若還未在項目中添加cplex的引用，可以參閱上一篇文章。本文主要介紹利用C#求解線性規划的步驟，對線性規划模型進行數據填充的兩種方法，以及一些cplex函數的功能和用法。包括以下幾個步驟：
描述
先花時間理清問題。明確決策變量及其取值范圍，目標函數，約束條件，已知的數據。后面代碼的編寫也是沿着這個思路，先理清問題后面的工作會更有效率。以如下問題為例：
先建立數學模型：
令：i產品在j機器上加工的小時數為xij
決策變量：x11,x12,x21,x22
目標函數：Min(z)=50x11+70x12+50x21+70x22
約束條件：
x12+x22<=112,
x11+x21<=104,
20x11+40x12=3200,
10x21+30x22=2000,
xij>=0(i=1,2;j=1,2)
模型
創建模型對象
//實例化一個空模型 Cplex cplexModel = new Cplex();
方法1：使用行方法填充模型
//生成決策變量並約束范圍
INumVar[][] deVar=new INumVar[1][];//交叉數組用於存儲決策變量
double[]lb= {0.0, 0.0, 0.0,0.0}; //lb(low bound)與ub定義決策變量的上下界
double[]ub={double.MaxValue,double.MaxValue,double.MaxValue,double.MaxValue};
string []deVarName={"x11","x12","x21","x22"};//決策變量名
INumVar[]x=cplexModel.NumVarArray(4,lb,ub,deVarName);//生成決策變量
deVar[0]=x;
//生成目標函數
double[]objCoef={50.0,70.0,50.0,70.0};//目標函數系數(object coefficient)
cplexModel.AddMinimize(cplexModel.ScalProd(x, objCoef));//數量相乘（scalar product）
//生成約束條件
IRange[][] rng = new IRange[1][];//存放約束
rng[0] = new IRange[4];
//AddLe為<=，AddGe為>=,AddEq為=
rng[0][0] = cplexModel.AddLe(
cplexModel.Sum(cplexModel.Prod(1.0, x[3]),
cplexModel.Prod( 1.0, x[1])), 112.0, "c1");
rng[0][1] = cplexModel.AddLe(
cplexModel.Sum(cplexModel.Prod(1.0, x[0]),
cplexModel.Prod( 1.0, x[2])), 104.0, "c2");
rng[0][2] = cplexModel.AddEq(
cplexModel.Sum(cplexModel.Prod(20.0, x[0]),
cplexModel.Prod( 40.0, x[1])), 3200.0, "c3");
rng[0][3] = cplexModel.AddEq(
cplexModel.Sum(cplexModel.Prod(10.0, x[2]),
cplexModel.Prod( 30.0, x[3])), 2000.0, "c4");
方法2：使用列方法填充模型
IObjective obj =cplexModel.AddMinimize();//目標函數，此時是空的
//約束
IRange[][] rng=new IRange[1][];
rng[0]=new IRange[4];
rng[0][0] = cplexModel.AddRange(-double.MaxValue, 112.0, "c1");//<=112
rng[0][1] = cplexModel.AddRange(-double.MaxValue, 104.0, "c2");
rng[0][2] = cplexModel.AddRange(3200.0,3200.0, "c3");//=3200
rng[0][3] = cplexModel.AddRange(2000.0,2000.0, "c4");
//簡化引用的書寫
IRange r0 = rng[0][0];
IRange r1 = rng[0][1];
IRange r2 = rng[0][2];
IRange r3 = rng[0][3];
//決策變量
INumVar[][]deVar=new INumVar[1][];
deVar[0]=new INumVar[4];//4個決策變量
deVar[0][0] = cplexModel.NumVar(cplexModel.Column(obj, 50.0).And(
cplexModel.Column(r1, 1.0).And(
cplexModel.Column(r2, 20.0))),
0.0, double.MaxValue, "x11");//最后一行為取值和名稱
deVar[0][1] = cplexModel.NumVar(cplexModel.Column(obj, 70.0).And(
cplexModel.Column(r0, 1.0).And(
cplexModel.Column(r2, 40.0))),
0.0, double.MaxValue, "x12");
deVar[0][2] = cplexModel.NumVar(cplexModel.Column(obj, 50.0).And(
cplexModel.Column(r1, 1.0).And(
cplexModel.Column(r3, 10.0))),
0.0, double.MaxValue, "x21");
deVar[0][3] = cplexModel.NumVar(cplexModel.Column(obj, 70.0).And(
cplexModel.Column(r0, 1.0).And(
cplexModel.Column(r3, 30.0))),
0.0, double.MaxValue, "x22");
求解模型並展示
if (cplexModel.Solve())
{
int nvars = cplexModel.GetValues(deVar[0]).Length;
for (int j = 0; j < nvars; ++j)
{
cplexModel.Output().WriteLine("Variable " + j +": Value = " + cplexModel.GetValues(deVar[0])[j] );
}
}
導出模型
cplexModel.ExportModel("lpex1.lp");
文件在“你的項目\bin\debug”顯示如下圖：
完整代碼和求解結果
using ILOG.Concert;
using ILOG.CPLEX;
using System;
public class LPex1
{
public static void Main(string[] args)
{
try
{
//實例化一個空模型
Cplex cplexModel = new Cplex();
//生成決策變量並賦值
INumVar[][] deVar = new INumVar[1][];
double[] lb = { 0.0, 0.0, 0.0, 0.0 };
double[] ub = { double.MaxValue, double.MaxValue, double.MaxValue, double.MaxValue };
string[] deVarName = { "x11", "x12", "x21", "x22" };
INumVar[] x = cplexModel.NumVarArray(4, lb, ub, deVarName);
deVar[0] = x;
//目標函數
double[] objCoef = { 50.0, 70.0, 50.0, 70.0 };//目標函數系數(object coefficient)
cplexModel.AddMinimize(cplexModel.ScalProd(x, objCoef));
//約束條件
IRange[][] rng = new IRange[1][];
rng[0] = new IRange[4];
rng[0][0] = cplexModel.AddLe(cplexModel.Sum(cplexModel.Prod(1.0, x[3]),
cplexModel.Prod(1.0, x[1])), 112, "c1");
rng[0][1] = cplexModel.AddLe(cplexModel.Sum(cplexModel.Prod(1.0, x[0]),
cplexModel.Prod(1.0, x[2])), 104.0, "c2");
rng[0][2] = cplexModel.AddEq(cplexModel.Sum(cplexModel.Prod(20.0, x[0]),
cplexModel.Prod(40.0, x[1])), 3200.0, "c3");
rng[0][3] = cplexModel.AddEq(cplexModel.Sum(cplexModel.Prod(10.0, x[2]),
cplexModel.Prod(30.0, x[3])), 2000.0, "c4");
cplexModel.ExportModel("lpex1.lp");
if (cplexModel.Solve())
{
int nvars = cplexModel.GetValues(deVar[0]).Length;
for (int j = 0; j < nvars; ++j)
{
cplexModel.Output().WriteLine("Variable " + j +": Value = " + cplexModel.GetValues(deVar[0])[j] );
}
}
cplexModel.End();
}
catch (ILOG.Concert.Exception e)
{
System.Console.WriteLine("Concert exception '" + e + "' caught");
}
Console.ReadKey();
}
}
決策變量較多時，請使用循環。本文重在入門和對cplex庫中一些概念的理解。