【求解器】| Java调用CPLEX求解MIP设置初始解

• 用到的函数
• 具体案例

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

max⁡∑i=110xis.t.xi⩽1,∀i=1,⋯,10,0⩽xi⩽100,∀i=1,⋯,10,xi∈Z,∀i=1,⋯,10.\begin{aligned} \max \quad &\sum_{i=1}^{10} x_i \\ s.t. \quad& x_i \leqslant 1, && \forall i = 1, \cdots, 10, \\ &0 \leqslant x_{i} \leqslant 100,&& \forall i = 1, \cdots, 10, \\ &x_{i} \in \mathbb{Z}, && \forall i = 1, \cdots, 10. \end{aligned} maxs.t.​i=1∑10​xi​xi​⩽1,0⩽xi​⩽100,xi​∈Z,​​∀i=1,⋯,10,∀i=1,⋯,10,∀i=1,⋯,10.​

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

/*author: Liu Xinglu institute: Tsinghua Universitydate: 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。