5.5.5. Java 的MIQP建模和优化¶
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 MIQP题示例 中的问题。
首先，引入头文件：
25import java.util.*;
并创建优化模型：
31 MDOModel model = new MDOModel(env);
32 model.set(MDO.StringAttr.ModelName, "MIQP_01");
接下来，我们通过 MDOModel.set 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、名称和类型（有关 MDOModel.set 和 MDOModel.addVar 的详细使用方式，请参考 JAVA API）：
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, 0.0, 'I', "x0");
41 x[1] = model.addVar(0.0, MDO.INFINITY, 0.0, 'C', "x1");
42 x[2] = model.addVar(0.0, MDO.INFINITY, 0.0, 'C', "x2");
43 x[3] = model.addVar(0.0, MDO.INFINITY, 0.0, 'C', "x3");
接着，我们开始添加线性约束：
64 double[][] consV = new double[][] {
65 { 1.0, 1.0, 2.0, 3.0 },
66 { 1.0, 0, -1.0, 6.0 }
67 };
68
69 MDOLinExpr tempLinExpr1 = new MDOLinExpr();
70 tempLinExpr1.addTerms(consV[0], x);
71 model.addConstr(tempLinExpr1, MDO.GREATER_EQUAL, 1.0, "c0");
72
73 MDOLinExpr tempLinExpr2 = new MDOLinExpr();
74 tempLinExpr2.addTerms(consV[1], x);
75 model.addConstr(tempLinExpr2, MDO.EQUAL, 1.0, "c1");
76
然后，我们开始设置二次目标函数。我们创建一个二次表达式 MDOQuadExpr , 再调用 MDOQuadExpr.addTerms 来设置目标函数线性部分。这里
obj_idx 表示线性部分的索引，obj_val 表示与 obj_idx 中的索引相对应的非零系数值。
49 int obj_nnz = 4;
50 MDOVar[] obj_idx = new MDOVar[] { x[0], x[1], x[2], x[3] };
51 double[] obj_val = new double[] { 1.0, 1.0, 1.0, 1.0 };
52 obj.addTerms(obj_val, obj_idx);
然后，调用 MDOQuadExpr.addTerms 来设置目标的二次项系数 \(Q\)。
其中，qo_values 表示要添加的二次项的系数，qo_col1 和 qo_col2 表示与qo_values相对应的二次项的第一个变量和第二个变量。
55 int qo_nnz = 5;
56 MDOVar[] qo_col1 = new MDOVar[] { x[0], x[1], x[2], x[3], x[0] };
57 MDOVar[] qo_col2 = new MDOVar[] { x[0], x[1], x[2], x[3], x[1] };
58 double[] qo_values = new double[] { 0.5, 0.5, 0.5, 0.5, 0.5 };
59 obj.addTerms(qo_values, qo_col1, qo_col2);
最后，我们调用 MDOModel.setObjective 设定优化目标与方向。
62
问题输入完成后，调用 MDOModel.optimize 求解优化问题：
79
示例 MdoMIQPEx1.java 提供了完整源代码：
1/**
2 * Description
3 * -----------
4 *
5 * Mixed IntegerQuadratic optimization (row-wise input).
6 *
7 * Formulation
8 * -----------
9 * Minimize
10 * obj: 1 x0 + 1 x1 + 1 x2 + 1 x3
11 * + 1/2 [ x0^2 + x1^2 + x2^2 + x3^2 + x0 x1]
12 * Subject To
13 * c0 : 1 x0 + 1 x1 + 2 x2 + 3 x3 >= 1
14 * c1 : 1 x0 - 1 x2 + 6 x3 = 1
15 * Bounds
16 * 0 <= x0 <= 10
17 * 0 <= x1
18 * 0 <= x2
19 * 0 <= x3
20 * x0 integer
21 * End
22 */
23
24import com.alibaba.damo.mindopt.*;
25import java.util.*;
26
27public class MdoMIQPEx1 {
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, "MIQP_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, 0.0, 'I', "x0");
41 x[1] = model.addVar(0.0, MDO.INFINITY, 0.0, 'C', "x1");
42 x[2] = model.addVar(0.0, MDO.INFINITY, 0.0, 'C', "x2");
43 x[3] = model.addVar(0.0, MDO.INFINITY, 0.0, 'C', "x3");
44
45 // Create a QuadExpr for quadratic objective
46 MDOQuadExpr obj = new MDOQuadExpr();
47
48 // Add objective linear term: 1 x0 + 1 x1 + 1 x2 + 1 x3
49 int obj_nnz = 4;
50 MDOVar[] obj_idx = new MDOVar[] { x[0], x[1], x[2], x[3] };
51 double[] obj_val = new double[] { 1.0, 1.0, 1.0, 1.0 };
52 obj.addTerms(obj_val, obj_idx);
53
54 // Add quadratic part in objective: 1/2 [ x0^2 + x1^2 + x2^2 + x3^2 + x0 x1]
55 int qo_nnz = 5;
56 MDOVar[] qo_col1 = new MDOVar[] { x[0], x[1], x[2], x[3], x[0] };
57 MDOVar[] qo_col2 = new MDOVar[] { x[0], x[1], x[2], x[3], x[1] };
58 double[] qo_values = new double[] { 0.5, 0.5, 0.5, 0.5, 0.5 };
59 obj.addTerms(qo_values, qo_col1, qo_col2);
60
61 model.setObjective(obj, MDO.MINIMIZE);
62
63 // Add constraints.
64 double[][] consV = new double[][] {
65 { 1.0, 1.0, 2.0, 3.0 },
66 { 1.0, 0, -1.0, 6.0 }
67 };
68
69 MDOLinExpr tempLinExpr1 = new MDOLinExpr();
70 tempLinExpr1.addTerms(consV[0], x);
71 model.addConstr(tempLinExpr1, MDO.GREATER_EQUAL, 1.0, "c0");
72
73 MDOLinExpr tempLinExpr2 = new MDOLinExpr();
74 tempLinExpr2.addTerms(consV[1], x);
75 model.addConstr(tempLinExpr2, MDO.EQUAL, 1.0, "c1");
76
77 // Solve the problem.
78 model.optimize();
79
80 // Step 4. Retrive model status and objective.
81 // For MIP(MILP,MIQP, MIQCP) problems, if the solving process
82 // terminates early due to reasons such as timeout or interruption,
83 // the model status will indicate termination by timeout (or
84 // interruption, etc.). However, suboptimal solutions may still
85 // exist, making it necessary to check the SolCount property.
86 if (model.get(MDO.IntAttr.Status) == MDO.OPTIMAL || model.get(MDO.IntAttr.Status) == MDO.SUB_OPTIMAL ||
87 model.get(MDO.IntAttr.SolCount) != 0) {
88 System.out.println("Optimal objective value is: " + model.get(MDO.DoubleAttr.ObjVal));
89 System.out.println("Decision variables: ");
90 for (int i = 0; i < 4; i++) {
91 System.out.println( "x[" + i + "] = " + x[i].get(MDO.DoubleAttr.X));
92 }
93 }
94 else {
95 System.out.println("No feasible solution.");
96 }
97 } catch (Exception e) {
98 System.out.println("Exception during optimization");
99 e.printStackTrace();
100 } finally {
101 model.dispose();
102 env.dispose();
103 }
104 }
105}