Microsoft Solver Foundation 对一个简单的 ILP 给出了错误的答案

我想使用 Microsoft Solver Foundation 解决 C# 中的二元线性问题。我不知道为什么我得到了错误的答案。目标值应该是 41.1，但我得到 213。5 个变量的值应该是 1，其他变量应该是 0。但是我得到了很多错误值的变量。

矩阵每行的总和应 约束_arr我得到了正确的限制。

谢谢你的帮助。

定义决策变量：

        SolverContext context = SolverContext.GetContext();
        Model model = context.CreateModel();
        Decision[,] x = new Decision[name_column.Length, 7];

        for (int i = 0; i < name_column.Length; i++)
        {
            for (int j = 0; j < 7; j++)
            {
                x[i, j] = new Decision(Domain.IntegerRange(0,1), "x" + i + j);
            }
        }

        for (int i = 0; i < name_column.Length; i++)
        {
            for (int j = 0; j < 7; j++)
            {
                model.AddDecisions(x[i, j]);
            }
        }

创建约束并将其添加到模型中：

Term[] Constraint_arr = new Term[name_column.Length];
        Term tempC;
        int jj;
        for (int i = 0; i < name_column.Length; i++)
        {
            tempC = 0;
            for (jj= 0; jj < 7; jj++)
            {
                if(vars_Matrix[i,jj] == 1)
                {
                    tempC += x[i,jj];
                }
            }
            Constraint_arr[i] = tempC;
            model.AddConstraints("constraint" + i, Constraint_arr[i] <= 1);
        }

创建目标函数：

        Term objective_Func = 0;
        Term tempZ;
        for (int i = 0; i < name_column.Length; i++)
        {
            tempZ = 0;
            for (int j = 0; j < 7; j++)
            {
                tempZ += x[i, j] * ratio[i];
            }
            objective_Func+= tempZ;
        }

        model.AddGoal("Goal", GoalKind.Maximize, objective_Func);

打印答案：

        Solution solution = context.Solve(new SimplexDirective());

        Report report = solution.GetReport();

        for (int i = 0; i < name_column.Length; i++)
        {
            for (int j = 0; j < 7; j++)
            {
                Console.Write(x[i, j]);
            }
            Console.WriteLine();
        }

        
        Console.Write("{0}", report);
        Console.ReadLine();

以下 MiniZinc 模型的目标最大值为 14：

set of int: rows = 1..5;
set of int: cols = 1..7;
array[rows, cols] of 0..1: vars_Matrix = [|0, 0, 1, 0, 1, 1, 1
                                          |0, 0, 1, 1, 0, 1, 1
                                          |0, 0, 1, 0, 0, 0, 0
                                          |0, 0, 1, 1, 0, 1, 1
                                          |0, 0, 0, 0, 1, 0, 0|];
                                          
array[cols] of var 0..1: c;
var int: obj;

%  constraint 
%      obj = sum(i in rows)(
%              sum(j in cols) (
%                c[i] * vars_Matrix[i, j]
%              )
%            );

constraint
  obj = sum([ sum([ c[i] * vars_Matrix[i, j] | j in cols ]) | i in rows ]);    

solve maximize(obj);                                     

Output

c = array1d(1..7, [1, 1, 1, 1, 1, 1, 1]);
obj = 14;     

从以下 Z3py 模型得到相同的结果：

    from z3 import *
    
    s = Optimize()
    
    Rows = range(5);
    Cols = range(7);
    vars_Matrix = [[0, 0, 1, 0, 1, 1, 1],
                   [0, 0, 1, 1, 0, 1, 1],
                   [0, 0, 1, 0, 0, 0, 0],
                   [0, 0, 1, 1, 0, 1, 1],
                   [0, 0, 0, 0, 1, 0, 0]]
                                              
    c = [Int("c" + str(i+1)) for i in Rows]
    obj = Int("obj")
    
    for i in Rows:
        s.add(c[i] >= 0, c[i] <= 1)
    
    s.add(obj == Sum( [ Sum( [ c[i] * vars_Matrix[i][j] for j in Cols ] ) for i in Rows ] ))
    
    s.maximize(obj)
    
    if sat == s.check():
        print(s.model())
    else:
        print("No solution. Sorry!")