5.3.6. C# 的QP建模和优化¶
在本节中，我们将使用 MindOpt C# API，以按行输入的形式来建模以及求解 二次规划问题示例 中的问题。
首先，创建优化模型：
32 // Create model
33 MDOEnv env = new MDOEnv();
34 MDOModel model = new MDOModel(env);
35 model.Set(MDO.StringAttr.ModelName, "QP_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 C# API）：
42 // Add variables.
43 MDOVar[] x = new MDOVar[4];
44 x[0] = model.AddVar(0.0, 10.0, 1.0, 'C', "x0");
45 x[1] = model.AddVar(0.0, MDO.INFINITY, 1.0, 'C', "x1");
46 x[2] = model.AddVar(0.0, MDO.INFINITY, 1.0, 'C', "x2");
47 x[3] = model.AddVar(0.0, MDO.INFINITY, 1.0, 'C', "x3");
接着，我们开始添加线性约束：
49 // Add constraints.
50 double[][] consV = new double[][]
51 {
52 new double[] { 1.0, 1.0, 2.0, 3.0},
53 new double[] { 1.0, 0, -1.0, 6.0}
54 };
55
56 MDOLinExpr tempLinExpr1 = new MDOLinExpr();
57 tempLinExpr1.AddTerms(consV[0], x);
58 model.AddConstr(tempLinExpr1, MDO.GREATER_EQUAL, 1.0, "c0");
59
60 MDOLinExpr tempLinExpr2 = new MDOLinExpr();
61 tempLinExpr2.AddTerms(consV[1], x);
62 model.AddConstr(tempLinExpr2, MDO.EQUAL, 1.0, "c1");
然后，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。
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。
64 // Create a QuadExpr for quadratic objective
65 MDOQuadExpr obj = new MDOQuadExpr();
66
67 // Add objective linear term: 1 x0 + 1 x1 + 1 x2 + 1 x3
68 int obj_nnz = 4;
69 MDOVar[] obj_idx = new MDOVar[] { x[0], x[1], x[2], x[3] };
70 double[] obj_val = new double[] { 1.0, 1.0, 1.0, 1.0 };
71 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。
73 // Add quadratic part in objective: 1/2 [ x0^2 + x1^2 + x2^2 + x3^2 + x0 x1]
74 int qo_nnz = 5;
75 MDOVar[] qo_col1 = new MDOVar[] { x[0], x[1], x[2], x[3], x[0] };
76 MDOVar[] qo_col2 = new MDOVar[] { x[0], x[1], x[2], x[3], x[1] };
77 double[] qo_values = new double[] { 0.5, 0.5, 0.5, 0.5, 0.5 };
78 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。
80 model.SetObjective(obj, MDO.MINIMIZE);
问题输入完成后，调用 MDOModel.Optimize 求解优化问题：
83 model.Optimize();
示例 MdoQoEx1.cs 提供了完整源代码：
1/**
2 * Description
3 * -----------
4 *
5 * Linear optimization (row-wise input).
6 *
7 * Formulation
8 * -----------
9 *
10 * Minimize
11 * obj: 1 x0 + 1 x1 + 1 x2 + 1 x3
12 * + 1/2 [ x0^2 + x1^2 + x2^2 + x3^2 + x0 x1]
13 * Subject To
14 * c0 : 1 x0 + 1 x1 + 2 x2 + 3 x3 >= 1
15 * c1 : 1 x0 - 1 x2 + 6 x3 = 1
16 * Bounds
17 * 0 <= x0 <= 10
18 * 0 <= x1
19 * 0 <= x2
20 * 0 <= x3
21 * End
22 */
23
24using Mindopt;
25
26namespace Example
27{
28 public class MdoQoEx1
29 {
30 public static void Main(string[] args)
31 {
32 // Create model
33 MDOEnv env = new MDOEnv();
34 MDOModel model = new MDOModel(env);
35 model.Set(MDO.StringAttr.ModelName, "QP_01");
36
37 try
38 {
39 // Change to minimization problem.
40 model.Set(MDO.IntAttr.ModelSense, MDO.MINIMIZE);
41
42 // Add variables.
43 MDOVar[] x = new MDOVar[4];
44 x[0] = model.AddVar(0.0, 10.0, 1.0, 'C', "x0");
45 x[1] = model.AddVar(0.0, MDO.INFINITY, 1.0, 'C', "x1");
46 x[2] = model.AddVar(0.0, MDO.INFINITY, 1.0, 'C', "x2");
47 x[3] = model.AddVar(0.0, MDO.INFINITY, 1.0, 'C', "x3");
48
49 // Add constraints.
50 double[][] consV = new double[][]
51 {
52 new double[] { 1.0, 1.0, 2.0, 3.0},
53 new double[] { 1.0, 0, -1.0, 6.0}
54 };
55
56 MDOLinExpr tempLinExpr1 = new MDOLinExpr();
57 tempLinExpr1.AddTerms(consV[0], x);
58 model.AddConstr(tempLinExpr1, MDO.GREATER_EQUAL, 1.0, "c0");
59
60 MDOLinExpr tempLinExpr2 = new MDOLinExpr();
61 tempLinExpr2.AddTerms(consV[1], x);
62 model.AddConstr(tempLinExpr2, MDO.EQUAL, 1.0, "c1");
63
64 // Create a QuadExpr for quadratic objective
65 MDOQuadExpr obj = new MDOQuadExpr();
66
67 // Add objective linear term: 1 x0 + 1 x1 + 1 x2 + 1 x3
68 int obj_nnz = 4;
69 MDOVar[] obj_idx = new MDOVar[] { x[0], x[1], x[2], x[3] };
70 double[] obj_val = new double[] { 1.0, 1.0, 1.0, 1.0 };
71 obj.AddTerms(obj_val, obj_idx);
72
73 // Add quadratic part in objective: 1/2 [ x0^2 + x1^2 + x2^2 + x3^2 + x0 x1]
74 int qo_nnz = 5;
75 MDOVar[] qo_col1 = new MDOVar[] { x[0], x[1], x[2], x[3], x[0] };
76 MDOVar[] qo_col2 = new MDOVar[] { x[0], x[1], x[2], x[3], x[1] };
77 double[] qo_values = new double[] { 0.5, 0.5, 0.5, 0.5, 0.5 };
78 obj.AddTerms(qo_values, qo_col1, qo_col2);
79
80 model.SetObjective(obj, MDO.MINIMIZE);
81
82 // Solve the problem and populate optimization result.
83 model.Optimize();
84
85 if (model.Get(MDO.IntAttr.Status) == MDO.Status.OPTIMAL)
86 {
87 Console.WriteLine($"Optimal objective value is: {model.Get(MDO.DoubleAttr.ObjVal)}");
88 Console.WriteLine("Decision variables: ");
89 for (int i = 0; i < 4; i++)
90 Console.WriteLine( $"x[{i}] = {x[i].Get(MDO.DoubleAttr.X)}");
91 }
92 else
93 {
94 Console.WriteLine("No feasible solution.");
95 }
96 }
97 catch (Exception e)
98 {
99 Console.WriteLine("Exception during optimization");
100 Console.WriteLine(e.Message);
101 }
102 finally
103 {
104 model.Dispose();
105 env.Dispose();
106 }
107 }
108 }
109}