5.2.5. Java 的MILP建模与优化¶
在本节中，我们将使用 MindOpt JAVA API，以按行输入的形式来建模以及求解 混合整数线性规划问题示例 中的问题。
首先，引入 Java 包：
24import com.alibaba.damo.mindopt.*;
并创建优化模型：
30 MDOEnv env = new MDOEnv();
31 MDOModel model = new MDOModel(env);
32 model.set(MDO.StringAttr.ModelName, "MILP_01");
接下来，我们通过 MDOModel.set 设置模型属性 ModelSense，将目标函数设置为 最小化，并调用 MDOModel.addVar 来添加四个优化变量，定义其下界、上界、类型和名称（有关模型属性内容及其设置可参考 属性, 其他API请参考 JAVA API）：
35 // Change to minimization problem.
36 model.set(MDO.IntAttr.ModelSense, MDO.MINIMIZE);
37
38 // Add variables.
39 MDOVar[] x = new MDOVar[4];
40 x[0] = model.addVar(0.0, 10.0, 1.0, 'I', "x0");
41 x[1] = model.addVar(0.0, MDO.INFINITY, 2.0, 'I', "x1");
42 x[2] = model.addVar(0.0, MDO.INFINITY, 1.0, 'I', "x2");
43 x[3] = model.addVar(0.0, MDO.INFINITY, 1.0, 'C', "x3");
接着，我们开始添加线性约束：
45 // Add constraints.
46 double[][] consV = new double[][]{
47 { 1.0, 1.0, 2.0, 3.0},
48 { 1.0, 0, -1.0, 6.0}
49 };
50
51 MDOLinExpr tempLinExpr1 = new MDOLinExpr();
52 tempLinExpr1.addTerms(consV[0], x);
53 model.addConstr(tempLinExpr1, MDO.GREATER_EQUAL, 1.0, "c0");
54
55 MDOLinExpr tempLinExpr2 = new MDOLinExpr();
56 tempLinExpr2.addTerms(consV[1], x);
57 model.addConstr(tempLinExpr2, MDO.EQUAL, 1.0, "c1");
问题输入完成后，再调用 MDOModel.optimize 求解优化问题：
60 model.optimize();
最后用 MDOModel.get 和模型属性值 ObjVal 来查看优化结果和最优目标值，以及 MDOVar.get 和变量属性值 X 来查看优化解的目标值。 其他的属性值请查看 属性 章节。
62 if (model.get(MDO.IntAttr.Status) == MDO.OPTIMAL) {
63 System.out.println("Optimal objective value is: " + model.get(MDO.DoubleAttr.ObjVal));
64 System.out.println("Decision variables: ");
65 for(int i = 0; i < 4; i++) {
66 System.out.println( "x[" + i + "] = " + x[i].get(MDO.DoubleAttr.X));
67 }
68 }
69 else {
70 System.out.println("No feasible solution.");
71 }
示例 MdoMiloEx1.java 提供了完整源代码：
1/*
2 * Description
3 * -----------
4 *
5 * Mixed Integer Linear optimization (row-wise input).
6 *
7 * Formulation
8 * -----------
9 *
10 * Minimize
11 * obj: 1 x0 + 2 x1 + 1 x2 + 1 x3
12 * Subject To
13 * c1 : 1 x0 + 1 x1 + 2 x2 + 3 x3 >= 1
14 * c2 : 1 x0 - 1 x2 + 6 x3 = 1
15 * Bounds
16 * 0 <= x0 <= 10
17 * 0 <= x1
18 * 0 <= x2
19 * 0 <= x3
20 * Integers
21 * x0 x1 x2
22 * End
23 */
24import com.alibaba.damo.mindopt.*;
25import java.util.*;
26
27public class MdoMiloEx1 {
28 public static void main(String[] args) throws MDOException {
29 // Create model
30 MDOEnv env = new MDOEnv();
31 MDOModel model = new MDOModel(env);
32 model.set(MDO.StringAttr.ModelName, "MILP_01");
33
34 try{
35 // Change to minimization problem.
36 model.set(MDO.IntAttr.ModelSense, MDO.MINIMIZE);
37
38 // Add variables.
39 MDOVar[] x = new MDOVar[4];
40 x[0] = model.addVar(0.0, 10.0, 1.0, 'I', "x0");
41 x[1] = model.addVar(0.0, MDO.INFINITY, 2.0, 'I', "x1");
42 x[2] = model.addVar(0.0, MDO.INFINITY, 1.0, 'I', "x2");
43 x[3] = model.addVar(0.0, MDO.INFINITY, 1.0, 'C', "x3");
44
45 // Add constraints.
46 double[][] consV = new double[][]{
47 { 1.0, 1.0, 2.0, 3.0},
48 { 1.0, 0, -1.0, 6.0}
49 };
50
51 MDOLinExpr tempLinExpr1 = new MDOLinExpr();
52 tempLinExpr1.addTerms(consV[0], x);
53 model.addConstr(tempLinExpr1, MDO.GREATER_EQUAL, 1.0, "c0");
54
55 MDOLinExpr tempLinExpr2 = new MDOLinExpr();
56 tempLinExpr2.addTerms(consV[1], x);
57 model.addConstr(tempLinExpr2, MDO.EQUAL, 1.0, "c1");
58
59 // Step 3. Solve the problem and populate the result.
60 model.optimize();
61
62 if (model.get(MDO.IntAttr.Status) == MDO.OPTIMAL) {
63 System.out.println("Optimal objective value is: " + model.get(MDO.DoubleAttr.ObjVal));
64 System.out.println("Decision variables: ");
65 for(int i = 0; i < 4; i++) {
66 System.out.println( "x[" + i + "] = " + x[i].get(MDO.DoubleAttr.X));
67 }
68 }
69 else {
70 System.out.println("No feasible solution.");
71 }
72 } catch (Exception e) {
73 System.out.println("Exception during optimization");
74 e.printStackTrace();
75 } finally {
76 model.dispose();
77 env.dispose();
78 }
79 }
80}