为什么 Gurobi 中探索的节点数显示为零？

Question

我在Gurobi实现了一个数学模型，我想知道为什么探索的节点数是0。跟踪文件如下所示：

Optimize a model with 276 rows, 492 columns and 1434 nonzeros
Model has 324 general constraints
Variable types: 0 continuous, 492 integer (492 binary)
Coefficient statistics:
  Matrix range     [1e+00, 5e+02]
  Objective range  [2e-02, 8e-02]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+00, 8e+03]
Found heuristic solution: objective 3900
Presolve removed 335 rows and 570 columns
Presolve time: 0.01s
Presolved: 265 rows, 246 columns, 1302 nonzeros
Variable types: 0 continuous, 246 integer (246 binary)

Root relaxation: objective 3.900689e+03, 43 iterations, 0.00 seconds

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0 3900.68909    0    9 3900.00000 3900.68909  0.02%     -    0s
H    0     0                    3900.6420000 3900.68909  0.00%     -    0s

Explored 0 nodes (104 simplex iterations) in 0.03 seconds
Thread count was 8 (of 8 available processors)

Solution count 2: 3900.64 3900 
Pool objective bound 3900.69

Optimal solution found (tolerance 1.00e-04)
Best objective 3.900642000000e+03, best bound 3.900689090909e+03, gap 0.0012%
Optimal objective: 3900.64

上面说找到了最优解，这点我同意，但这是正常情况吗？

不得不说我的数学模型的输入量很小，有道理吗？

谢谢。

Answer 1

Gurobi 在根节点中求解了您的模型，因为启发式算法找到了 objective 值为 3900.6420000 的可行解。这个解决方案在期望的 MIP 差距之内，因此在 Gurobi 开始真正构建分支定界树之前解决过程已经完成。根节点被视为节点零。这是它最后说它没有探索任何节点的方式。

为什么 Gurobi 中探索的节点数显示为零？

Why number of explored nodes in Gurobi is showing zero?

python

mathematical-optimization

gurobi