5.5.3. MIQP Modeling and Optimization in C++ΒΆ
In this section, we will utilize MindOpt C++ API to model and solve the problem in Example of Mixed Integer Quadratic Programming.
Include the header files:
27#include <vector>
Create an optimization model model:
36 MDOEnv env = MDOEnv();
37 MDOModel model = MDOModel(env);
Next, we set the optimization sense to minimization via MDOModel::set(). Then, we call MDOModel::addVar() to add four variables, which define upper bounds, lower bounds, names and types.
(for more details on MDOModel::set() and MDOModel::addVar(), please refer to C++ API)
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"));
We call MDOaddconstr() to input the linear constraints into model:
52 x.push_back(model.addVar(0.0, MDO_INFINITY, 0.0, MDO_CONTINUOUS, "x3"));
53
54 /* Add constraints. */
Then, we create a quadratic expression MDOQuadExpr and call MDOQuadExpr::addTerms
to set the linear part of the objective function. obj_idx represents the indices of the linear terms, obj_val represents the corresponding non-zero coefficient values in obj_idx, and obj_nnz represents the number of non-zero elements in the linear part.
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};
We call MDOQuadExpr::addTerms
to set the quadratic terms of the objective. Here, qo_values represents the coefficients of all the non-zero quadratic terms, while qo_col1 and qo_col2 respectively represent its row and column indices. qo_nnz represents the number of non-zero quadratic terms.
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.
Lastly, we call MDOModel::setObjective to set the objective and the direction to be optimized.
72 *
Once the model is constructed, we call Model.optimize() to solve the problem:
61 model.optimize();
The complete example code is shown in MdoMIQPEx1.cpp :
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 and populate optimization result. */
107 /*------------------------------------------------------------------*/
108 /* Solve the problem. */
109 model.optimize();
110
111 if(model.get(MDO_IntAttr_Status) == MDO_OPTIMAL)
112 {
113 cout << "Optimal objective value is: " << model.get(MDO_DoubleAttr_ObjVal) << endl;
114 cout << "Decision variables:" << endl;
115 int i = 0;
116 for (auto v : x)
117 {
118 cout << "x[" << i++ << "] = " << v.get(MDO_DoubleAttr_X) << endl;
119 }
120 }
121 else
122 {
123 cout<< "No feasible solution." << endl;
124 }
125
126 }
127 catch (MDOException& e)
128 {
129 std::cout << "Error code = " << e.getErrorCode() << std::endl;
130 std::cout << e.getMessage() << std::endl;
131 }
132 catch (...)
133 {
134 std::cout << "Error during optimization." << std::endl;
135 }
136
137 return static_cast<int>(MDO_OKAY);
138}