5.2.6. MILP Modeling and Optimization in C#ΒΆ
In this section, we will utilize MindOpt C# API to model and solve the linear optimization problem in Example of Mixed-Integer Linear Programming.
First of all, we create an optimization model model:
31 // Create model
32 MDOEnv env = new MDOEnv();
33 MDOModel model = new MDOModel(env);
34 model.Set(MDO.StringAttr.ModelName, "MILP_01");
Next, we set the optimization sense to minimization via MDOModel.Set and add four decision variables using MDOModel.AddVar to specify their lower and upper bounds, variable types and names (please refer to Attributes for the detailed usage of model attributes, and C# API for other cs API information):
38 // Change to minimization problem.
39 model.Set(MDO.IntAttr.ModelSense, MDO.MINIMIZE);
40
41 // Add variables.
42 MDOVar[] x = new MDOVar[4];
43 x[0] = model.AddVar(0.0, 10.0, 1.0, 'I', "x0");
44 x[1] = model.AddVar(0.0, MDO.INFINITY, 2.0, 'I', "x1");
45 x[2] = model.AddVar(0.0, MDO.INFINITY, 1.0, 'I', "x2");
46 x[3] = model.AddVar(0.0, MDO.INFINITY, 1.0, 'C', "x3");
Next, We input the linear constraints:
49 double[][] consV = new double[][]{
50 new double[] { 1.0, 1.0, 2.0, 3.0},
51 new double[] { 1.0, 0, -1.0, 6.0}
52 };
53
54 MDOLinExpr tempLinExpr1 = new MDOLinExpr();
55 tempLinExpr1.AddTerms(consV[0], x);
56 model.AddConstr(tempLinExpr1, MDO.GREATER_EQUAL, 1.0, "c0");
57
58 MDOLinExpr tempLinExpr2 = new MDOLinExpr();
59 tempLinExpr2.AddTerms(consV[1], x);
60 model.AddConstr(tempLinExpr2, MDO.EQUAL, 1.0, "c1");
Once the model is constructed, we call MDOModel.Optimize to solve the problem:
63 model.Optimize();
We can retrieive the optimal objective value using MDOModel.Get and model attribute ObjVal, as well as optimal solutions using MDOVar.Get and attribute X. For other attributes please check Attributes.
65 if (model.Get(MDO.IntAttr.Status) == MDO.Status.OPTIMAL)
66 {
67 Console.WriteLine($"Optimal objective value is: {model.Get(MDO.DoubleAttr.ObjVal)}");
68 Console.WriteLine("Decision variables: ");
69 for(int i = 0; i < 4; i++)
70 Console.WriteLine($"x[{i}] = {x[i].Get(MDO.DoubleAttr.X)}");
71 }
72 else
73 {
74 Console.WriteLine("No feasible solution.");
75 }
Complete example codes are provided in MdoMiloEx1.cs.
1/**
2 * Description
3 * -----------
4 * Mixed Integer Linear optimization (row-wise input).
5 *
6 * Formulation
7 * -----------
8 * Minimize
9 * obj: 1 x0 + 2 x1 + 1 x2 + 1 x3
10 * Subject To
11 * c0 : 1 x0 + 1 x1 + 2 x2 + 3 x3 >= 1
12 * c1 : 1 x0 - 1 x2 + 6 x3 = 1
13 * Bounds
14 * 0 <= x0 <= 10
15 * 0 <= x1
16 * 0 <= x2
17 * 0 <= x3
18 * Integers
19 * x0 x1 x2
20 * End
21 */
22
23using Mindopt;
24
25namespace Example
26{
27 public class MdoMiloEx1
28 {
29 public static void Main(string[] args)
30 {
31 // Create model
32 MDOEnv env = new MDOEnv();
33 MDOModel model = new MDOModel(env);
34 model.Set(MDO.StringAttr.ModelName, "MILP_01");
35
36 try
37 {
38 // Change to minimization problem.
39 model.Set(MDO.IntAttr.ModelSense, MDO.MINIMIZE);
40
41 // Add variables.
42 MDOVar[] x = new MDOVar[4];
43 x[0] = model.AddVar(0.0, 10.0, 1.0, 'I', "x0");
44 x[1] = model.AddVar(0.0, MDO.INFINITY, 2.0, 'I', "x1");
45 x[2] = model.AddVar(0.0, MDO.INFINITY, 1.0, 'I', "x2");
46 x[3] = model.AddVar(0.0, MDO.INFINITY, 1.0, 'C', "x3");
47
48 // Add constraints.
49 double[][] consV = new double[][]{
50 new double[] { 1.0, 1.0, 2.0, 3.0},
51 new double[] { 1.0, 0, -1.0, 6.0}
52 };
53
54 MDOLinExpr tempLinExpr1 = new MDOLinExpr();
55 tempLinExpr1.AddTerms(consV[0], x);
56 model.AddConstr(tempLinExpr1, MDO.GREATER_EQUAL, 1.0, "c0");
57
58 MDOLinExpr tempLinExpr2 = new MDOLinExpr();
59 tempLinExpr2.AddTerms(consV[1], x);
60 model.AddConstr(tempLinExpr2, MDO.EQUAL, 1.0, "c1");
61
62 // Solve the problem and populate the result.
63 model.Optimize();
64
65 if (model.Get(MDO.IntAttr.Status) == MDO.Status.OPTIMAL)
66 {
67 Console.WriteLine($"Optimal objective value is: {model.Get(MDO.DoubleAttr.ObjVal)}");
68 Console.WriteLine("Decision variables: ");
69 for(int i = 0; i < 4; i++)
70 Console.WriteLine($"x[{i}] = {x[i].Get(MDO.DoubleAttr.X)}");
71 }
72 else
73 {
74 Console.WriteLine("No feasible solution.");
75 }
76 }
77 catch (Exception e)
78 {
79 Console.WriteLine("Exception during optimization");
80 Console.WriteLine(e.Message);
81 }
82 finally
83 {
84 model.Dispose();
85 env.Dispose();
86 }
87 }
88 }
89}