5.2.2. MILP Modeling and Optimization in CΒΆ
In this section, we will utilize MindOpt C API to model and solve the MILP problem in Example of Mixed-Integer Linear Programming.
First of all, include the header files:
27#include "Mindopt.h"
Create an optimization model m:
58 CHECK_RESULT(MDOemptyenv(&env));
59 CHECK_RESULT(MDOstartenv(env));
60 CHECK_RESULT(MDOnewmodel(env, &m, MODEL_NAME, 0, NULL, NULL, NULL, NULL, NULL));
Next, we set the optimization sense to minimization via MDOsetintattr() and add four decision variables using MDOaddvar() (please refer to C API for more detailed usages of C API):
65 /* Change to minimization problem. */
66 CHECK_RESULT(MDOsetintattr(m, MODEL_SENSE, MDO_MINIMIZE));
67
68 /* Add variables. */
69 CHECK_RESULT(MDOaddvar(m, 0, NULL, NULL, 1.0, 0, 10.0, MDO_INTEGER, "x0"));
70 CHECK_RESULT(MDOaddvar(m, 0, NULL, NULL, 2.0, 0, MDO_INFINITY, MDO_INTEGER, "x1"));
71 CHECK_RESULT(MDOaddvar(m, 0, NULL, NULL, 1.0, 0, MDO_INFINITY, MDO_INTEGER, "x2"));
72 CHECK_RESULT(MDOaddvar(m, 0, NULL, NULL, 1.0, 0, MDO_INFINITY, MDO_CONTINUOUS, "x3"));
Then we set the constraint matrix \(A\). There are two rows in \(A\) and we use the following four arrays to represent this matrix. In this context, row1_idx and row2_idx represent the positions of the non-zero elements in the first and second row of \(A\), respectively. Meanwhile, row1_val and row2_val hold the values of corresponding non-zero elements.
49 int row1_idx[] = { 0, 1, 2, 3 };
50 double row1_val[] = { 1.0, 1.0, 2.0, 3.0 };
51 int row2_idx[] = { 0, 2, 3 };
52 double row2_val[] = { 1.0, -1.0, 6.0 };
We call MDOaddconstr() to input the linear constraints into the model m:
74 /* Add constraints. */
75 CHECK_RESULT(MDOaddconstr(m, 4, row1_idx, row1_val, MDO_GREATER_EQUAL, 1.0, "c0"));
76 CHECK_RESULT(MDOaddconstr(m, 3, row2_idx, row2_val, MDO_EQUAL, 1.0, "c1"));
Once the model is constructed, we call MDOoptimize() to solve the problem:
81 CHECK_RESULT(MDOoptimize(m));
Then, we can retrieive the optimal objective value and solutions as follows:
82 CHECK_RESULT(MDOgetintattr(m, STATUS, &status));
83 if (status == MDO_OPTIMAL)
84 {
85 CHECK_RESULT(MDOgetdblattr(m, OBJ_VAL, &obj));
86 printf("The optimal objective value is %f\n", obj);
87
88 for (i = 0; i < 4; ++i)
89 {
90 CHECK_RESULT(MDOgetdblattrelement(m, X, i, &x));
91 printf("x%d = %f\n", i, x);
92 }
93 }
94 else
95 {
96 printf("No feasible solution exists\n");
97 }
Lastly, we call MDOfreemodel() and MDOfreeenv() to free the model:
30#define RELEASE_MEMORY \
31 MDOfreemodel(m); \
32 MDOfreeenv(env);
102 RELEASE_MEMORY;
Complete example codes are provided in MdoMiLoEx1.c.
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 <stdio.h>
26#include <stdlib.h>
27#include "Mindopt.h"
28
29/* Macro to check the return code */
30#define RELEASE_MEMORY \
31 MDOfreemodel(m); \
32 MDOfreeenv(env);
33#define CHECK_RESULT(code) { int res = code; if (res != 0) { fprintf(stderr, "Bad code: %d\n", res); RELEASE_MEMORY; exit(res); } }
34#define MODEL_NAME "MILP_01"
35#define MODEL_SENSE "ModelSense"
36#define STATUS "Status"
37#define OBJ_VAL "ObjVal"
38#define X "X"
39
40int main(void)
41{
42 /* Creat Model. */
43 MDOenv *env;
44 MDOmodel *m;
45 double obj, x;
46 int status, i;
47
48 /* Model data. */
49 int row1_idx[] = { 0, 1, 2, 3 };
50 double row1_val[] = { 1.0, 1.0, 2.0, 3.0 };
51 int row2_idx[] = { 0, 2, 3 };
52 double row2_val[] = { 1.0, -1.0, 6.0 };
53
54 /*------------------------------------------------------------------*/
55 /* Step 1. Create environment and model. */
56 /*------------------------------------------------------------------*/
57 /* Create an empty model. */
58 CHECK_RESULT(MDOemptyenv(&env));
59 CHECK_RESULT(MDOstartenv(env));
60 CHECK_RESULT(MDOnewmodel(env, &m, MODEL_NAME, 0, NULL, NULL, NULL, NULL, NULL));
61
62 /*------------------------------------------------------------------*/
63 /* Step 2. Input model. */
64 /*------------------------------------------------------------------*/
65 /* Change to minimization problem. */
66 CHECK_RESULT(MDOsetintattr(m, MODEL_SENSE, MDO_MINIMIZE));
67
68 /* Add variables. */
69 CHECK_RESULT(MDOaddvar(m, 0, NULL, NULL, 1.0, 0, 10.0, MDO_INTEGER, "x0"));
70 CHECK_RESULT(MDOaddvar(m, 0, NULL, NULL, 2.0, 0, MDO_INFINITY, MDO_INTEGER, "x1"));
71 CHECK_RESULT(MDOaddvar(m, 0, NULL, NULL, 1.0, 0, MDO_INFINITY, MDO_INTEGER, "x2"));
72 CHECK_RESULT(MDOaddvar(m, 0, NULL, NULL, 1.0, 0, MDO_INFINITY, MDO_CONTINUOUS, "x3"));
73
74 /* Add constraints. */
75 CHECK_RESULT(MDOaddconstr(m, 4, row1_idx, row1_val, MDO_GREATER_EQUAL, 1.0, "c0"));
76 CHECK_RESULT(MDOaddconstr(m, 3, row2_idx, row2_val, MDO_EQUAL, 1.0, "c1"));
77
78 /*------------------------------------------------------------------*/
79 /* Step 3. Solve the problem and populate optimization result. */
80 /*------------------------------------------------------------------*/
81 CHECK_RESULT(MDOoptimize(m));
82 CHECK_RESULT(MDOgetintattr(m, STATUS, &status));
83 if (status == MDO_OPTIMAL)
84 {
85 CHECK_RESULT(MDOgetdblattr(m, OBJ_VAL, &obj));
86 printf("The optimal objective value is %f\n", obj);
87
88 for (i = 0; i < 4; ++i)
89 {
90 CHECK_RESULT(MDOgetdblattrelement(m, X, i, &x));
91 printf("x%d = %f\n", i, x);
92 }
93 }
94 else
95 {
96 printf("No feasible solution exists\n");
97 }
98
99 /*------------------------------------------------------------------*/
100 /* Step 4. Free the model. */
101 /*------------------------------------------------------------------*/
102 RELEASE_MEMORY;
103
104 return 0;
105}