档。
1.软件下载
首先从S:\shared\Zechun.HU\CPLEX 12.1中下载安装程序和相关的说明文档，其中CZ3VBEN.exe是安装程序，access.ilm是license，这两个是必须的组件。
2.安装
点击CZ3VBEN.exe安装程序，安装过程很简单（建议不要安装到C盘），和普通软件没有不同。
3.导入license
需要设置环境变量，具体的方法如下：右击“计算机”—选择属性—左边栏选择“高级系统设置”—选择“环境变量”—在“用户变量”中新建变量名：ILOG_LICENSE_FILE，设置变量值为access.ilm的路径（点击属性就可以查到）
4.设置路径
搞定了之后，就转战到matlab中设置路径。
将安装得到的ILOG文件夹放到matlab目录下的toolbox中
进入matlab程序，依次点击file—set Path—Add with subfolders（非常重要！），将刚刚拖到toolbox下的ILOG选中，就OK了。
5.最后，为了验证安装有效性，可以在matlab窗口测试help cplex，如果显示一堆说明文
档，就装成功了。
同时左下角的toolbox中也可以看到IBM ILOG的相关标识。
注：现在实验室的服务器上已经有升级到12.2，安装过程大同小异，若有什么新的注意事项，欢迎更新。
By 丁华杰
2011-4-28。
Rcplex 0.3-6 用户手册说明书
Package‘Rcplex’April6,2023Version0.3-6Title R Interface to CPLEXDescription R interface to CPLEX solvers for linear,quadratic,and(linear and quadratic)mixed inte-ger programs.Support for quadratically constrained programming is available.See thefile``IN-STALL''for details on how to install the Rcplex package in Linux/Unix-like and Windows sys-tems.Support for sparse matrices is provided by an S3-style class``sim-ple_triplet_matrix''from package slam and by objects from the Matrix package class hierarchy. LazyLoad yesDepends R(>=2.6.0),slamImports methodsEnhances MatrixSystemRequirements IBM ILOG CPLEX libraries and headersLicense LGPL(>=2.0)URL https:///projects/rcplexNeedsCompilation yesAuthor Hector Corrada Bravo[aut],Kurt Hornik[ctb](<https:///0000-0003-4198-9911>),Stefan Theussl[aut,cre](<https:///0000-0002-6523-4620>)Maintainer Stefan Theussl<****************************>Repository CRANDate/Publication2023-04-0611:40:11UTCR topics documented:Rcplex (2)Rcplex.close (6)Rcplex_solve_QCP (7)Index101Rcplex Solve optimization problem with CPLEXDescriptionInterface to CPLEX solvers for linear quadratic and(linear or quadratic)mixed-integer programs.The general statement of the problem ismin 12x Qx+c xs.t Ax≤blb≤x≤ubIf Q==NULL then the problem is linear,if any value of the vtype argument is"B"or"I"then the prob-lem is a mixed-integer program.The control argument is used to set CPLEX’s many parameters.See details.The objsense determines if the problem is a maximization or minimization problem.The sense argument is used to set the constraint directions.UsageRcplex(cvec,Amat,bvec,Qmat=NULL,lb=0,ub=Inf,control=list(),objsense=c("min","max"),sense="L",vtype=NULL,n=1)Argumentscvec The linear coefficient of the objective functionAmat The constraint matrix(requires ncol(Amat)==length(cvec))bvec The constraints right-hand side(requires length(bvec)==nrow(Amat))Qmat The quadratic coefficient of the objective function.If NULL the problem is lin-ear.If not NULL,it must be a symmetric positive semidefinite matrix of sizelength(cvec)by length(cvec).Default NULLlb Lower bound on the problem variables.If length(lb)==1then lb is the lowerbound of all variables.Otherwise,length(lb)==length(cvec).Set lb=-Infto have no lower bound.Default0.ub Upper bound on the problem variables.See lb for further details.Default Inf.control A list of CPLEX parameters.See*Details*objsense Either"max"or"min",determines the optimization direction.Default"min"sense The direction of the inequality in each constraint.If length(sense)==1then thesame value is taken for each constraint.Can be one of"L"(less than or equal),"G"(reater than or equal)or"E"(equal).Requires length(sense)==length(bvec).Default"L".vtype Determines the type of each problem variable.Can be one of"C"(continuous), "I"(integer)or"B"(binary).If length(vtype)==1the same value is taken forall variables.Otherwise,requires length(vtype)==length(ctype).Default"C".n Determines the maximal number of solutions the solver should return in case of an MIP with more than one solution at optimum.If CPLEX should searchfor"all"solutions then n has to be set to NA.In CPLEX this is also calledpopulating the solution pool.The parameters solnpoolagap,solnpoolgap,and solnpoolintensity influence the search for multiple solutions(see alsothe control argument below for details).Available from CPLEX11.0on.Rcplex()raises a warning if an older version of CPLEX is used and n>1.De-fault1.DetailsMatrices A and C may be sparse matrices from a class in the hierarchy defined by the Matrix pack-age.In that case,the internal casting functions are used to create the proper data structures to pass to CPLEX,which is similar to the column-major storage mode defined by the dgCMatrix-class defined by the Matrix package.We also provide a simple S3-style class for sparse matrices simple_triplet_matrix,as used in the relations package.Matrices A and C can be objects of this class.See the examples for example usage.simple_triplet_matrix objects MUST be in column-major order.The control argument can be used to set CPLEX’s many parameters,including the particular algorithm used for solving the given problem.See the ILOG CPLEX Parameters guide for further details.The following parameters are supported:trace:Turn CPLEX output on(1)or off(0).Default1.maxcalls:Number of calls to the CPLEX optimizer before license is released.Set to1to get a new license on every call to Rcplex.Can be any positive number.Default500.method:Algorithm to use(Default0):0:Automatic:CPLEX chooses algorithm automatically1:Primal Simplex2:Dual Simplex3:Network Simplex4:Barrierpreind:Turn presolver on(1)or off(0).Default1.aggind:Limit on the number of applications of the aggregator.Possible Values:-1(automatic),0 (do not use),any positive integeritlim:Maximum number of simplex iterations.Can be any nonnegative number.Default1e8.epagap:Absolute MIP optimality gap tolerance.Can be any nonnegative number.Default1e-6.epgap:Relative MIP optimality gap tolerance.Can be any nonnegative number.Default1e-4.tilim:Time limit in seconds of call to optimizer.Can be any nonnegative number.Default1e75.disjcuts:Indicator for disjunctive cuts used in MIP solver.Must be in-1:3.Default0(automatic).mipemphasis:Indicator for MIP solver emphasis.Must be in0:4.Default0(balance optimality and feasibility)cliques:Indicator for clique cuts in MIP solver.Must be in-1:2.Default0(automatic)nodesel:Node selection strategy in MIP solver.Must be in0:3.Default1(best-bound search).probe:Probe level in MPI solver.Must be-1:3.Default0(automatic)varsel:Variable selection strategy in MIP solver.Must be in-1:4.Default0(choose best method automatically).flowcovers:Indicator forflowcover cuts in MIP solver.Must be in-1:2.Default0(automatic).solnpoolagap:Sets an absolute tolerance on the objective value for the solutions in the solution pool.Can be any nonnegative real number.Ignored in versions<11.0of CPLEX.Default0 solnpoolgap:Sets a relative tolerance on the objective value for the solutions in the solution pool.Can be any nonnegative real number.Ignored in versions<11.0of CPLEX.Default0 solnpoolintensity:Controls the trade-off between the number of solutions generated for the solu-tion pool and the amount of time and memory consumed.Must be in0:4.Ignored in versions<11.0of CPLEX.Default0(automatic).round:Flag indicating if integer solutions for MIPs should be rounded before returning.In some cases,CPLEX returns slightly infeasible integer solutions.Setting this option to1ensures that the returned solution is integral by rounding.Default0(no rounding).ValueReturns a list with the following components,or,if n>1a list of length equal to the number of optimal solutions containing the following components for each solution:xopt Values of problem variables at optimum.obj Value of objective function at optimum.status Solution status.See CPLEX documentation for meaning of status codes.extra List with extra information about solution with componentsslack:Values of slack variables for inequality constraints.nodecnt:(IF MIP PROBLEM)Number of nodes in the search tree evaluatedlambda:(IF NOT MIP PROBLEM)Values of dual variables at optimumAuthor(s)Hector Corrada Bravo and Stefan TheusslReferencesIBM ILOG CPLEX Optimization Studio documentationSee AlsoRcplex.close,optimExamples##A linear program(this is lpex1.c in the CPLEX examples)cvec<-c(1,2,3)Amat<-matrix(c(-1,1,1,-1,3,-1),byrow=TRUE,nc=3)bvec<-c(20,-30)ub<-c(40,Inf,Inf)res<-Rcplex(cvec,Amat,bvec,ub=ub,objsense="max",sense=c( L , G )) print(res)##A linear program with random data##use the barrier methodn=20;m=25nnz<-trunc(.2*m*n)##entries in simple_triplet_matrix clas##*must*be in column major ordernnz<-sort(sample(m*n,nnz,replace=FALSE)-1)Amat<-simple_triplet_matrix(i=(nnz%%m)+1,j=trunc(nnz/m)+1,v=rnorm(nnz),nrow=m,ncol=n)x0<-runif(n)b<-as.matrix(Amat)%*%x0cvec<-rnorm(n)res<-Rcplex(cvec,Amat,b,sense= E ,control=list(method=4))print(res)##A quadratic problem(this is qpex1.c in the CPLEX examples)cvec<-c(1,2,3)Qmat<-matrix(c(-33,6,0,6,-22,11.5,0,11.5,-11),byrow=TRUE,nc=3)Amat<-matrix(c(-1,1,1,1,-3,1),byrow=TRUE,nc=3)bvec<-c(20,30)ub<-c(40,Inf,Inf)res<-Rcplex(cvec,Amat,bvec,Qmat,ub=ub,objsense="max")print(res)##A mixed integer linear program(mipex1.c in the CPLEX examples) cvec<-c(1,2,3,1)Amat<-matrix(c(-1,1,1,10,1,-3,1,0,0,1,0,-3.5),6Rcplex.close byrow=TRUE,nc=4)bvec<-c(20,30,0)lb<-c(0,0,0,2)ub<-c(40,Inf,Inf,3)vtype<-c(rep("C",3),"I")res<-Rcplex(cvec,Amat,bvec,lb=lb,ub=ub,sense=c("L","L","E"),objsense="max",vtype=vtype)print(res)##A mixed integer quadratic programcvec<-c(1,2,3,1)Qmat<-matrix(c(-33,6,0,0,6,-22,11.5,0,0,11.5,-11,0,0,0,0,0),byrow=TRUE,nc=4)Amat<-matrix(c(-1,1,1,10,1,-3,1,0,0,1,0,-3.5),byrow=TRUE,nc=4)bvec<-c(20,30,0)ub<-c(40,Inf,Inf,3)vtype<-c(rep("C",3),"I")res<-Rcplex(cvec,Amat,bvec,Qmat=Qmat,ub=ub,sense=c("L","L","E"),objsense="max",vtype=vtype)print(res)Rcplex.close()Rcplex.close Release CPLEX licenseDescriptionThis function releases the currently held CPLEX license.UsageRcplex.close()Author(s)Hector Corrada BravoSee AlsoRcplexRcplex_solve_QCP Solve quadratically constrained optimization problem with CPLEXDescriptionInterface to CPLEX solvers for quadratically constrained linear,quadratic,and mixed-integer pro-grams.The general statement of the problem ismin 12x Qx+c xs.t Ax≤band a i x+x Q i x≤r i fori=1,...,qlb≤x≤ubIf Q==NULL then the problem is linear,if any value of the vtype argument is"B"or"I"then the prob-lem is a mixed-integer program.The control argument is used to set CPLEX’s many parameters.See details.The objsense determines if the problem is a maximization or minimization problem.The sense argument is used to set the constraint directions.UsageRcplex_solve_QCP(cvec,Amat,bvec,Qmat=NULL,QC,lb=0,ub=Inf,sense="L",objsense=c("min","max"),vtype =NULL,n=1,control=list())Argumentscvec The linear coefficient of the objective functionAmat The constraint matrix(requires ncol(Amat)==length(cvec))bvec The constraints right-hand side(requires length(bvec)==nrow(Amat))Qmat The quadratic coefficient of the objective function.If NULL the problem is lin-ear.If not NULL,it must be a symmetric positive semidefinite matrix of sizelength(cvec)by length(cvec).Default NULLQC a list with three elements:QC,dir,and b.The element QC is a list with the quadratic part Q,a matrix,and the linear part of the constraint L,a numeric(currently nonzero values are not supported).dir has the same meaning asargument sense and b as bvec.lb Lower bound on the problem variables.If length(lb)==1then lb is the lower bound of all variables.Otherwise,length(lb)==length(cvec).Set lb=-Infto have no lower bound.Default0.ub Upper bound on the problem variables.See lb for further details.Default Inf.control A list of CPLEX parameters.See*Details*objsense Either"max"or"min",determines the optimization direction.Default"min"sense The direction of the inequality in each constraint.If length(sense)==1then thesame value is taken for each constraint.Can be one of"L"(less than or equal),"G"(reater than or equal)or"E"(equal).Requires length(sense)==length(bvec).Default"L".vtype Determines the type of each problem variable.Can be one of"C"(continuous),"I"(integer)or"B"(binary).If length(vtype)==1the same value is taken forall variables.Otherwise,requires length(vtype)==length(ctype).Default"C".n Determines the maximal number of solutions the solver should return in caseof an MIP with more than one solution at optimum.If CPLEX should searchfor"all"solutions then n has to be set to NA.In CPLEX this is also calledpopulating the solution pool.The parameters solnpoolagap,solnpoolgap,and solnpoolintensity influence the search for multiple solutions(see alsothe control argument below for details).Available from CPLEX11.0on.Rcplex()raises a warning if an older version of CPLEX is used and n>1.De-fault1.DetailsSee function link[Rcplex]{Rcplex}()for more information about sparse matrix representation and control arguments.ValueReturns a list with the following components,or,if n>1a list of length equal to the number of optimal solutions containing the following components for each solution:xopt Values of problem variables at optimum.obj Value of objective function at optimum.status Solution status.See CPLEX documentation for meaning of status codes.extra List with extra information about solution with componentsslack:Values of slack variables for inequality constraints.nodecnt:(IF MIP PROBLEM)Number of nodes in the search tree evaluatedlambda:(IF NOT MIP PROBLEM)Values of dual variables at optimumAuthor(s)Hector Corrada Bravo and Stefan TheusslReferencesIBM ILOG CPLEX Optimization Studio documentationSee AlsoRcplex.close,optimExamples##objective functionc<-c(1,2,3)Q<-matrix(c(-33,6,0,6,-22,11.5,0,11.5,-11),nrow=3)##constraints##linear partA<-matrix(c(-1,1,1,-3,1,1),nrow=2)dir<-c("L","L")b<-c(20,30)##quadratic partQC<-list(QC=list(Q=list(diag(1,nrow=3)),L=NULL),dir="L",b=1)##boundsub<-c(40,Inf,Inf)##solveres<-Rcplex_solve_QCP(c,A,b,Q,ub=ub,QC=QC,sense=dir,objsense="max") print(res)##solve MIQCPres<-Rcplex_solve_QCP(c,A,b,Q,ub=ub,QC=QC,sense=dir,objsense="max",vtype=c("C","I","C")) ##quadratic and linear partQC<-list(QC=list(Q=list(diag(1,nrow=3)),L=list(c(3,4,-3))),dir="L",b=1)##solveres<-Rcplex_solve_QCP(c,A,b,Q,ub=ub,QC=QC,sense=dir,objsense="max") print(res)Rcplex.close()Index∗optimizeRcplex,2Rcplex_solve_QCP,7∗utilitiesRcplex.close,6optim,4,8Rcplex,2,6Rcplex.close,4,6,8Rcplex_solve_QCP,710。
cplex 指数函数
CPLEX是IBM提供的一个优化建模工具，它可以帮助用户定义和解决线性规划、混合整数规划和其他优化问题。
在CPLEX中，可以使用各种函数和运算符来定义表达式，包括指数函数。
在CPLEX中，可以使用`exp`函数来定义指数函数。
`exp`函数接受一个参数，表示指数函数的基数，并返回该基数的指数值。
例如，如果要在CPLEX模型中定义一个指数函数`f(x) = e^x`，可以使用以下表达式：
```
f(x) = exp(x);
```
请注意，CPLEX还提供了其他函数和运算符，可以帮助您定义更复杂的数学表达式。
要了解更多关于CPLEX的功能和语法，请参考IBM的官方文档或教程。
(完整word版)cplex翻译完全版
CPLEX 121. 简介................................................................. 3..2. 怎么用Cplex运行模型 (3)3. Cplex 概览........................................................... 3..3.1线性规划......................................................... 3.3.2二次约束规划....................................................4.3.3混合整数规划....................................................4.3.4可行松弛性...................................................... 5.3.5解池：产生和保持多解........................................... 5.4. GAMS 选项.......................................................... .9..5. Cplex选项总结 (10)5.1预处理和一般选项 (10)5.2单纯形法选项................................................... 1.25.3单纯形法的限制选项 (12)5.4单纯形法的容限选项 (13)5.5障碍特殊选项.................................................. 1.35.6筛选特殊选项................................................... 1.35.7混合整数规划选项 (13)5.8混合整数规划限制选项 (15)5.9混合整数规划解池选项 (16)5.10混合整数规划容许度选项....................................... 1.65.11输出选项...................................................... 1.75.12 GAMS/Cplex选项文件......................................... 1.76. 特殊备注 (18)6.1物理内存限制................................................... 1.86.2使用特殊有序集 (18)6.3使用半连续半整数变量 (19)6.4为求解MIP问题耗尽内存 (19)6.5不能证明整数最优 (20)6.6从混合整数规划的解开始 (20)6.7使用可行松弛性 (21)7. GAMS/ CPLE）日志文件 (22)8. CPLEX选项的详细说明 (25)1.简介GAMS/Cplex是一种用于GAMS （The General Algebraic Modeling System通用代数建模系统）的求解器，它使得用户可以把GAMS（通用代数建模系统的）的高级建模功能跟Cplex优化器的优势结合起来。
matlabCplex使用
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matlabCplex使 用
安装cplex 安装yalmip 示例 % value:5 constraint:2 % max z=2x1+x2+4x3+3x4+x5 % 2x2+x3+4x4+2x5<=54 % 3x1+4x2+5x3-x4-x5<=62 % x1,x2<=0,x3<=3.32,x4<=0.678,x5<=2.57
x=intvar(1,5); f=[1 1 3 4 2]*(x'.^2)-[8 2 3 1 2]*x';F=set(0<=x<=99); F=F+set([1 1 1 1 1]*x'<=400)+set([1 2 2 1 6]*x'<=800)+set(2*x(1)+x(2)+6*x(3)<=800); F=F+set(x(3)+x(4)+5*x(5)<=200);solvesdp(F,-f);
%% another % max z=4x1+6x2+2x3 % -x1+3x2<=8 % -x2+3x3<=10 % 5x1-x3<=8 % x1,x2,x3>=0且为整数
% 目标函数 决策变量，整数型：intvar 连续型：sdpvar 二值型：binvar x=intvar(1,3); f=[4 6 2]*x'; % 约束x1,x2,x3 F=set(x>0)+set([-1 3 0]*x'<=8)+set([0 -1 3]*x'<=10)+set([5 0 -1]*x'<=8); %在约束F下求目标函数f最大值 solvesdp(F,-f); % 查看目标函数 double(f) % 查看各变量取值 double(x)
cplex教程六
第六章 IBM ILOG CPLEX在动车组运用优化中的应用
（四）运行求解：
运行配置文件后，求解结果如下： // solution (optimal) with objective 2 AX = [[1 0 0] [0 1 0] [0 0 1]]; BX = [[1 0 0] [0 1 0] [0 0 1]]; 这说明该运行图最少需要模型求解的2台加上牵引跨0点运行 线6的1台总共3台机车进行牵引。
这是一个多目标规划模型，第一个目标是使用的机车数最小； 第二个目标是机车在站的停留时间最短；第三个目标是机车 的运用最均衡。第一个目标的优先级别高于第二个高于第三 个，在求解中可先利用CPLEX对第一个目标进行求解，然后
第一个目标作为约束，对第二个目标进行求解，然后将第二
个目标作为约束，对第三个目标求解。得出的结果，即为机 车周转图的优化结果。
min 2 x12 d12 x14 d14 x16 d16 90 x32d32 x34d 34 x36d 36 90 x52d 52 x54d 54 x56d 56 90
2 2 2
x21d 21 x41d 41 x61d 61 180 x23d 23 x43d 43 x63d 63 180 x25d 25 x45d 45 x65d 65 180
第六章 IBM ILOG CPLEX在动车组运用优化中的应用 有时上述的机车周转问题根据区段和线路实际情况的不同， 需要考虑如下的因素： 1. 运行图中上下行列车数是否相等。 2. 牵引区段是否固定。 3.机车的牵引定数是否都相同。 4.是否考虑单机走行。 这些因素要根据实际情况添加相应的约束，相应的模型的复 杂程度会有所增加。
cplex中文教程 第四章
第四章IBM ILOG CPLEX在高速铁路列车运行图编制中的应用 数据文件：
例1：假定2列中速列车，1列高速列车，5个车站。
数据文件编码为：
nctrain=2; nhtrain=1; nstation=5; a=[4,4,4,4,4]; d=[3,3,3,3,3]; r=[[24,8,20,38],[24,8,20,38],[16,6,13,25]]; b=[[1,1,1,1,1],[1,1,1,1,1],[1,1,1,1,1]]; c=[[2,2,2,2,2],[2,2,2,2,2],[2,2,2,2,2]]; w=[[0,0,0,0,0],[0,0,0,0,0],[0,0,0,0,0]]; M=100000000; e=[[0,0,0,0,0],[0,0,0,0,0],[0,0,0,0,0]];
停站时间约束
yik xi变
k 2Sik ik qij (i 1, 2, j
, N ; k 2,3,
, m 1)
, N ; k 2,3,
, m 1)
第四章IBM ILOG CPLEX在高速铁路列车运行图编制中的应用
第四章IBM ILOG CPLEX在高速铁路列车运行图编制中的应用 例2求解结果：
// solution (optimal) with objective 1606 x = [[0 17 39 59 101 129 152] y = [[0 17 40 59 102 129 152] [0 21 43 63 106 135 159] [3 22 43 65 106 136 159] [0 26 54 79 131 164 191] [6 26 55 81 132 164 191] [0 59 81 101 143 171 194] [42 59 82 101 144 171 194] [0 63 85 105 147 174 197] [45 64 85 107 147 174 197] [0 66 88 108 151 180 204] [48 67 88 110 151 181 204] [0 73 102 127 180 215 243] [51 74 103 129 181 216 243] [0 110 131 151 194 223 246] [94 110 131 153 194 223 246] [0 114 136 156 198 226 249] [97 114 137 156 199 226 249] [0 117 140 162 206 234 257]] [100 117 141 164 207 234 257]]
C#调用Cplex学习笔记
使用C#调用Cplex学习笔记1.构建约束及目标函数调用cplexCplex Model = new Cplex（）；表示建立一个新的cplex模型主要介绍一些基本的结构：Model.AddEq（函数1，函数2）函数1=函数2Model.AddLe（函数1，函数2）函数1<=函数2Model.AddGe（函数1，函数2）函数1>=函数2Model.Sum （函数1，函数2）函数1+函数2Model.Prod （double var，函数2）值*函数2Model.ScalProd(double[]vals,INumVar[]vars) 一维矩阵*矩阵并求和2.Model.AddMinimize（目标函数）表示求解目标函数（求最小）Model.AddMaximize（目标函数）表示求解目标函数（求最大）3.第一部分：构建常量和决策变量第二部分：构建约束及目标函数第三部分：输出决策变量4.定义变量（类似于C#的编码规则，将INumVar类似于int，是一个类型）（1）一个变量：INumVar var= Model.NumVar(0.0,1.0,NumVarType.Bool) ;【括号中，变量的下限、上限、类型-布尔类型】（2）一维（int）整形变量INumVar [] var =Model.NumVarArray(5,0.0,1.0,NumVarType.Int); 【括号中，变量的数组个数下限、上限、类型-布尔类型】（3）二维（double）变量：INumVar [][] var = new INumVar [3][];for(int i=0;i<3;i++){Var[i]= Model.NumVarArray(5,0.0,20 ,NumVarType.Double);}（4）三维0,1决策变量：INumVar[][][] XIJK = new INumVar[4][][];for (int i = 0; i < 4; i++）{XIJK[i] = new INumVar[5][];for (int j = 0; j < 5; j++){XIJK[i][j]=Model.NumVarArray(7,0.0,1.0,NumVarType.Bool)；}}一些小方法：1.Model.NumVarArray(int n, double lb, double ub, NumVarType type);//添加决策变量括号中的四项依次是个数，下界，上界，变量类型比如：C = Model.NumVarArray(NumberOfJobs + 2, 0.0, System.Double.MaxValue, NumVarType.Float); 浮点型变量--连续类型B=Model.NumVarArray(NumberOfMachines, 0.0, 1.0, NumVarType.Bool);布尔型变量还有NumVarType.Int 整数型--离散类型2. Model.NumVar(0.0, System.Double.MaxValue, NumVarType.Float);//括号中的三项依次是下界，上界，变量类型3.Model.Prod(1.0, X) 1*x 数相乘Model.ScalProd(x, y) 相当于，矩阵x每点和y对应点每点相乘后相加。
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第一章IBM ILOG CPLEX概述之：界面介绍
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第一章IBM ILOG CPLEX概述
CPLEX简介
CPLEX是IBM公司中的一个优化引擎。 该优化引擎用来求解线性规划（LP）、二次规划（QP）、
带约束的二次规划（QCQP）、二阶锥规划（SOCP）等四 类基本问题，以及相应的混合整数规划（MIP）问题。 CPLEX具有的优势：
（1）能解决一些非常困难的行业问题； （2）求解速度非常快； （3）有时还提供超线性加速功能的优势。
第一章IBM ILOG CPLEX概述
CPLEX简介
软件IBM ILOG CPLEX Optimization Studio中自带该优化引 擎。IBM ILOG CPLEX Optimization Studio具有执行速度快、 其自带的语言简单易懂、并且与众多优化软件及语言兼容 （与C++，JAVA，EXCEL，Matlab等都有接口），因此在 西方国家应用十分广泛。由于在中国还刚刚全面推广不久， 因此应用还不是很广，但是发展空间很大。