5.3.3. QP Modeling and Optimization in C++ΒΆ
In this chapter, we will use MindOpt C++ API to model and solve the problem in Example of Quadratic Programming.
Include the header file:
24#include "MindoptCpp.h"
Create an optimization model model:
31 /*------------------------------------------------------------------*/
32 /* Step 1. Create environment and model. */
33 /*------------------------------------------------------------------*/
34 MDOEnv env = MDOEnv();
35 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 /* Change to minimization problem. */
43 model.set(MDO_IntAttr_ModelSense, MDO_MINIMIZE);
44
45 /* Add variables. */
46 std::vector<MDOVar> x;
47 x.push_back(model.addVar(0.0, 10.0, 0.0, MDO_CONTINUOUS, "x0"));
48 x.push_back(model.addVar(0.0, MDO_INFINITY, 0.0, MDO_CONTINUOUS, "x1"));
49 x.push_back(model.addVar(0.0, MDO_INFINITY, 0.0, MDO_CONTINUOUS, "x2"));
50 x.push_back(model.addVar(0.0, MDO_INFINITY, 0.0, MDO_CONTINUOUS, "x3"));
We call MDOaddconstr() to input the linear constraints into model:
52 /* Add constraints. */
53 model.addConstr(1.0 * x[0] + 1.0 * x[1] + 2.0 * x[2] + 3.0 * x[3], MDO_GREATER_EQUAL, 1.0, "c0");
54 model.addConstr(1.0 * x[0] - 1.0 * x[2] + 6.0 * x[3], MDO_EQUAL, 1.0, "c1");
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 /*Create a QuadExpr. */
57 MDOQuadExpr obj = MDOQuadExpr(0.0);
58
59 /* Add objective linear term: 1 x0 + 1 x1 + 1 x2 + 1 x3 */
60 int obj_nnz = 4;
61 MDOVar obj_idx[] = { x[0], x[1], x[2], x[3] };
62 double obj_val[] = { 1.0, 1.0, 1.0, 1.0} ;
63 obj.addTerms(obj_val, obj_idx, obj_nnz);
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 /* Add objective quadratic term: 1/2 [ x0^2 + x1^2 + x2^2 + x3^2 + x0 x1] */
65 int qo_nnz = 5;
66 MDOVar qo_col1[] = { x[0], x[1], x[2], x[3], x[0] };
67 MDOVar qo_col2[] = { x[0], x[1], x[2], x[3], x[1] };
68 double qo_values[] = { 0.5, 0.5, 0.5, 0.5, 0.5 };
69 obj.addTerms(qo_values, qo_col1, qo_col2, qo_nnz);
Lastly, we call MDOModel::setObjective to set the objective and the direction to be optimized.
72 model.setObjective(obj, MDO_MINIMIZE);
Once the model is constructed, we call MDOModel::optimize() to solve the problem:
78 model.optimize();
The complete example code is shown in MdoQoEx1.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 * End
22 */
23#include <iostream>
24#include "MindoptCpp.h"
25#include <vector>
26
27using namespace std;
28
29int main(void)
30{
31 /*------------------------------------------------------------------*/
32 /* Step 1. Create environment and model. */
33 /*------------------------------------------------------------------*/
34 MDOEnv env = MDOEnv();
35 MDOModel model = MDOModel(env);
36
37 try
38 {
39 /*------------------------------------------------------------------*/
40 /* Step 2. Input model. */
41 /*------------------------------------------------------------------*/
42 /* Change to minimization problem. */
43 model.set(MDO_IntAttr_ModelSense, MDO_MINIMIZE);
44
45 /* Add variables. */
46 std::vector<MDOVar> x;
47 x.push_back(model.addVar(0.0, 10.0, 0.0, MDO_CONTINUOUS, "x0"));
48 x.push_back(model.addVar(0.0, MDO_INFINITY, 0.0, MDO_CONTINUOUS, "x1"));
49 x.push_back(model.addVar(0.0, MDO_INFINITY, 0.0, MDO_CONTINUOUS, "x2"));
50 x.push_back(model.addVar(0.0, MDO_INFINITY, 0.0, MDO_CONTINUOUS, "x3"));
51
52 /* Add constraints. */
53 model.addConstr(1.0 * x[0] + 1.0 * x[1] + 2.0 * x[2] + 3.0 * x[3], MDO_GREATER_EQUAL, 1.0, "c0");
54 model.addConstr(1.0 * x[0] - 1.0 * x[2] + 6.0 * x[3], MDO_EQUAL, 1.0, "c1");
55
56 /*Create a QuadExpr. */
57 MDOQuadExpr obj = MDOQuadExpr(0.0);
58
59 /* Add objective linear term: 1 x0 + 1 x1 + 1 x2 + 1 x3 */
60 int obj_nnz = 4;
61 MDOVar obj_idx[] = { x[0], x[1], x[2], x[3] };
62 double obj_val[] = { 1.0, 1.0, 1.0, 1.0} ;
63 obj.addTerms(obj_val, obj_idx, obj_nnz);
64
65 /* Add objective quadratic term: 1/2 [ x0^2 + x1^2 + x2^2 + x3^2 + x0 x1] */
66 int qo_nnz = 5;
67 MDOVar qo_col1[] = { x[0], x[1], x[2], x[3], x[0] };
68 MDOVar qo_col2[] = { x[0], x[1], x[2], x[3], x[1] };
69 double qo_values[] = { 0.5, 0.5, 0.5, 0.5, 0.5 };
70 obj.addTerms(qo_values, qo_col1, qo_col2, qo_nnz);
71
72 model.setObjective(obj, MDO_MINIMIZE);
73
74 /*------------------------------------------------------------------*/
75 /* Step 3. Solve the problem and populate optimization result. */
76 /*------------------------------------------------------------------*/
77 /* Solve the problem. */
78 model.optimize();
79
80 if(model.get(MDO_IntAttr_Status) == MDO_OPTIMAL)
81 {
82 cout << "Optimal objective value is: " << model.get(MDO_DoubleAttr_ObjVal) << endl;
83 cout << "Decision variables:" << endl;
84 int i = 0;
85 for (auto v : x)
86 {
87 cout << "x[" << i++ << "] = " << v.get(MDO_DoubleAttr_X) << endl;
88 }
89 }
90 else
91 {
92 cout<< "No feasible solution." << endl;
93 }
94
95 }
96 catch (MDOException& e)
97 {
98 std::cout << "Error code = " << e.getErrorCode() << std::endl;
99 std::cout << e.getMessage() << std::endl;
100 }
101 catch (...)
102 {
103 std::cout << "Error during optimization." << std::endl;
104 }
105
106 return static_cast<int>(MDO_OKAY);
107}