Apache常见的SimplexSolver ObjectiveFunction，用于最大化矩阵

Question

我试图通过使用apache-commons的Simplex解算器来解决以下线性问题：org.apache.commons.math3.optim.linear.SimplexSolver。

n是行数
m是列数
L是每行总和值的全局限制

这是我到目前为止所做的：

List<LinearConstraint> constraints = new ArrayList<>();

double[][] A = calculateAValues();
// m = count of columns
// constraint 1: the sum of values in all column must be <= 1
for(int i = 0; i < m; i++) {
    double[] v = new double[n];
    for(int j=0; j < n; j++) {
        v[j] = 1;
    }
    constraints.add(new LinearConstraint(v, Relationship.LEQ, 1));
}
// n = count of rows
// constraint 2: sum of a_i,j in all row must be <= L (Limit)
for(int i = 0; i < n; i++) {
    double[] v = new double[m];
    for(int j=0; j < m; j++) {
        v[j] =  A[i][j];
    }
    constraints.add(new LinearConstraint(v, Relationship.LEQ, L));
}

double[] objectiveCoefficients = new double[n * m];
for(int i = 0; i < n * m; ++i) {
    objectiveCoefficients[i] = 1;
}

LinearObjectiveFunction objective = new LinearObjectiveFunction(objectiveCoefficients, 0);
LinearConstraintSet constraintSet = new LinearConstraintSet(constraints);

SimplexSolver solver = new SimplexSolver();
PointValuePair solution = solver.optimize(objective, constraintSet, GoalType.MAXIMIZE);
return solution.getValue();

我无法正确获得目标函数，也可能缺少其他一些东西。到目前为止，我的所有尝试都产生了UnboundedSolutionException。

Answer 1

错误似乎在线性约束的系数数组中。

您有checkLevel(1,4)个变量因此约束的系数数组和目标函数的长度必须为n*m。不幸的是，n*m如果它们比目标函数的数组短，则会静默扩展约束数组。因此，您的代码未指定导致无限制解决方案的正确约束。

约束1：所有列中的值之和必须为＆lt; = 1

SimplexSolver

约束2：所有行中a_i，j的总和必须为＆lt; = L（限制）

for(int j=0; j<m; j++)
{
    double[] v = new double[n*m];
    for(int i=0; i<n; i++)
        v[i*n + j] = 1;
    constraints.add(new LinearConstraint(v, Relationship.LEQ, 1));
}

目标coffecifients：

// n = count of rows
for(int i=0; i<n; i++)
{
    double[] v = new double[n*m];
    for(int j=0; j<m; j++)
        v[i*n + j] = A[i][j];
    constraints.add(new LinearConstraint(v, Relationship.LEQ, L));
}

由于约束2，约束double[] objectiveCoefficients = new double[n * m]; Arrays.fill(objectiveCoefficients, 1.0); LinearObjectiveFunction objective = LinearObjectiveFunction(objectiveCoefficients, 0); 已经完成。 也许使用x_ij <= 1明确指定0 <= x_ij的约束会更清楚：

NonNegativeConstraint