5.2.3. C++ 的MILP建模和优化¶
在本节中，我们将使用 MindOpt C++ 语言的 API 来建模以及求解 混合整数线性规划问题示例 中的问题。
5.2.3.1. 按行输入：MdoMiloEx1¶
首先，引入头文件：
27#include "MindoptCpp.h"
并创建优化模型：
33 /*------------------------------------------------------------------*/
34 /* Step 1. Create a model and change the parameters. */
35 /*------------------------------------------------------------------*/
36 /* Create an empty model. */
37 MdoModel model;
接下来，我们通过 mindopt::MdoModel::setIntAttr() 将目标函数设置为 最小化 ，并调用 mindopt::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 mindopt::MdoModel::setIntAttr() 和 mindopt::MdoModel::addVar() 的详细使用方式，请参考 C++ 接口函数）：
41 /*------------------------------------------------------------------*/
42 /* Step 2. Input model. */
43 /*------------------------------------------------------------------*/
44 /* Change to minimization problem. */
45 model.setIntAttr(MDO_INT_ATTR::MIN_SENSE, MDO_YES);
46
47 /* Add variables. */
48 std::vector<MdoVar> x;
49 x.push_back(model.addVar(0.0, 10.0, 1.0, "x0", MDO_YES));
50 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, "x1", MDO_YES));
51 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, "x2", MDO_YES));
52 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, "x3", MDO_NO));
Note
在函数 mindopt::MdoModel::addVar() 中，最后一个参数位是 is_integer ，设置为 MDO_YES 代表这个变量是整形变量。
接着，我们开始添加线性约束：
54 /* Add constraints. */
55 model.addCons(1.0, MDO_INFINITY, 1.0 * x[0] + 1.0 * x[1] + 2.0 * x[2] + 3.0 * x[3], "c0");
56 model.addCons(1.0, 1.0, 1.0 * x[0] - 1.0 * x[2] + 6.0 * x[3], "c1");
问题输入完成后，再调用 mindopt::MdoModel::solveProb() 求解优化问题，并通过 mindopt::MdoModel::displayResults() 查看优化结果：
58 /*------------------------------------------------------------------*/
59 /* Step 3. Solve the problem and populate the result. */
60 /*------------------------------------------------------------------*/
61 /* Solve the problem. */
62 model.solveProb();
63 model.displayResults();
文件链接 MdoMiloEx1.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 * 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#include <iostream>
25#include <vector>
26#include "MindoptCpp.h"
27
28using namespace mindopt;
29
30int main(void)
31{
32 /*------------------------------------------------------------------*/
33 /* Step 1. Create a model and change the parameters. */
34 /*------------------------------------------------------------------*/
35 /* Create an empty model. */
36 MdoModel model;
37
38 try
39 {
40 /*------------------------------------------------------------------*/
41 /* Step 2. Input model. */
42 /*------------------------------------------------------------------*/
43 /* Change to minimization problem. */
44 model.setIntAttr(MDO_INT_ATTR::MIN_SENSE, MDO_YES);
45
46 /* Add variables. */
47 std::vector<MdoVar> x;
48 x.push_back(model.addVar(0.0, 10.0, 1.0, "x0", MDO_YES));
49 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, "x1", MDO_YES));
50 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, "x2", MDO_YES));
51 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, "x3", MDO_NO));
52
53 /* Add constraints. */
54 model.addCons(1.0, MDO_INFINITY, 1.0 * x[0] + 1.0 * x[1] + 2.0 * x[2] + 3.0 * x[3], "c0");
55 model.addCons(1.0, 1.0, 1.0 * x[0] - 1.0 * x[2] + 6.0 * x[3], "c1");
56
57 /*------------------------------------------------------------------*/
58 /* Step 3. Solve the problem and populate the result. */
59 /*------------------------------------------------------------------*/
60 /* Solve the problem. */
61 model.solveProb();
62 model.displayResults();
63 }
64 catch (MdoException & e)
65 {
66 std::cerr << "===================================" << std::endl;
67 std::cerr << "Error : code <" << e.getResult() << ">" << std::endl;
68 std::cerr << "Reason : " << model.explainResult(e.getResult()) << std::endl;
69 std::cerr << "===================================" << std::endl;
70
71 return static_cast<int>(e.getResult());
72 }
73
74 return static_cast<int>(MDO_OKAY);
75}