cplex中文教程 第五章
(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。
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。
『实践』Yalmip+Ipopt+Cplex使用手册（文末附程序）
『实践』Yalmip+Ipopt+Cplex使⽤⼿册（⽂末附程序）Yalmip+Ipopt+Cplex使⽤⼿册(⽂末附程序)1.软件版本Cplex 12.6.2，Matlab R2014a， 3.12.9，2.Cplex添加⽅法破解版下载地址：其中community-edition可以免费试⽤，但最多只能计算1000个变量或1000个约束条件的优化问题。
点击安装，安装步骤默认操作即可。
点击Matlab中的，点击，找到路径并将其添加，最后点击即可。
然后在Matlab命令⾏窗⼝输⼊，出现帮助⽂档，代表添加成功。
3.Ipopt添加⽅法需要的组件：VC_redist.x64和ww_ifort_redist_intel64_2017.0.109.msi链接2：在打开的界⾯中选择图1-1即可。
图1Ipopt下载地址：（最新版本3.12.9）Ipopt下载链接：链接：https:///s/1tWBRJ7syW-WctcL1LkB06w 密码：1n3m （以前的版本3.12.6）下载下来后解压缩，打开⽂件，⽬录如下图1-2。
图2打开MATLAB，设置路径-》添加并包含⼦⽂件夹-》选择Ipopt路径-》保存。
见下图1-3。
图3右键运⾏图2中的opti_Install。
出现提⽰让你安装optiMEXFiles_mexw64_2_27，回车⼏下，弹出窗⼝，找到optiMEXFiles_mexw64_2_27（不需要⾃⼰⼿动解压）选中即可。
VC_redist.x64和ww_ifort_redist_intel64_2017.0.109.msi ，这两个组件⾃⼰⼿动安装，注意版本即可。
注意下图中框框中的组件我已经安装好了，如果没有安装，是会有提⽰的。
IPOPT 3.12.94.Yalmip添加⽅法下载地址：https://yalmip.github.io/（最新版本）下载链接：/s/1eRBhRlK 密码：dv4o（之前版本）将下载的⽂件解压，设置路径-》添加并包含⼦⽂件夹-》选择Yalmip路径-》保存。
Cplex学习笔记
Cplex学习笔记thedualsimplexmethodisthefirstchoiceforoptimizingalinearprogrammingproblem,esp eciallyforprimal-degenerateproblemswithlittlevariabilityintherighthandsidecoefficientsbutsignif icantvariabilityinthecostcoefficients.PrimarSimpleXOptimizer有时会更好地解决变量数量显著增加约束数量的问题，或者解决成本系数中几乎没有变化的问题。
六百五十四networkoptimizermayhaveapositiveimpactonperformanceofnetworkstructure 屏障优化因子和方法在大型稀疏问题上是有效的siftingwasdevelopedtoexploitthecharacteristicsofmodelswithlargeaspectratios(th atis,alargeratioofthenumberofcolumnstothenumberofrows).并行优化器多线程计算机平台简言之：原始变量多于约束对偶右停左变，边界大型稀疏阵筛选行列数差大。
要保存基本安全文件：libraryroutinecpxmbasewrite,afterthecalltotheoptimizer.然后从该文件中更新更新基础：cpxreadcopybase.如果解决问题所需的迭代次数与不足的次数大致相同，那么你做得很好。
如果迭代次数比行数（或更多）大三倍，则完全有可能通过改变为UALSimplexOptimizer或Primind implexOptimizer设置定价算法的参数DPRI来提高性能ifyouobservethatyourproblemhasdifficultystayingfeasibleduringitssolution,theny oushouldconsideranalternativescalingmethod.scaindparametersettingsforscalingme thods斯坎德价值意义-1noscaling0平衡缩放（默认）1缩放缩放671cplex学习手册STL标准模板库简称STL，即标准模板库。
CPLEX中文教程(第七章)
CPLEX中文教程(第七章)第七章：IBMILOGCPLE某在公交乘务排班优化问题中的应用(一)公交乘务排班优化问题概述公交乘务排班问题属活动资源的优化利用问题。
一般是根据给定的乘务任务、乘务规则等条件，考虑一定的优化目标，对乘务员(组)的出乘时间、地点，担当的乘务任务、时刻，退乘时间、地点等做出具体安排，以确保一定周期内的所有乘务任务被执行。
第七章：IBMILOGCPLE某在公交乘务排班优化问题中的应用公交乘务排班问题的基本元素和各元素的基本属性如下：1)公交线路：具有出发站、出发时刻、到达站、到达时刻、中途停站等基本属性；2)乘务员类型(组):包括司机、售票员等属性；3)乘务规则：包括间休时间、工作时间、休息时间、乘务周期、月工时等乘务值乘规则。
4)目标函数:乘务成本最小、需要的乘务员数量最少等。
5)约束条件:乘务员的工作时间必须满足乘务规则；每个线路、每个班次都必须有乘务员值乘；乘务员劳动负衡均衡等约束条件。
第七章：IBMILOGCPLE某在公交乘务排班优化问题中的应用例1.下面是某条线路的基本情况：1、该线路的开收班时间：冬令(12月~3月):6:20~18:10,夏令(4月~11月):6:15~18:202、该线路的司机人数：15人3、该线路排班间隔：平时：8~10分钟/班；上下班高峰(6:00~8:30,11:30~13:30,16:30~18:00):4~8分钟/班节假日：5~10分钟/班4、该线路的运行时间：正常：80~85分钟/班高峰：100~120分钟/班规定：(1)司机每天上班时间不超过8小时；(2)司机连续开车不得超过4小时；(3)每名司机至少每月完成120班次。
问题一：针对五月份的节假日和非节假日，分别求出每日最少班次总数；问题二：阐述你对上述规定的理解，并根据你的理解建立适当的数学模型，合理地设计五月份该线路的司机排班方案。
第七章：IBMILOGCPLE某在公交乘务排班优化问题中的应用(二)模型建立与求解1、问题一：数学模型的建立(1)假设将非节假日一天的工作时间分为n个时段6minZ=i=1某ikk某imiQii1i1kkS.T.某imimkQii1i18mi104mi8k1,2,3,4,5,6.k1,2,3,4,5,6.i2,4,6.i1,3,5.Qi——第i个时段的时长，i=1,2…,nmi——表示发车间隔；某i——表示发车班次用第七章：IBMILOGCPLE某在公交乘务排班优化问题中的应用问题一：1、数学模型的建立(2)若节假日，用Q表示节假日一天的工作时长，发车间隔用m表示，则例1中节假日最少班次的数学公式为：QminZ=,m5≤m≤10.第七章：IBMILOGCPLE某在公交乘务排班优第七章：IBMILOGCPLE某在公交乘务排班优化问题中的应用问题一的模型文件(续):某["T1"]某m["T1"]+某["T2"]某m["T2"]+(某["T3"]-1)某m["T3"]<=Q["T1"]+Q["T2"]+Q["T3"];Q["T1"]+Q["T2"]+Q["T3"]<=某["T1"]某m["T1"]+某["T2"]某m["T2"]+某["T3"]某m["T3"];某["T1"]某m["T1"]+某["T2"]某m["T2"]+某["T3"]某m["T3"]+(某["T4"]1)某m["T4"]<=Q["T1"]+Q["T2"]+Q["T3"]+Q["T4"];Q["T1"]+Q["T2"]+Q["T3"] +Q["T4"]<=某["T1"]某m["T1"]+某["T2"]某m["T2"]+某["T3"]某m["T3"]+某["T4"]某m["T4"];某["T1"]某m["T1"]+某["T2"]某m["T2"]+某["T3"]某m["T3"]+某["T4"]某m["T4"]+(某["T5"]1)某m["T5"]<=Q["T1"]+Q["T2"]+Q["T3"]+Q["T4"]+Q["T5"];Q["T1"]+Q["T2"] +Q["T3"]+Q["T4"]+Q["T5"]<=某["T1"]某m["T1"]+某["T2"]某m["T2"]+某["T3"]某m["T3"]+某["T4"]某m["T4"]+某["T5"]某m["T5"];某["T1"]某m["T1"]+某["T2"]某m["T2"]+某["T3"]某m["T3"]+某["T4"]某m["T4"]+某["T5"]某m["T5"]+(某["T6"]1)某m["T6"]<=Q["T1"]+Q["T2"]+Q["T3"]+Q["T4"]+Q["T5"]+Q["T6"];Q["T1"] +Q["T2"]+Q["T3"]+Q["T4"]+Q["T5"]+Q["T6"]<=某["T1"]某m["T1"]+某["T2"]某m["T2"]+某["T3"]某m["T3"]+某["T4"]某m["T4"]+某["T5"]某m["T5"]+某["T6"]某m["T6"];}第七章：IBMILOGCPLE某在公交乘务排班优化问题中的应用求解结果：高峰期(6:158:30)发车时间班次1234567891011121314151617平时(8:3011:30)发车时间08:3108:4108:5109:0109:1109:2109:3109:4109:5110:0110:1110:2110: 3110:4110:5111:0111:1111:21班次181920222223242526272829303132333435高峰期(11:3013:30)发车时间11:3111:3911:4711:5512:0312:1112:1912:2712:3512:4312:5112:5913: 0713:1513:23班次363738394041424344454647484950平时(13:3016:30)发车时间13:3113:4113:5114:0114:1114:2114:3114:4114:5115:0115:1115:2115: 3115:4115:5116:0116:1116:21班次515253545556575859606162636465666768高峰期(16:3018:00)发车时间16:3116:3916:4716:5517:0317:1117:1917:2717:3517:4317:5117:59班次697071727374757677787980平时(18:0018:20)发车时间18:0718:17班次8182//olution(optimal)withobjective82某=[17181518122]06:1506:2306:3106:3906:4706:5507:0307:1107:19据此，得到该线路非节假日的最少班次排班如右：07:2707:3507:4307:5107:5908:0708:1508:23第七章：IBMILOGCPLE某在公交乘务排班优化问题中的应用求解结果：发车时间班次123456789101112发车时间08:1508:2508:3508:4508:5509:0509:1509:2509:3509:4509:5510:05班次131415161718192022222324时间(6:20-18:10)发车时间10:1510:2510:3510:4510:5511:0511:1511:2511:3511:4511:5512:05班次252627282930313233343536发车时间12:1512:2512:3512:4512:5513:0513:1513:2513:3513:4513:5514:05班次373839404142434445464748发车时间14:1514:2514:3514:4514:5515:0515:1515:2515:3515:4515:5516:05班次495051525354555657585960发车时间16:1516:2516:3516:4516:5517:0517:1517:2517:3517:4517:5518:0518:15班次61626364656667686970717273节假日的最少班次排班如右：06:1506:2506:3506:4506:5507:0507:1507:2507:3507:4507:5508:05第七章：IBMILOGCPLE某在公交乘务排班优化问题中的应用问题二：1、数学模型的建立(1)非节假日目标函数：min约束条件：某jj119式中：ai——表示非节假日一天内第i个司机工作的高峰班次数bi——表示非节假日一天内第i个司机工作的非高峰班次数某j——表示司机排班情况(aij119j119某j)44(bi某j)38第七章：IBMILOGCPLE某在公交乘务排班优化问题中的应用司机排班情况第七章：IBMILOGCPLE某在公交乘务排班优化问题中的应用模型编码：{tring}Categorie={"C1","C2","C3","C4","C5","C6","C7","C8","C9","C10","C11","C12","C13","C14","C15","C16","C17","C18","C19"};inta [Categorie]=[0,0,0,0,0,1,1,1,1,1,2,2,2,2,3,3,3,4,4];intb[Categor ie]=[1,2,3,4,5,0,1,2,3,4,0,1,2,3,0,1,2,0,1];dvarint+某[Categorie]in0..50;minimizeum(oinCategorie)某[o];ubjectto{um(oinCategorie)a[o]某某[o]==44;um(oinCategorie)b[o]某某[o]==38;}第七章：IBMILOGCPLE某在公交乘务排班优化问题中的应用求解结果：//olution(optimal)withobjective17某=[01005000000000000011]该结果给出了一天需要的最少司机人数为17人，同时给出了一个可行的排班方案，即17位司机中，有1位采用第2种排班情况，有5位采用第5种排班情况，有11位采用第19种排班情况。
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]];
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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]]
CPLEX Tutorial Handout
CPLEX Tutorial HandoutWhat Is ILOG CPLEX?ILOG CPLEX is a tool for solving linear optimization problems, commonly referred to as Linear Programming (LP) problems, of the form:Maximize (or Minimize) c1x1 + c2x2 +...+ c n x nsubject to a11x1 + a12x2 +...+ a1n x n ~ b1a21x1 + a22x2 +...+ a2n x n ~ b2...a m1x1 + a m2x2 +...+ a mn x n ~b mwith these bounds l1x1u1...l n x n u nwhere ~ can be , , or =, and the upper bounds u i and lower bounds l i may be positive infinity, negative infinity, or any real number.The elements of data you provide as input for this LP are:Objective function coefficients c1, c2, ... , c nConstraint coefficients a11, a21, ... , a n1...a m1, a m2, ..., a mnRight-hand sides b1, b2, ... , b mUpper and lower bounds u1, u2, ... , u n and l1, l2, ... , l nThe optimal solution that ILOG CPLEX computes and returns is: Variables x1, x2, ... , x nILOG CPLEX also can solve several extensions to LP:• Network Flow problems, a special case of LP that CPLEX can solve much faster by exploiting the problem structure.• Quadratic Programming (QP) problems, where the LP objective function is expanded to include quadratic terms.• Mixed Integer Programming (MIP) problems, where any or all of the LP or QP variables are further restricted to take integer values in the optimal solution and where MIP itself is extended to includeconstructs like Special Ordered Sets (SOS) and semi-continuous variables.ILOG CPLEX ComponentsCPLEX comes in three forms to meet a wide range of users' needs:• The CPLEX Interactive Optimizer is an executable program that can read a problem interactively or from files in certain standard formats, solve the problem, and deliver the solution interactively or into text files. The program consists of the file cplex.exe on Windows platforms or cplex on UNIXplatforms.• Concert Technology is a set of C++, Java, and .NET class libraries offering an API that includes modeling facilities to allow the programmer to embed CPLEX optimizers in C++, Java, or .NETapplications. The following table lists the files that contain the libraries.Microsoft Windows UNIXC++ ilocplex.lib concert.lib libilocplex.a libconcert.aJava cplex.jar cplex.jarC#.NET ILOG.CPLEX.dllILOG.CONCERT.dll• The CPLEX Callable Library is a C library that allows the programmer to embed ILOG CPLEX optimizers in applications written in C, Visual Basic, FORTRAN, or any other language that can callC functions.The library is provided in files cplex.lib and cplex.dll on Windows platforms, and inlibcplex.a, libcplex.so, and libcplex.sl on UNIX platforms.Solving an LP with ILOG CPLEXThe problem to be solved is:Maximize x1 + 2x2 + 3x3subject to -x1 + x2 + x3 20x1 - 3x2 + x3 30with these bounds 0 x1 400 x2 +0 x3 +Using the Interactive OptimizerThe following sample is screen output from a CPLEX Interactive Optimizer session where the model of an example is entered and solved. CPLEX> indicates the CPLEX prompt, and text following this prompt is user input.Welcome to CPLEX Interactive Optimizer 9.0.0with Simplex, Mixed Integer & Barrier OptimizersCopyright (c) ILOG 1997-2003CPLEX is a registered trademark of ILOGType 'help' for a list of available commands.Type 'help' followed by a command name for moreinformation on commands.CPLEX> enter exampleEnter new problem ['end' on a separate line terminates]:maximize x1 + 2 x2 + 3 x3subject to -x1 + x2 + x3 <= 20x1 - 3 x2 + x3 <=30bounds0 <= x1 <= 400 <= x20 <= x3endCPLEX> optimizeTried aggregator 1 time.No LP presolve or aggregator reductions.Presolve time = 0.00 sec.Iteration log . . .Iteration: 1 Dual infeasibility = 0.000000Iteration: 2 Dual objective = 202.500000Dual simplex - Optimal: Objective = 2.025*******e+002Solution time = 0.01 sec. Iterations =2 (1)CPLEX> display solution variables x1-x3Variable Name Solution Valuex1 40.000000x2 17.500000x3 42.500000CPLEX> quitConcert Technology for Java Users• Creating a model• Solving that model• Querying results after solving• Handling error conditionsILOG Concert Technology allows your application to call ILOG CPLEX directly. This Java interface supplies a rich means for you to use Java objects to build your optimization model. The IloCplex class implements the ILOG Concert Technology interface for creating variables and constraints. It also provides functionality for solving Mathematical Programing (MP) problems and accessing solution information.Compiling ILOG CPLEX Applications in ILOG Concert TechnologyFor this, you add the cplex.jar file to your classpath. This is most easily done by passing the command-line option to the Java compiler javac:-classpath <path_to_cplex.jar>In the java command line, the following should be added.-Djava.library.path=<path_to_shared_library>See the makefile at /wangym .The Anatomy of an ILOG Concert Technology ApplicationTo use the ILOG CPLEX Java interfaces, you need to import the appropriate packages into your application. This is done with the lines:import ilog.concert.*;import ilog.cplex.*;As for every Java application, an ILOG CPLEX application is implemented as a method of a class. In this discussion, the method will be the static main method. The first task is to create an IloCplex object. It is used to create all the modeling objects needed to represent the model. For example, an integer variable with bounds 0 and 10 is created by calling cplex.intVar(0, 10), where cplex is the IloCplex object.Since Java error handling in ILOG CPLEX uses exceptions, you should include the ILOG Concert Technology part of an application in a try/catch statement. All the exceptions thrown by any ILOG Concert Technology method are derived from IloException. Thus IloException should be caught in the catch statement.In summary, here is the structure of a Java application that calls ILOG CPLEX:import ilog.concert.*;import ilog.cplex.*;static public class Application {static public main(String[] args) {try {IloCplex cplex =new IloCplex();// create model and solve it} catch (IloException e) {System.err.println("Concert exception caught: " + e);}}}Create the ModelThe IloCplex object provides the functionality to create an optimization model that can be solved with IloCplex. The interface functions for doing so are defined by the ILOG Concert Technology interface IloModeler and its extension IloMPModeler. These interfaces define the constructor functions for modeling objects of the following types, which can be used with IloCplex:IloNumVar modeling variablesIloRange ranged constraints of the type lb <= expr <= ubIloObjective optimization objectiveIloNumExpr expression using variablesModeling variables are represented by objects implementing the IloNumVar interface defined by ILOG Concert Technology. Here is how to create three continuous variables, all with bounds 0 and 100: IloNumVar[] x = cplex.numVarArray(3, 0.0, 100.0);There is a wealth of other functions for creating arrays or individual modeling variables. The documentation for IloModeler and IloMPModeler will give you the complete list.Modeling variables are typically used to build expressions, of type IloNumExpr, for use in constraints or the objective function of an optimization model. For example the expression:x[0] + 2*x[1] + 3*x[2]can be created like this:IloNumExpr expr = cplex.sum(x[0], cplex.prod(2.0, x[1]),cplex.prod(3.0, x[2]));Another way of creating an object representing the same expression is to use an IloLinearNumExpr expression. Here is how:IloLinearNumExpr expr = cplex.linearNumExpr();expr.addTerm(1.0, x[0]);expr.addTerm(2.0, x[1]);expr.addTerm(3.0, x[2]);The advantage of using IloLinearNumExpr over the first way is that you can more easily build up your linear expression in a loop, which is what is typically needed in more complex applications. Interface IloLinearNumExpr is an extension of IloNumExpr, and thus can be used anywhere an expression can be used. As mentioned before, expressions can be used to create constraints or an objective function for a model. Here is how to create a minimization objective for the above expression:IloObjective obj =cplex.minimize(expr);In addition to creating an objective, IloCplex must be instructed to use it in the model it solves. This is done by adding the objective to IloCplex via:cplex.add(obj);Every modeling object that is to be used in a model must be added to the IloCplex object. The variables need not be explicitly added as they are treated implicitly when used in the expression of the objective. More generally, every modeling object that is referenced by another modeling object which itself has been added to IloCplex, is implicitly added to IloCplex as well.There is a shortcut notation for creating and adding the objective to IloCplex:cplex.addMinimize(expr);Since the objective is not otherwise accessed, it does not need to be stored in the variable obj.Adding constraints to the model is just as easy. For example, the constraint-x[0] + x[1] + x[2] <= 20.0can be added by calling:cplex.addLe(cplex.sum(cplex.negative(x[0]), x[1], x[2]), 20);Again, many methods are provided for adding other constraint types, including equality constraints, greater than or equal to constraints, and ranged constraints. Internally, they are all represented as IloRange objects with appropriate choices of bounds, which is why all these methods return IloRange objects. Also, note that the expressions above could have been created in many different ways, including the use of IloLinearNumExpr. Solve the ModelIloCplex.solve()IloCplex.solveRelaxed()IloCplex.getStatus.The returned value tells you what ILOG CPLEX found out about the model: whether it found the optimal solution or only a feasible solution, whether it proved the model to be unbounded or infeasible, or whethernothing at all has been determined at this point. Even more detailed information about the termination of the solver call is available through the method IloCplex.getCplexStatus.Query the ResultsIf the solve method succeeded in finding a solution, you will then want to access that solution. The objective value of that solution can be queried using a statement like this:double objval = cplex.getObjValue();Similarly, solution values for all the variables in the array x can be queried by calling:double[] xval =cplex.getValues(x);More solution information can be queried from IloCplex, including slacks and, depending on the algorithm that was applied for solving the model, duals, reduced cost information, and basis information.Building and Solving a Small LP Model in JavaThe example LPex1.java, part of the standard distribution of ILOG CPLEX, is a program that builds a specific small LP model and then solves it. This example follows the general structure found in many ILOG CPLEX Concert Technology applications, and demonstrates three main ways to construct a model: • Modeling by Rows;• Modeling by Columns;Example LPex1.javaMaximize x1 + 2x2 + 3x3subject to -x1 + x2 + x3 20x1 - 3x2 + x3 30with these bounds 0 x1 400 x2 +0 x3 +Program for building and solving the exampleimport ilog.concert.*;import ilog.cplex.*;public class Example {public static void main(String[] args) {try {IloCplex cplex =new IloCplex();double[] lb ={0.0, 0.0, 0.0};double[] ub ={40.0, Double.MAX_VALUE, Double.MAX_VALUE};IloNumVar[] x =cplex.numVarArray(3, lb, ub);double[] objvals ={1.0, 2.0, 3.0};cplex.addMaximize(cplex.scalProd(x, objvals));cplex.addLe(cplex.sum(cplex.prod(-1.0, x[0]),cplex.prod( 1.0, x[1]),cplex.prod( 1.0, x[2])), 20.0);cplex.addLe(cplex.sum(cplex.prod( 1.0, x[0]),cplex.prod(-3.0, x[1]),cplex.prod( 1.0, x[2])), 30.0);if ( cplex.solve() ) {cplex.out().println("Solution status =" + cplex.getStatus());cplex.out().println("Solution value =" + cplex.getObjValue()); double[] val =cplex.getValues(x);int ncols =cplex.getNcols();for (int j =0; j < ncols; ++j)cplex.out().println("Column: " + j + " Value =" + val[j]);}cplex.end();}catch (IloException e) {System.err.println("Concert exception '" + e + "' caught");}}}Compile and run% javac example.java% java exampleor if you use makefile% makeComplete Code of LPex1.java// ----------------------------------------------------------------------- // File: examples/src/LPex1.java// Version 9.0// ----------------------------------------------------------------------- // Copyright (C) 2001-2003 by ILOG.// All Rights Reserved.// Permission is expressly granted to use this example in the// course of developing applications that use ILOG products.// ----------------------------------------------------------------------- //// LPex1.java - Entering and optimizing an LP problem//// Demonstrates different methods for creating a problem. The user has to // choose the method on the command line://// java LPex1 -r generates the problem by adding constraints// java LPex1 -c generates the problem by adding variables// java LPex1 -n generates the problem by adding expressions//import ilog.concert.*;import ilog.cplex.*;public class LPex1 {static void usage() {System.out.println("usage: LPex1 <option>");System.out.println("options: -r build model row by row");System.out.println("options: -c build model column by column");System.out.println("options: -n build model nonzero by nonzero");}public static void main(String[] args) {if ( args.length != 1 || args[0].charAt(0) != `-' ) {usage();return;}try {// Create the modeler/solver objectIloCplex cplex =new IloCplex();IloNumVar[][] var =new IloNumVar[1][];IloRange[][] rng =new IloRange[1][];// Evaluate command line option and call appropriate populate method.// The created ranges and variables are returned as element 0 of arrays// var and rng.switch ( args[0].charAt(1) ) {case `r': populateByRow(cplex, var, rng);break;case `c': populateByColumn(cplex, var, rng);break;case `n': populateByNonzero(cplex, var, rng);break;default: usage();return;}// write model to filecplex.exportModel("lpex1.lp");// solve the model and display the solution if one was foundif ( cplex.solve() ) {double[] x =cplex.getValues(var[0]);double[] dj =cplex.getReducedCosts(var[0]);double[] pi =cplex.getDuals(rng[0]);double[] slack =cplex.getSlacks(rng[0]);cplex.output().println("Solution status =" + cplex.getStatus()); cplex.output().println("Solution value =" + cplex.getObjValue());int ncols =cplex.getNcols();for (int j =0; j < ncols; ++j) {cplex.output().println("Column: " + j +" Value =" + x[j] +" Reduced cost =" + dj[j]);}int nrows =cplex.getNrows();for (int i =0; i < nrows; ++i) {cplex.output().println("Row : " + i +" Slack =" + slack[i] +" Pi =" + pi[i]);}}cplex.end();}catch (IloException e) {System.err.println("Concert exception `" + e + "` caught");}}// The following methods all populate the problem with data for the following // linear program://// Maximize// x1 + 2 x2 + 3 x3// Subject To// - x1 + x2 + x3 <=20// x1 - 3 x2 + x3 <=30// Bounds// 0 <=x1 <=40// End//// using the IloMPModeler APIstatic void populateByRow(IloMPModeler model,IloNumVar[][] var,IloRange[][] rng) throws IloException {double[] lb ={0.0, 0.0, 0.0};double[] ub ={40.0, Double.MAX_VALUE, Double.MAX_VALUE};IloNumVar[] x =model.numVarArray(3, lb, ub);var[0] =x;double[] objvals ={1.0, 2.0, 3.0};model.addMaximize(model.scalProd(x, objvals));rng[0] =new IloRange[2];rng[0][0] =model.addLe(model.sum(model.prod(-1.0, x[0]),model.prod( 1.0, x[1]),model.prod( 1.0, x[2])), 20.0);rng[0][1] =model.addLe(model.sum(model.prod( 1.0, x[0]),model.prod(-3.0, x[1]),model.prod( 1.0, x[2])), 30.0);}static void populateByColumn(IloMPModeler model,IloNumVar[][] var,IloRange[][] rng) throws IloException {IloObjective obj =model.addMaximize();rng[0] =new IloRange[2];rng[0][0] =model.addRange(-Double.MAX_VALUE, 20.0);rng[0][1] =model.addRange(-Double.MAX_VALUE, 30.0);IloRange r0 =rng[0][0];IloRange r1 =rng[0][1];var[0] =new IloNumVar[3];var[0][0] =model.numVar(model.column(obj, 1.0).and(model.column(r0, -1.0).and(model.column(r1, 1.0))),0.0, 40.0);var[0][1] =model.numVar(model.column(obj, 2.0).and(model.column(r0, 1.0).and(model.column(r1, -3.0))),0.0, Double.MAX_VALUE);var[0][2] =model.numVar(model.column(obj, 3.0).and(model.column(r0, 1.0).and(model.column(r1, 1.0))),0.0, Double.MAX_VALUE);}static void populateByNonzero(IloMPModeler model,IloNumVar[][] var,IloRange[][] rng) throws IloException { double[] lb ={0.0, 0.0, 0.0};double[] ub ={40.0, Double.MAX_VALUE, Double.MAX_VALUE}; IloNumVar[] x =model.numVarArray(3, lb, ub);var[0] =x;double[] objvals ={1.0, 2.0, 3.0};model.add(model.maximize(model.scalProd(x, objvals)));rng[0] =new IloRange[2];rng[0][0] =model.addRange(-Double.MAX_VALUE, 20.0);rng[0][1] =model.addRange(-Double.MAX_VALUE, 30.0);rng[0][0].setExpr(model.sum(model.prod(-1.0, x[0]),model.prod( 1.0, x[1]),model.prod( 1.0, x[2])));rng[0][1].setExpr(model.sum(model.prod( 1.0, x[0]),model.prod(-3.0, x[1]),model.prod( 1.0, x[2])));}}。
CPLEX简要文档(法语)
Exemple 2
Résoudre le problème
IloCplex mycplex(model); mycplex.exportModel("TPM.lp"); mycplex.setOut(env.getNullStream()); mycplex.setWarning(env.getNullStream()); mycplex.solve();
Un problème d’ordonnancement de machine parallèle
Exemple 2
//Déclarer l’environement et le modèle IloEnv env; IloModel model(env);
//déclarer variables NumVar3Matrix x(env,M); for(k=0;k<M;k++) x[k]=NumVarMatrix(env,N+2); for(k=0;k<M;k++) for(i=0;i<=N+1;i++) x[k][i]=IloNumVarArray(env,N+2,0,1,ILOBOOL); IloNumVarArray Cj(env,DIMEN+1,0,IloInfinity,ILOINT); IloNumVarArray Tj(env,DIMEN+1,0,IloInfinity,ILOINT); IloNumVarArray Obj(env,2,0,IloInfinity,ILOINT);
Exemple 2
Contraints
for (j=1;j<=N;j++) {
cplex算法切负荷
cplex算法切负荷
CPLEX算法是一种高效的数学规划求解工具，可以用于优化问题的求解，包括线性规划、整数规划、混合规划等。
在电力系统中，CPLEX 算法可以应用于切负荷问题的求解。
切负荷是指在电力系统中，由于负荷过大或发电机出现故障等原因，需要切断一部分负荷以保证电力系统的安全稳定运行。
切负荷问题是一个典型的优化问题，其目标是在保证电力系统安全的前提下，最小化切断的负荷量。
CPLEX算法可以通过数学规划建立切负荷的数学模型，将切负荷问题转化为一个线性规划问题或混合整数规划问题，并利用高效的求解算法求解最优解。
在实际应用中，CPLEX算法可以帮助电力系统运行人员快速准确地做出切负荷决策，保证电力系统的稳定运行。
总之，CPLEX算法是一种强大的数学规划工具，可以应用于切负荷等优化问题的求解，在电力系统运行中具有重要的应用价值。
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CPLEX中文教程(第七章)
（一）公交乘务排班优化问题概述
公交乘务排班问题属活动资源的优化利用问题。一般是根 据给定的乘务任务、乘务规则等条件，考虑一定的优化目 标，对乘务员(组)的出乘时间、地点，担当的乘务任务、时 刻，退乘时间、地点等做出具体安排，以确保一定周期内 的所有乘务任务被执行。
第七章：IBM ILOG CPLEX在公交乘务排班优化问题中的应用
例1. 下面是某条线路的基本情况： 1、该线路的开收班时间： 冬令（12月~3月）：6:20~18:10，夏令（4月~11月）：6:15~18:20 2、该线路的司机人数：15人 3、该线路排班间隔： 平时：8~10分钟/班； 上下班高峰（6:00~8:30，11:30~13:30，16:30~18:00）：4~8分钟/班 节假日：5~10分钟/班 4、该线路的运行时间： 正常：80~85分钟/班 高峰：100~120分钟/班 规定：（1）司机每天上班时间不超过8小时；（2）司机连续开车不得超 过4小时；（3）每名司机至少每月完成120班次。 问题一：针对五月份的节假日和非节假日，分别求出每日最少班次总数； 问题二：阐述你对上述规定的理解，并根据你的理解建立适当的数学模型， 合理地设计五月份该线路的司机排班方案。
第七章：IBM ILOG CPLEX在公交乘务排班优化问题中的应用 公交乘务排班问题的基本元素和各元素的基本属性如下： 1）公交线路：具有出发站、出发时刻、到达站、到达时刻、 中途停站等基本属性； 2）乘务员类型（组）：包括司机、售票员等属性； 3）乘务规则：包括间休时间、工作时间、休息时间、乘务周 期、月工时等乘务值乘规则。 4）目标函数:乘务成本最小、需要的乘务员数量最少等。 5）约束条件:乘务员的工作时间必须满足乘务规则；每个线路、 每个班次都必须有乘务员值乘；乘务员劳动负衡均衡等约束 条件。
cplex 分段函数
cplex 分段函数
CPLEX分段函数是指在优化问题中使用的一种函数形式，它由多个线性函数片段组成，每个片段在一个特定的区间内有效。
这种函数形式常用于一些约束条件的表示，如分段线性约束，分段常数约束等。
CPLEX分段函数的一般形式如下：
f(x)= Σi=1n aix+bii≤xi≤ci
其中，a_i、b_i、c_i是常数，x是自变量。
这个函数定义了n 个线性函数片段，每个片段在区间[bi,ci]内有效。
在实际应用中，CPLEX分段函数通常用于约束条件的表示。
例如，对于一个优化问题，我们可能需要限制某个变量在不同的取值范围内具有不同的系数，这时就可以通过分段函数来实现。
CPLEX分段函数还可以用于优化目标的表达。
例如，如果我们需要将某个优化目标表示为一个由不同线性函数组成的分段函数形式，那么也可以使用CPLEX分段函数来实现。
总之，CPLEX分段函数是在优化问题中非常常用的一种函数形式，它可以方便地表示各种约束条件和优化目标，帮助我们更好地求解复杂的优化问题。
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matlab中利用yalmip调用cplex求解鲁棒模型的例子-概述说明以及解释
matlab中利用yalmip调用cplex求解鲁棒模型的例子-概述说明以及解释1.引言1.1 概述在实际工程中，我们经常需要面对各种不确定性因素，并且对于这些因素需要建立鲁棒的数学模型来进行优化和求解。
鲁棒模型的求解是一个复杂而且困难的问题，需要借助于先进的数学工具和优化软件来实现。
本文将介绍如何利用Matlab中的YALMIP工具箱和CPLEX优化软件来求解鲁棒模型的问题。
通过本文的示例，读者可以了解到如何利用这两个工具来构建并求解复杂的鲁棒模型，以及如何分析模型的结果和讨论其实际应用价值。
通过本文的学习，读者将掌握利用YALMIP和CPLEX工具求解鲁棒模型的方法和技巧，为实际工程问题的求解提供了一种全新的思路和工具。
1.2 文章结构:本文将分为三个主要部分，分别是引言、正文和结论。
在引言部分，我们将介绍本文的背景和意义，概述所要讨论的内容，以及对文章结构进行简要说明。
正文部分将分为三个小节：Matlab简介、YALMIP简介和CPLEX简介。
在Matlab简介中，我们将介绍Matlab的概念和基本用法，为后续讨论做好铺垫；在YALMIP简介中，我们将介绍YALMIP这个优化建模工具箱的特点和用法；在CPLEX简介中，我们将介绍CPLEX这个优化软件的特点和用法。
最后，在结论部分，我们将以一个实例分析的形式展示如何利用YALMIP调用CPLEX求解鲁棒模型，并对结果进行讨论和展望未来研究方向。
1.3 目的本文的主要目的是介绍如何利用Matlab中的YALMIP工具包和CPLEX求解器来解决鲁棒优化问题。
通过具体的实例分析，帮助读者了解如何使用这些工具来建立和求解鲁棒模型，提高优化问题的稳健性和可靠性。
通过本文的阐述，读者可以学习到如何在Matlab环境下进行鲁棒优化建模和求解，为实际问题的解决提供了一个参考和指导。
同时，本文还旨在促进相关领域的交流与学习，推动鲁棒优化方法在实践中的应用和推广。
CPLEX学习笔记
1、二次约束即约束最高阶次为2；
2、I LOG OPL的文件介绍：
项目文件（.prj）包含了相应的各种文件和与一个问题相关的参数。
它组织相关的模型和数据文件，并提供一种方便的方法来维护相关文件和运行选择之间的关系。
在项目中：
a)模型文件（.mod）声明了数据项目，但是并不需要初始化它们；
b)数据文件（.dat）包含了在模型中声明的数据的初始化；
c)设置文件（.ops）当你决定改变一个或多个数学规划和其他选择的缺省值是，该文件保存用户定义的值；
3、ILOG OPL 和电子表格
OPL 模型可以对电子表格进行读写。
首先模型需要利用SheetConnection 指令与电子表格建立连接。
这是在.dat 文件中进行的，而不是在.mod 文件中：
1）在.mod 文件中准确的编写你的模型，模型要与数据独立。
2）将与电子表格的连接插到.dat 文件中。
语法为：SheetConnection sheet(“mySheet.xls”);
一个项目中.Mod只能有一个，但.dat可以有多个。
设置断点。
ILOG 脚本和OPL结合主要有两种方式，一种是嵌入Execute语句，一种是用main函数。
二者都在mod文件中。
前者主要是用于设置参数、数据的前处理（如数组初始化）和后处理，后者可以提供很强的综合能力，例如参数设置、数据处理、控制程序运行流程、设置改变模型参数重新运行模型等等。
cplex lecture
杜玉泉博士研究生y q y duyuquan2006@ /duyuquan 南开大学物流技术研究中心❝南开大学物流技术研究中心09级博士生Hunting jobs now!❝导师：陈秋双教授❝专业：控制理论与控制工程（OR indeed）❝研究方向：优化与决策、物流与供应链管理❝Helps in CPLEX improvements l f f❝Helps in CPLEX interface of YALMIP❝My blog is now included into the blogORsphere导师：❝陈秋双教授❝天津市运筹学会的诸多老师M f ili it纲都业富My familiarity: 杜纲、陈秋双、黄正海、都业富、刘卫华、李勇建S i li t i CPLEX d YALMIP❝Specialists in CPLEX and YALMIP✓IBM ILOG CPLEX Optimization Studio R&DJohn Cui (崔友志) Say hello?John Cui()Say hello?✓Linköping UniversityJohan LöfbergJohan Löfberg❝目的(NOT my original motivation)✓帮助OR/MS领域（理论、工程）的研究生和年青教师在学习cplex的过程中避免走过多的弯路，减少浪费时间，尽快掌握cplex推广p在中国的应用（学术、商业）✓cplex❝形式✓不是正式的讲座（讲解、聊天、问答）不是正式的讲座（讲解聊天问答）✓没有漂亮的PPT （For time reasons）✓电脑桌面+声音将被录制(on Internet?)11. 如何选择合适的优化软件？——优化软件杂谈CPLEX/Gurobi/Mosek/Xpress/Lingo/Google OR-tools/COIN-OR solvers 2;2. 初识CPLEX(软件申请; 体系结构—功能+求解引擎)3. 不同学习和应用背景的人如何以合适的方式使用CPLEX? Modeling Interfaces: C/C++/Java/.NET/python/ Excel connector /MATLAB Modeling Interfaces:C//Java/NET/python/Excel connector MATLAB toolbox + YALMIP /Interactive Optimizer4. CPLEX模型分解与Lagrangian Relaxation / Column Generation (Danzig-Wolfe Decomposition) / Benders Decomposition (Combinatorial; Logic-based)5. 几个简单的例子6. 优化软件、人的智慧与算法设计7. 如何获得帮助？（中文、英文）8. 初学者Q&A学QCPLEX/Gurobi/Mosek/Xpress/Lingo/Google ❝CPLEX/Gurobi/Mosek/Xpress/Lingo/Google OR-tools/COIN-OR solvers❝学术（性能+使用方便性（软件成熟度））benchmark (一定可信么？性能：benchmark (定可信么？)使用方便性：软件功能；是否能方便地加入用户自定义算法❝商业（价格+服务和技术支持）—>❝学术界>商业界？License!❝软件申请：对学术界全功能、完全免费开放❝体系结构CPLEX O ti i ti St di 123M d l D l T lCPLEX Optimization Studio 12.3Model Development Tools CPLEX Studio (IDE) -OPL Modeling Language ILOG Concert Technology (C++NET Java)Optimization Engines ILOG Concert Technology (C++, .NET, Java)Connectors•Microsoft Excel•MSFMATLABMath Programming CPLEX OptimizersConstraint Programming CPLEX CP Optimizer •MATLAB •AMPL•Python (Mixed integer) LP/QP/QCQP/SOCP (Especially suitable for scheduling problem)Tools •CPLEX InteractiveRunning with multiple parallel CPUs by default南开大学物流技术研究中心杜玉泉M d li I t f C//J /NET/th /❝Modeling Interfaces C/C++/Java/.NET/python/ Excel connector /MATLAB toolbox + YALMIP /Interactive Optimizer/OPL❝学术界：学习背景、编程能力、项目需要（是否需要开发GUI ）、研究or 教学、建模or 调试❝商业界：已有系统YALMIP: modeling/formulation and solving解❝模型分解及其思想Lagrangian Relaxation / Column GenerationRelaxation/Column Generation (Danzig-Wolfe Decomposition) / Benders Decomposition (Combinatorial; Logic-based)❝如何获得CPLEX例子？个简单的例❝一个简单的例子一个含有❝个含有for循环的例子❝Log信息如何获得？优化软件的能力（模型的类型求解性能）❝优化软件的能力（模型的类型、求解性能）人的智慧：user cuts (valid inequalities)智能优化算法i iti l l ti h i ti 智能优化算法：initial solution; heuristics ❝智能优化算法（Heuristics ）的能力人的智慧发掘问题结构（最优解性质劣解性质）人的智慧：发掘问题结构（最优解性质；劣解性质）优化软件：lower bound; initial solution ❝算法设计：智能优化算法+优化软件+人的智慧MP(Math. Prog.) + CP(Constraint Prog.)英文(Forum first)❝(Forum first)（1）CPLEX: CPLEX forum; John Cui（2）Gurobi: Gurobi forum; Zonghao GuMosek:Mosek forum;Tech Support（3）Mosek: Mosek forum; Tech. Support （4）YALMIP: YALMIP forum; Johan Löfberg OR-exchange （Sponsored By INFORMS now ）❝中文（1）CPLEX: ZPLEX 论坛（诸多有经验的CPLEX 用户）QQ 群: 84410202; 109961893泉E-mail: John Cui; 杜玉泉（2）Gurobi: Zonghao Gu; 杜玉泉（3）Mosek: 杜玉泉泉（4）YALMIP: 杜玉泉Email (John Cui): jcui@1). 软件的申请和使用（版本、变量和约束限制、更新）？2)CPLEX 2). CPLEX 的License 如何安装？3). 在MS VS 2008/2010中使用CPLEX 如何对项目进行设置？4). CPLEX/Gurobi 到底能求解多大规模的问题（变量和约束数目）？5). CPLEX 有没有中文的文档和书籍（教材）？6). CPLEX 如何快速上手？7)“O t f M ”7). 使用CPLEX 时出现“Out of Memory”的问题怎么办？8). 如何把动态生成的user cuts 关注到B&C 算法中？9).9). 在哪里找到CPLEX 求解的Log 信息？10). 如何去寻找想要的CPLEX 代码示例？11). 非线性优化问题如何来求解？(CPLEX 能求解哪些问题？)12)Q (S l 12). 非凸的QP 问题如何求解？(SDP relaxation 的效果问题)天津大学孙静、吴小调的问题Any questions ?Cheers!y Thank you!。
Cplex学习笔记
Cplex学习笔记The dual simplex method is the first choice for optimizing a linear programming problem, especially for primal-degenerate problems with little variability in the righthand side coefficients but significant variability in the cost coefficients.Primal Simplex Optimizerwill sometimes work better on problems where the number of variables exceeds the number of constraints significantly, or on problems that exhibit little variability in the costcoefficients.654Network Optimizer may have a positive impact on performance of network structureThe barrier optimizer offers an approach particularly efficient on large, sparse（稀疏的）problemsSifting was developed to exploit the characteristics of models with large aspect ratios (that is, a large ratio of the number of columns to the number of rows).The concurrent optimizer（并行优化）多线程计算机平台简言之：原始变量多于约束对偶右停左变，边界大型稀疏阵筛选行列数差大。
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T集 t节
600 N40=60 N41=250 N42=180
550 2.5
500 3.0 2.0
N30=130 N31=100 N20=300
5个支点方向的直达车流图
第五章 IBM ILOG CPLEX在车流组织优化中的应用 （二） 货物列车编组计划的整数规划模型 变量定义： ������ （1）������������������ ——表示车流（i, j）（含������������ 后方站发往������������ 站改 ������ 编中转的车流）在������������ 站改编的车流量，这里i>j>k，������������������ 为非负整数； （2）������������������ ——0-1变量，表示是否开行列流，若开行，则 ������������������ = 1，反之������������������ = 0，这里i>j。 （3）������ ——所有直达列流在始发站产生的集结车小时 集 总消耗； （4）������ ——所有直达车流在图中支点站的改编车小时 改 总消耗；
第五章 IBM ILOG CPLEX在车流组织优化中的应用 求解结果：
即：min������ = 2360车 · h，根据运行结果可得出最优货物列车 耗 编组计划图：
A4
A3
A2
A1
A0
TБайду номын сангаас t节
600
550 2.5 60+250
500 3.0 2.0
130+300 N43+180 N32+180+130+130 N21+100 N10+60
第五章 IBM ILOG CPLEX在车流组织优化中的应用 （一）货物列车编组计划的数学描述 方向上各技术站所产生的车流应以不同的组合方式编入适当 的列车而将其送往各自的目的地，这些车流的每一种组合方 式为一个编组计划方案。满足划为单独编组到达站基本条件 的车流在一定条件下与其他车流合并编组可能会得到更多的 车小时节省。列车编组计划方案一方面要保证有尽可能大的 经济效果，使方案车小时消耗总额最小或节省最大；另一方 面，方案的选择还必须考虑实际执行的可能性。
第五章 IBM ILOG CPLEX在车流组织优化中的应用 约束条件： 第3组 考虑远程车流压缩到站与较短车流合并的情况
1 ������40 ������41 − ������40 ≥ 0（8） 2 2 （������40 + ������41 ）������42 − ������40 − ������41 ≥ 0（9） 1 （������40 + ������30 ）������31 − ������30 ≥ 0（10）
第五章 IBM ILOG CPLEX在车流组织优化中的应用
例1：如图这是一个具有5个支点站方向的单组列车编组计划， 表示5个支点方向的直达车流， ������ 表示从某站开行直达列车的集结车小时， 集 ������ 表示车流在某站改编时所消耗的车小时。问在不考虑各个站改编能力 节 的情况下，如何编制一个单组列车编组计划，使得总消耗的车小时最小？
第五章 IBM ILOG CPLEX在车流组织优化中的应用 约束条件： 第1组 考虑������������ 站发出的车流有：
3 2 1 ������40 + ������40 + ������40 + ������40 ������40 = ������40 3 2 ������41 + ������41 + ������41 ������41 = ������41 3 ������42 + ������42 ������42 = ������42
第五章 IBM ILOG CPLEX在车流组织优化中的应用 （三）运用CPLEX求解
dvar int+ X402 in 0..60; dvar int+ X401 in 0..60; dvar int+ X403 in 0..60; dvar int+ X413 in 0..250; dvar int+ X412 in 0..250; dvar int+ X423 in 0..180; dvar int+ X302 in 0..720; dvar int+ X301 in 0..720; dvar int+ X312 in 0..720; dvar int+ X201 in 0..300; //定义决策变量中的整数变量 dvar boolean x40; dvar boolean x41; dvar boolean x42; dvar boolean x30; dvar boolean x31; dvar boolean x20; //定义决策变量中的0-1变量（布尔型变量）
（2） （3） （4）
第五章 IBM ILOG CPLEX在车流组织优化中的应用 约束条件： 第2组 考虑中间各支点站发出的车流
3 2 1 ������30 − ������30 + （������40 + ������30 ）������30 − ������40 ≥ ������30 （5） 2 3 ������31 + （������41 + ������31 ）������31 − ������41 ≥ ������31 （6） 1 2 2 ������20 + （������40 + ������30 + ������20 ）������20 − ������40 − ������30 ≥ ������20 （7）
第五章 IBM ILOG CPLEX在车流组织优化中的应用
（四）求解结果：
/ solution (optimal) with objective 2360 x40 = 0; x41 = 1; x42 = 0; x30 = 0; x31 = 0; x20 = 1; X403 = 0; X413 = 0; X423 = 180; X402 = 0; X412 = 0; X302 = 130; X312 = 100; X401 = 60; X301 = 0; X201 = 0;
第五章 IBM ILOG CPLEX在车流组织优化中的应用
目标函数表达式为： min������ = ������ + ������ 改 耗 集 = ������40 + ������41 + ������42 ������ 4 + ������30 + ������31 ������ 3 集 集 3 3 3 + ������20 ������ 2 + ������40 + ������41 + ������42 ������ 3 节 集 2 2 2 2 + ������40 + ������41 + ������30 + ������31 ������ 2 节 1 1 1 + ������40 + ������30 + ������20 ������ 1 节
模 型 文 件 编 码
第五章 IBM ILOG CPLEX在车流组织优化中的应用 模型文件编码（续）：
minimize 600*(x40+x41+x42)+550*(x30+x31)+500*x20+2.5*(X403+X413+X 423)+3*(X402+X412+X302+X312) +2*(X401+X301+X201); //目标 函数 subject to { X403+X402+X401+60*x40 ==60;//① X413+X412+250*x41==250; //② X423+180*x42==180;//③ X302-X301+190*x30 -X403>=130;//④ X312+350*x31 -X413>=100;//⑤ X201+490*x20 -X402-X302>=300;//⑥ 60*x41 -X401<=0;//⑦ 310*x42 -X402-X412>=0;//⑧ 190*x31 -X301>=0;//⑨ ①~⑨是第二节中约束条件（3）~（11）