[SCIP] Solving the first node mip optimal

[Çiya Aydoğan]

Hello,
I implement a branch and price algorithm for a minimization problem using
SCIP in C++. I begin with artificial variables that have high objective
coefficients. I have a time limit for solving the problem. I noticed that
sometimes SCIP cannot find any better solution than the initial solution.
But, I write the lp file of the first node after column generation is done
and solve it by using the MIP solver. The solver finds the optimal solution
and it is much better than the initial solution. Is there any way to solve
mip of the first node after no eligible variable is found?
An example is below. After the first node is processed, the primal bound is
still 1.754146e+06. But, I know there exists a better solution if it is
solved as mixed integer programming.

 time | node  | left  |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows
|cuts |sepa|confs|strbr|  dualbound   | primalbou
nd  |  gap   | compl.
 23.0s|     1 |     0 |  2410 |     - |  4995k |   0 |1060 |  90 |  90 |
0 |  0 |   0 |   0 |      --      | 1.754146e
+06 |    Inf | unknown
 24.0s|     1 |     0 |  2440 |     - |  5029k |   0 |1070 |  90 |  90 |
0 |  0 |   0 |   0 |      --      | 1.754146e
+06 |    Inf | unknown
 24.0s|     1 |     0 |  2457 |     - |  5029k |   0 |1080 |  90 |  90 |
0 |  0 |   0 |   0 |      --      | 1.754146e
+06 |    Inf | unknown
 24.0s|     1 |     0 |  2485 |     - |  5029k |   0 |1090 |  90 |  90 |
0 |  0 |   0 |   0 |      --      | 1.754146e
+06 |    Inf | unknown
 25.0s|     1 |     0 |  2507 |     - |  5029k |   0 |1100 |  90 |  90 |
0 |  0 |   0 |   0 |      --      | 1.754146e
+06 |    Inf | unknown
 25.0s|     1 |     0 |  2522 |     - |  5160k |   0 |1110 |  90 |  90 |
0 |  0 |   0 |   0 |      --      | 1.754146e
+06 |    Inf | unknown
 25.0s|     1 |     0 |  2534 |     - |  5160k |   0 |1120 |  90 |  90 |
0 |  0 |   0 |   0 |      --      | 1.754146e
+06 |    Inf | unknown
 26.0s|     1 |     0 |  2539 |     - |  5160k |   0 |1129 |  90 |  90 |
0 |  0 |   0 |   0 |      --      | 1.754146e
+06 |    Inf | unknown
 26.0s|     1 |     0 |  2545 |     - |  5160k |   0 |1136 |  90 |  90 |
0 |  0 |   0 |   0 |      --      | 1.754146e
+06 |    Inf | unknown
 26.0s|     1 |     0 |  2555 |     - |  5160k |   0 |1141 |  90 |  90 |
0 |  0 |   0 |   0 |      --      | 1.754146e
+06 |    Inf | unknown
 27.0s|     1 |     0 |  2563 |     - |  5160k |   0 |1146 |  90 |  90 |
0 |  0 |   0 |   0 |      --      | 1.754146e
+06 |    Inf | unknown
 27.0s|     1 |     0 |  2566 |     - |  5160k |   0 |1148 |  90 |  90 |
0 |  0 |   0 |   0 |      --      | 1.754146e
+06 |    Inf | unknown
 27.0s|     1 |     0 |  2573 |     - |  5214k |   0 |1152 |  90 |  90 |
0 |  0 |   0 |   0 |      --      | 1.754146e
+06 |    Inf | unknown
 28.0s|     1 |     0 |  2573 |     - |  5214k |   0 |1154 |  90 |  90 |
0 |  0 |   0 |   0 |      --      | 1.754146e
+06 |    Inf | unknown
 28.0s|     1 |     0 |  2573 |     - |  5295k |   0 |1154 |  90 |  90 |
0 |  0 |   0 |   0 | 5.548602e+05 | 1.754146e
+06 | 216.14%| unknown
 time | node  | left  |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows
|cuts |sepa|confs|strbr|  dualbound   | primalbou
nd  |  gap   | compl.
 28.0s|     1 |     2 |  3744 |     - |  5637k |   0 |1154 |  90 |  90 |
0 |  1 |   0 |   0 | 5.548602e+05 | 1.754146e
+06 | 216.14%| unknown
r30.0s|     3 |     2 |  3874 | 309.0 |simplero|   2 |1201 |  90 |  92 |
0 |  0 |   0 |   0 | 5.548602e+05 | 5.571678e
+05 |   0.42%| unknown
r53.0s|    10 |     4 |  5132 | 208.4 |simplero|   6 |1428 |  90 |  96 |
0 |  0 |   0 |   0 | 5.555913e+05 | 5.559756e
+05 |   0.07%|  30.94%

Best,
Çiya
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