constraint generation 约束生成方法(不知道我翻译得对不对)在网上资料相对较少,中文的资料更少。
因为传统的DFJ模型解决TSP问题需要求解指数级别的子集,因此constraint generation显得十分必要(就目前而言,120个节点的TSP也是分分钟解决)。
下面是基于constraint generation的代码。值得注意的是在运行constraint generation方法时,需要不断去检查得到的解是否是最优解,而且在添加约束时,不能每次只加一个环的节点(这样会导致速度变慢很多很多)
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileReader;
import java.io.IOException;
import java.util.ArrayList;
import ilog.concert.*;
import ilog.concert.IloCopyManager.Check;
import ilog.cplex.*;
public class Main {
public static int _cityNum;
public static double[][] _cityDis;
public static ArrayList<Integer> _set;
public static ArrayList<ArrayList<Integer>> _setPool;
public static ArrayList<Integer> _setCG;// for constraint generation
public static ArrayList<ArrayList<Integer>> _setCGPool;// for constraint
// generation
public static long _time;
public static double _ansLength;
public static double[][] _ansCity;
public static void main(String[] args) {
String filename = "E:\\JAVA\\TSP1\\data\\gr120.tsp";
// 读取标准化后的文件
ReadData(filename);
// 运行算法
CGsolve();// constraint generation
// 输出结果
WriteAns(filename + ".ans");
// 检查是否满足约束
// checkOpt();
System.out.println("finish");
}
// constraint generation 方法解决
public static void CGsolve() {
try {
_ansCity = new double[_cityNum][_cityNum];
IloCplex cplex = new IloCplex();
IloIntVar[][] x = new IloIntVar[_cityNum][_cityNum];// 0-1变量
// 设定变量取值范围
for (int i = 0; i < _cityNum; i++) {
for (int j = 0; j < _cityNum; j++) {
if (i != j)
x[i][j] = cplex.intVar(0, 1);
else
x[i][j] = cplex.intVar(0, 0);
}
}
// 目标函数
IloLinearNumExpr tempObj = cplex.linearNumExpr();
for (int i = 0; i < _cityNum; i++) {
tempObj.add(cplex.scalProd(x[i], _cityDis[i]));
}
cplex.addMinimize(tempObj);
// 添加约束 1 和 2
for (int i = 0; i < _cityNum; i++) {
IloLinearIntExpr constraint2 = cplex.linearIntExpr();
for (int j = 0; j < _cityNum; j++) {
constraint2.addTerm(x[j][i], 1);
}
cplex.addEq(cplex.sum(x[i]), 1);
cplex.addEq(constraint2, 1);
}
// constraint generation 运行 判断最优 添加约束 输出结果
int cnt = 0;
do {
long start = System.currentTimeMillis();
boolean success = cplex.solve();
long end = System.currentTimeMillis();
_time = end - start;
cnt++;
System.out.println("正在执行第-------- " + cnt + " 次");
if (success) {
_ansLength = cplex.getObjValue();
for (int i = 0; i < _cityNum; i++)
_ansCity[i] = cplex.getValues(x[i]);
} else {
System.out.println("cplex.solve() failed.");
break;
}
if (checkOpt())
break;
while (!_setCGPool.isEmpty()) {
_setCG = _setCGPool.get(0);
_setCGPool.remove(0);
IloLinearNumExpr expression = cplex.linearNumExpr();
for (int i = 0; i < _setCG.size(); i++)
for (int j = i + 1; j < _setCG.size(); j++) {
expression.addTerm(1, x[_setCG.get(i)][_setCG.get(j)]);
expression.addTerm(1, x[_setCG.get(j)][_setCG.get(i)]);// imp
}
cplex.addLe(expression, _setCG.size() - 1);
}
} while (true);
} catch (IloException e) {
// TODO Auto-generated catch block
e.printStackTrace();
}
}
// 检查是否满足条件 绕圈走一遍
public static boolean checkOpt() {
System.out.println("check\n--------------");
_setCGPool = new ArrayList<ArrayList<Integer>>();
boolean[] flag = new boolean[_cityNum];
for (int i = 0; i < _cityNum; i++) {
if (flag[i])
continue;
_setCG = new ArrayList<Integer>();
int st = i;
int cnt = 0;
System.out.println("\n");
while (true) {
System.out.print(st + " ");
_setCG.add(st);
flag[st] = true;
for (int j = 0; j < _cityNum; j++) {
if ((int) (_ansCity[st][j] + 0.00001) == 1) {
st = j;
break;
}
}
cnt++;
if (st == i || cnt >= _cityNum)
break;
}
_setCGPool.add(new ArrayList<Integer>(_setCG));
}
if (_setCGPool.size() == 1) {
System.out.println("\nsuccess");
return true;
} else {
System.out.println("\nfail");
return false;
}
}
// 输出答案
public static void WriteAns(String filename) {
System.out.print(filename + "\n------------------------------\n");
System.out.printf("rum time(sec)= %-10.2f\n", _time / 1000.0);
System.out.printf("min= %-10.2f\n", _ansLength);
for (int i = 0; i < _cityNum; i++) {
for (int j = 0; j < _cityNum; j++)
System.out.print((int) (_ansCity[i][j] + 0.00001) + " ");
System.out.println();
}
}
// 读取标准化后的数据
public static void ReadData(String filename) {
File file = new File(filename);
BufferedReader reader = null;
try {
System.out.println("正在读取" + filename);
reader = new BufferedReader(new FileReader(file));
String tempString = null;
tempString = reader.readLine();
_cityNum = Integer.parseInt(tempString.trim());
_cityDis = new double[_cityNum][_cityNum];
for (int i = 0; i < _cityNum; i++) {
tempString = reader.readLine();
String[] arg = tempString.split(" ");
for (int j = 0; j < arg.length; j++) {
_cityDis[i][j] = Double.parseDouble(arg[j]);
_cityDis[j][i] = _cityDis[i][j];
}
}
reader.close();
} catch (IOException e) {
e.printStackTrace();
} finally {
if (reader != null) {
try {
reader.close();
} catch (IOException e1) {
}
}
}
}
}