5.2.3. C++ 的MILP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 混合整数线性规划问题示例 中的问题。
首先，引入头文件：
27#include "MindoptCpp.h"
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() 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（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, 1.0, MDO_INTEGER, "x0"));
50 x.push_back(model.addVar(0.0, MDO_INFINITY, 2.0, MDO_INTEGER, "x1"));
51 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, MDO_INTEGER, "x2"));
52 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, MDO_CONTINUOUS, "x3"));
接着，我们开始添加线性约束：
54 /* Add constraints. */
55 model.addConstr(1.0 * x[0] + 1.0 * x[1] + 2.0 * x[2] + 3.0 * x[3] >= 1.0, "c0");
56 model.addConstr(1.0 * x[0] - 1.0 * x[2] + 6.0 * x[3] == 1.0, "c1");
问题输入完成后，再调用 MDOModel::optimize() 求解优化问题：
61 model.optimize();
最后用 MDOModel::get() 查看模型属性值 ObjVal 来查看优化解的目标值，可以用 MDOModel::get() 查看变量属性值 X 来查看优化解的目标值。更多的解获取可参考 属性 和头文件定义。
62 if(model.get(MDO_IntAttr_Status) == MDO_OPTIMAL)
63 {
64 cout << "Optimal objective value is: " << model.get(MDO_DoubleAttr_ObjVal) << endl;
65 cout << "Decision variables: " << endl;
66 int i = 0;
67 for (auto v : x)
68 {
69 cout << "x[" << i++ << "] = " << v.get(MDO_DoubleAttr_X) << endl;
70 }
71 }
72 else
73 {
74 cout<< "No feasible solution." << endl;
75 }
示例 MdoMiloEx1.cpp 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 * 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 * Integers
21 * x0 x1 x2
22 * End
23 */
24
25#include <iostream>
26#include <vector>
27#include "MindoptCpp.h"
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, 1.0, MDO_INTEGER, "x0"));
50 x.push_back(model.addVar(0.0, MDO_INFINITY, 2.0, MDO_INTEGER, "x1"));
51 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, MDO_INTEGER, "x2"));
52 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, 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] >= 1.0, "c0");
56 model.addConstr(1.0 * x[0] - 1.0 * x[2] + 6.0 * x[3] == 1.0, "c1");
57
58 /*------------------------------------------------------------------*/
59 /* Step 3. Solve the problem and populate optimization result. */
60 /*------------------------------------------------------------------*/
61 model.optimize();
62 if(model.get(MDO_IntAttr_Status) == MDO_OPTIMAL)
63 {
64 cout << "Optimal objective value is: " << model.get(MDO_DoubleAttr_ObjVal) << endl;
65 cout << "Decision variables: " << endl;
66 int i = 0;
67 for (auto v : x)
68 {
69 cout << "x[" << i++ << "] = " << v.get(MDO_DoubleAttr_X) << endl;
70 }
71 }
72 else
73 {
74 cout<< "No feasible solution." << endl;
75 }
76 }
77 catch (MDOException& e)
78 {
79 cout << "Error code = " << e.getErrorCode() << endl;
80 cout << e.getMessage() << endl;
81 }
82 catch (...)
83 {
84 cout << "Error during optimization." << endl;
85 }
86
87 return static_cast<int>(MDO_OKAY);
88}