Cplex Refiner：如何仅添加左手或右手的现有约束？

Question

cplex 精简器发现了破坏的约束。我想向用户展示有关其模型实际冲突的详细信息。

因此我想将矩阵的每个约束拆分为单独的约束。左撇子和右撇子。示例：

10 <= x1 <= 40

应该变成

10 <= x1 <= infinity
-infinity <= x1 <= 40

这在数学上是相等的。

IBM 关于 cplex 精炼器 (http://www-01.ibm.com/support/docview.wss?uid=swg21429472) 的示例使用这段代码来考虑约束：

for (int c1 = 0; c1 < rng.Length; c1++)
{
    constraints[c1] = rng[c1];
}

我稍微更新了它，以拆分约束（请注意：IBM 的示例大量使用约束数组的索引。所有这些位置也需要更新）

for (int c1 = 0; c1 < rng.Length; c1++)
{
    constraints[c1] = cplex.Ge(rng[c1].Expr, rng[c1].LB);
}
for (int c1 = 0; c1 < rng.Length; c1++)
{
    constraints[rng.Length + c1] = cplex.Le(rng[c1].Expr, rng[c1].UB);
}

这是我使用的模型文件。（x1 的边界显然与 c3 和 c4 冲突。）

 Maximize
      obj: x1 + 2 x2 + 3 x3
 Subject To
      c1:  x2 + x3 <= 20
      c2: x1 - 3 x2 + x3 <= 30
      c3: x1 <= 40
      c4: x1 >= 40
 Bounds
      10 <= x1 <= 10    
 Generals
      x1 x2 x3
 End

具有拆分约束的更新版本的代码打印出损坏的结果（先是左侧，然后是右侧）。它只显示 x1 是冲突的一部分（你不能认为它本身就是冲突。它需要有一个伙伴！）

Solution status = Infeasible
Model Infeasible, Calling CONFLICT REFINER
Number of SOSs=0
IloRange  : -infinity <= (1*x2 + 1*x3) <= infinity
IloRange  : -infinity <= (1*x1 - 3*x2 + 1*x3) <= infinity
IloRange  : -infinity <= (1*x1) <= infinity
IloRange  : 40 <= (1*x1) <= infinity
IloRange  : -infinity <= (1*x2 + 1*x3) <= 20
IloRange  : -infinity <= (1*x1 - 3*x2 + 1*x3) <= 30
IloRange  : -infinity <= (1*x1) <= 40
IloRange  : -infinity <= (1*x1) <= infinity
Lower bound of x1
Upper bound of x1
Lower bound of x2
Upper bound of x2
Lower bound of x3
Upper bound of x3
Conflict Refinement process finished: Printing Conflicts
 Proved : Upper bound of x1
Conflict Summary:
 Constraint conflicts = 0
 Variable Bound conflicts = 1
 SOS conflicts = 0
Calling FEASOPT

原版的双手约束打印出了预期的结果（c4和x1有部分冲突）

Solution status = Infeasible
Model Infeasible, Calling CONFLICT REFINER
Number of SOSs=0
IloRange c1 : -infinity <= (1*x2 + 1*x3) <= 20
IloRange c2 : -infinity <= (1*x1 - 3*x2 + 1*x3) <= 30
IloRange c3 : -infinity <= (1*x1) <= 40
IloRange c4 : 40 <= (1*x1) <= infinity
Lower bound of x1
Upper bound of x1
Lower bound of x2
Upper bound of x2
Lower bound of x3
Upper bound of x3
Conflict Refinement process finished: Printing Conflicts
 Proved : IloRange c4 : 40 <= (1*x1) <= infinity
 Proved : Upper bound of x1
Conflict Summary:
 Constraint conflicts = 1
 Variable Bound conflicts = 1
 SOS conflicts = 0
Calling FEASOPT

Answer 1

RefineConflict 的文档对 cons 参数说明如下：

An array of constraints. They may be IRange or IAnd constructs on a set of ranges. Only constraints directly added to the model can be specified.

在您修改后的代码段中，您正在向 constraints 数组添加新约束，其中未被添加到模型中（例如，您使用 Ge 方法而不是 AddGe 方法）。

我想您可以执行以下操作：

cplex.Remove(rng); // First remove the original constraints
for (int c1 = 0; c1 < rng.Length; c1++)
{
    IRange tmp = rng[c1];
    // Now, add new constraints to the model and save them in the constraints array.
    constraints[c1] = cplex.AddGe(tmp.Expr, tmp.LB);
    constraints[rng.Length + c1] = cplex.AddLe(tmp.Expr, tmp.UB);
}

您应该在调用 RefineConflict 之前添加以下行，以确保修改后的模型看起来像您期望的那样：

cplex.ExportModel("modified.lp");

Cplex Refiner：如何仅添加左手或右手的现有约束？

Cplex Refiner: How to add existing Constraints only left- or right-handed?

cplex