【求解器】| Java调用CPLEX求解MIP设置初始解

作者：刘兴禄，清华大学，清华大学深圳国际研究生院，清华-伯克利深圳学院，博士在读

用到的函数

• addMIPStart(IloNumVar[] vars, double[] values)
  

具体案例

考虑下面一个非常简单的整数规划模型

$$\begin{array}{rlrl}\max & \sum _{i=1}^{10}{x}_i& & \\ s.t.& x_i⩽1,& & \forall i=1,\cdots ,10,\\ & 0⩽x_i⩽100,& & \forall i=1,\cdots ,10,\\ & x_i\in \mathbb{Z},& & \forall i=1,\cdots ,10.\end{array}$$

下面是具体的代码中，我们设置$x_i=1,\forall i=1,\cdots ,10$.

/*
 author: Liu Xinglu 
 institute: Tsinghua University
 date: 2023-3-16
*/

package Test;

import ilog.concert.*;
import ilog.cplex.*;

public class Main {
    
    
	public static void main(String[] args) throws IloException {
    
    
		int num = 10;
		IloCplex cplex = new IloCplex();
		IloNumVar[] x = new IloNumVar[num];
		double[] initSol = new double[num]; 
		
		
		for(int i = 0; i < num; i++) {
    
    
//			x[i] = cplex.numVar(0, 10000);
			x[i] = cplex.intVar(0, 10000);
			initSol[i] = 1.0;
		}
		
		IloNumExpr obj = cplex.numExpr();
		for(int i = 0; i < num; i++) {
    
    
			obj = cplex.sum(obj, x[i]);
		}
		
		cplex.addMaximize(obj);
		
		for(int i = 0; i < num; i++) {
    
    
			IloNumExpr expr = cplex.numExpr();
			expr = cplex.sum(expr, x[i]);
			cplex.addLe(expr, 1);
		}
		
		
		cplex.addMIPStart(x, initSol);
		cplex.exportModel("MyTestModel.lp");
		cplex.solve();
		System.out.println(cplex.getObjValue());
	}
}

运行结果如下

1 of 1 MIP starts provided solutions.
MIP start 'm1' defined initial solution with objective 10.0000.
Tried aggregator 1 time.
MIP Presolve eliminated 10 rows and 10 columns.
All rows and columns eliminated.
Presolve time = 0.00 sec. (0.00 ticks)

Root node processing (before b&c):
  Real time             =    0.00 sec. (0.02 ticks)
Parallel b&c, 16 threads:
  Real time             =    0.00 sec. (0.00 ticks)
  Sync time (average)   =    0.00 sec.
  Wait time (average)   =    0.00 sec.
                          ------------
Total (root+branch&cut) =    0.00 sec. (0.02 ticks)
10.0

可以看到，设置成功了。日志中出现了下面的信息：

1 of 1 MIP starts provided solutions.
MIP start 'm1' defined initial solution with objective 10.0000.

这就说明设置初始解成功。