5.5.3. C++ 的MIQP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 MIQP题示例 中的问题。
首先，引入头文件：
27#include <vector>
并创建优化模型：
36 MDOEnv env = MDOEnv();
37 MDOModel model = MDOModel(env);
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（有关模型属性内容及其设置可参考 属性, 其他API请参考 C++ API）：
44 /* Change to minimization problem. */
45 model.set(MDO_IntAttr_ModelSense, MDO_MINIMIZE);
46
47 /* Add variables. */
48 std::vector<MDOVar> x;
49 x.push_back(model.addVar(0.0, 10.0, 0.0, MDO_INTEGER, "x0"));
50 x.push_back(model.addVar(0.0, MDO_INFINITY, 0.0, MDO_CONTINUOUS, "x1"));
接着，我们开始添加线性约束：
52 x.push_back(model.addVar(0.0, MDO_INFINITY, 0.0, MDO_CONTINUOUS, "x3"));
53
54 /* Add constraints. */
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，obj_nnz 代表线性部分的非零元的个数。
56 model.addConstr(1.0 * x[0] - 1.0 * x[2] + 6.0 * x[3], MDO_EQUAL, 1.0, "c1");
57
58 /*Create a QuadExpr. */
59 MDOQuadExpr obj = MDOQuadExpr(0.0);
60
61 /* Add objective linear term.*/
62 const MDOVar obj_idx[] = { x[0], x[1], x[2], x[3]};
63 const double obj_val[] = { 1.0, 1.0, 1.0, 1.0};
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，qo_nnz 表示二次项中的非零元个数。
64 obj.addTerms(obj_val, obj_idx, 4);
65
66 /* Add quadratic objective matrix Q.
67 *
68 * Note.
69 * 1. The objective function is defined as c^Tx + 1/2 x^TQx, where Q is stored with coordinate format.
70 * 2. Q will be scaled by 1/2 internally.
最后，我们调用 MDOModel::setObjective 设定优化目标与方向。
72 *
问题输入完成后，再调用 MDOModel::optimize() 求解优化问题：
78
示例 MdoMIQPEx1.cpp 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 * Integers
22 * x0
23 * End
24 */
25#include <iostream>
26#include "MindoptCpp.h"
27#include <vector>
28
29using namespace std;
30
31int main(void)
32{
33 /*------------------------------------------------------------------*/
34 /* Step 1. Create environment and model. */
35 /*------------------------------------------------------------------*/
36 MDOEnv env = MDOEnv();
37 MDOModel model = MDOModel(env);
38
39 try
40 {
41 /*------------------------------------------------------------------*/
42 /* Step 2. Input model. */
43 /*------------------------------------------------------------------*/
44 /* Change to minimization problem. */
45 model.set(MDO_IntAttr_ModelSense, MDO_MINIMIZE);
46
47 /* Add variables. */
48 std::vector<MDOVar> x;
49 x.push_back(model.addVar(0.0, 10.0, 0.0, MDO_INTEGER, "x0"));
50 x.push_back(model.addVar(0.0, MDO_INFINITY, 0.0, MDO_CONTINUOUS, "x1"));
51 x.push_back(model.addVar(0.0, MDO_INFINITY, 0.0, MDO_CONTINUOUS, "x2"));
52 x.push_back(model.addVar(0.0, MDO_INFINITY, 0.0, MDO_CONTINUOUS, "x3"));
53
54 /* Add constraints. */
55 model.addConstr(1.0 * x[0] + 1.0 * x[1] + 2.0 * x[2] + 3.0 * x[3], MDO_GREATER_EQUAL, 1.0, "c0");
56 model.addConstr(1.0 * x[0] - 1.0 * x[2] + 6.0 * x[3], MDO_EQUAL, 1.0, "c1");
57
58 /*Create a QuadExpr. */
59 MDOQuadExpr obj = MDOQuadExpr(0.0);
60
61 /* Add objective linear term.*/
62 const MDOVar obj_idx[] = { x[0], x[1], x[2], x[3]};
63 const double obj_val[] = { 1.0, 1.0, 1.0, 1.0};
64 obj.addTerms(obj_val, obj_idx, 4);
65
66 /* Add quadratic objective matrix Q.
67 *
68 * Note.
69 * 1. The objective function is defined as c^Tx + 1/2 x^TQx, where Q is stored with coordinate format.
70 * 2. Q will be scaled by 1/2 internally.
71 * 3. To ensure the symmetricity of Q, user needs to input only the lower triangular part.
72 *
73 * Q = [ 1.0 0.5 0 0 ]
74 * [ 0.5 1.0 0 0 ]
75 * [ 0.0 0.0 1.0 0 ]
76 * [ 0 0 0 1.0 ]
77 */
78
79 const double qo_values[] =
80 {
81 1.0,
82 0.5, 1.0,
83 1.0,
84 1.0
85 };
86 const MDOVar qo_col1[] =
87 {
88 x[0],
89 x[1], x[1],
90 x[2],
91 x[3]
92 };
93 const MDOVar qo_col2[] =
94 {
95 x[0],
96 x[0], x[1],
97 x[2],
98 x[3]
99 };
100
101 obj.addTerms(qo_values, qo_col1, qo_col2, 5);
102
103 model.setObjective(obj, MDO_MINIMIZE);
104
105 /*------------------------------------------------------------------*/
106 /* Step 3. Solve the problem. */
107 /*------------------------------------------------------------------*/
108 /* Solve the problem. */
109 model.optimize();
110
111 /*------------------------------------------------------------------*/
112 /* Step 4. Retrive model status and objective. */
113 /* For MIP(MILP,MIQP, MIQCP) problems, if the solving process */
114 /* terminates early due to reasons such as timeout or interruption, */
115 /* the model status will indicate termination by timeout (or */
116 /* interruption, etc.). However, suboptimal solutions may still */
117 /* exist, making it necessary to check the SolCount property. */
118 /*------------------------------------------------------------------*/
119 if (model.get(MDO_IntAttr_Status) == MDO_OPTIMAL || model.get(MDO_IntAttr_Status) == MDO_SUB_OPTIMAL ||
120 model.get(MDO_IntAttr_SolCount) != 0)
121 {
122 cout << "Optimal objective value is: " << model.get(MDO_DoubleAttr_ObjVal) << endl;
123 cout << "Decision variables:" << endl;
124 int i = 0;
125 for (auto v : x)
126 {
127 cout << "x[" << i++ << "] = " << v.get(MDO_DoubleAttr_X) << endl;
128 }
129 }
130 else
131 {
132 cout<< "No feasible solution." << endl;
133 }
134
135 }
136 catch (MDOException& e)
137 {
138 std::cout << "Error code = " << e.getErrorCode() << std::endl;
139 std::cout << e.getMessage() << std::endl;
140 }
141 catch (...)
142 {
143 std::cout << "Error during optimization." << std::endl;
144 }
145
146 return static_cast<int>(MDO_OKAY);
147}