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I have a hard problem where I fix some variables to solve it. However, the time elapsed in the root node is high. Is there a way to limit this time anf force the Gurobi start the ramification? I have used a more intensive use of heuristics, setting heuristics=0.5 but this not modify the result. Also, I have put MIPFocus=2 (focus in the optimality, because I have an integer solution) but the same occurs. Finally, I have generated agressive cuts, by setting Cuts=3 (very agressive cuts). Any hints for a hard problem where I have an integer solution and I want to improve it?
Below, the Gurobi report:

Gurobi Optimizer version 9.1.1 build v9.1.1rc0 (win64)
Thread count: 6 physical cores, 12 logical processors, using up to 12 threads
Optimize a model with 39532 rows, 354622 columns and 2115422 nonzeros
Model fingerprint: 0xd0f7b3b4
Variable types: 353702 continuous, 920 integer (920 binary)
Coefficient statistics:
  Matrix range     [3e-02, 2e+06]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+00, 1e+05]

User MIP start produced solution with objective 1.29497e+07 (1.65s)
Loaded user MIP start with objective 1.29497e+07
MIP start from previous solve did not produce a new incumbent solution
Processed MIP start in 3.43 seconds

Presolve removed 13263 rows and 150352 columns
Presolve time: 2.54s
Presolved: 26269 rows, 204270 columns, 798510 nonzeros
Variable types: 204030 continuous, 240 integer (240 binary)

Deterministic concurrent LP optimizer: primal and dual simplex
Showing first log only...

Presolve removed 89 rows and 15 columns
Presolved: 26180 rows, 204255 columns, 798115 nonzeros


Root simplex log...

Iteration    Objective       Primal Inf.    Dual Inf.      Time
       0    4.8264544e+06   3.619471e+05   1.790064e+11      7s
   85250    1.6296806e+07   3.139628e+01   6.082984e+08     10s
Concurrent spin time: 0.01s

Solved with dual simplex

Root relaxation: objective 1.254877e+07, 49428 iterations, 4.83 seconds

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

     0     0 1.2549e+07    0   69 1.2950e+07 1.2549e+07  3.10%     -   12s
     0     0 1.2561e+07    0   64 1.2950e+07 1.2561e+07  3.00%     -   18s
     0     0 1.2571e+07    0   60 1.2950e+07 1.2571e+07  2.92%     -   21s
     0     0 1.2607e+07    0   63 1.2950e+07 1.2607e+07  2.65%     -   23s
     0     0 1.2615e+07    0   67 1.2950e+07 1.2615e+07  2.58%     -   25s
     0     0 1.2616e+07    0   70 1.2950e+07 1.2616e+07  2.58%     -   26s
     0     0 1.2616e+07    0   72 1.2950e+07 1.2616e+07  2.58%     -   27s
     0     0 1.2616e+07    0   72 1.2950e+07 1.2616e+07  2.58%     -   27s
     0     0 1.2616e+07    0   72 1.2950e+07 1.2616e+07  2.58%     -   27s
     0     0 1.2616e+07    0   72 1.2950e+07 1.2616e+07  2.58%     -   28s
     0     0 1.2616e+07    0   72 1.2950e+07 1.2616e+07  2.58%     -   28s
     0     0 1.2616e+07    0   72 1.2950e+07 1.2616e+07  2.58%     -   28s
     0     0 1.2616e+07    0   72 1.2950e+07 1.2616e+07  2.58%     -   28s
     0     0 1.2616e+07    0   72 1.2950e+07 1.2616e+07  2.58%     -   28s
     0     0 1.2620e+07    0   56 1.2950e+07 1.2620e+07  2.54%     -   35s
     0     0 1.2635e+07    0   59 1.2950e+07 1.2635e+07  2.43%     -   43s
     0     0 1.2639e+07    0   68 1.2950e+07 1.2639e+07  2.40%     -   45s
     0     0 1.2641e+07    0   59 1.2950e+07 1.2641e+07  2.39%     -   48s
     0     0 1.2641e+07    0   58 1.2950e+07 1.2641e+07  2.38%     -   49s
     0     0 1.2641e+07    0   59 1.2950e+07 1.2641e+07  2.38%     -   50s
     0     0 1.2642e+07    0   59 1.2950e+07 1.2642e+07  2.38%     -   50s
     0     0 1.2642e+07    0   59 1.2950e+07 1.2642e+07  2.38%     -   51s
     0     0 1.2642e+07    0   59 1.2950e+07 1.2642e+07  2.38%     -   51s
     0     0 1.2653e+07    0   73 1.2950e+07 1.2653e+07  2.29%     -   68s
     0     0 1.2656e+07    0   77 1.2950e+07 1.2656e+07  2.27%     -   75s
     0     0 1.2657e+07    0   59 1.2950e+07 1.2657e+07  2.26%     -   77s
     0     0 1.2658e+07    0   77 1.2950e+07 1.2658e+07  2.25%     -   78s
     0     0 1.2658e+07    0   71 1.2950e+07 1.2658e+07  2.25%     -   79s
     0     0 1.2658e+07    0   71 1.2950e+07 1.2658e+07  2.25%     -   80s
     0     0 1.2661e+07    0   71 1.2950e+07 1.2661e+07  2.23%     -   94s
     0     0 1.2663e+07    0  100 1.2950e+07 1.2663e+07  2.21%     -  101s
     0     0 1.2663e+07    0   88 1.2950e+07 1.2663e+07  2.21%     -  103s
     0     0 1.2664e+07    0   96 1.2950e+07 1.2664e+07  2.21%     -  105s
     0     0 1.2664e+07    0   93 1.2950e+07 1.2664e+07  2.21%     -  106s
     0     0 1.2664e+07    0   94 1.2950e+07 1.2664e+07  2.21%     -  106s
     0     0 1.2668e+07    0   73 1.2950e+07 1.2668e+07  2.18%     -  120s
     0     0 1.2668e+07    0   42 1.2950e+07 1.2668e+07  2.18%     -  123s
     0     0 1.2668e+07    0   49 1.2950e+07 1.2668e+07  2.17%     -  125s
     0     0 1.2668e+07    0   54 1.2950e+07 1.2668e+07  2.17%     -  126s
     0     0 1.2670e+07    0   85 1.2950e+07 1.2670e+07  2.16%     -  138s
     0     0 1.2670e+07    0   51 1.2950e+07 1.2670e+07  2.16%     -  145s
     0     0 1.2671e+07    0   67 1.2950e+07 1.2671e+07  2.15%     -  147s
     0     0 1.2671e+07    0   75 1.2950e+07 1.2671e+07  2.15%     -  149s
     0     0 1.2671e+07    0   75 1.2950e+07 1.2671e+07  2.15%     -  151s
     0     0 1.2671e+07    0   59 1.2950e+07 1.2671e+07  2.15%     -  151s
     0     0 1.2673e+07    0   80 1.2950e+07 1.2673e+07  2.14%     -  164s
     0     0 1.2673e+07    0   68 1.2950e+07 1.2673e+07  2.13%     -  175s
     0     0 1.2674e+07    0   63 1.2950e+07 1.2674e+07  2.13%     -  176s
     0     0 1.2674e+07    0   87 1.2950e+07 1.2674e+07  2.13%     -  178s
     0     0 1.2674e+07    0   73 1.2950e+07 1.2674e+07  2.13%     -  179s
     0     0 1.2675e+07    0   85 1.2950e+07 1.2675e+07  2.12%     -  198s
     0     0 1.2676e+07    0   72 1.2950e+07 1.2676e+07  2.12%     -  206s
     0     0 1.2676e+07    0   78 1.2950e+07 1.2676e+07  2.12%     -  208s
     0     0 1.2676e+07    0  101 1.2950e+07 1.2676e+07  2.11%     -  211s
     0     0 1.2676e+07    0   86 1.2950e+07 1.2676e+07  2.11%     -  212s
     0     0 1.2677e+07    0   78 1.2950e+07 1.2677e+07  2.11%     -  225s
     0     0 1.2677e+07    0   74 1.2950e+07 1.2677e+07  2.10%     -  242s
     0     0 1.2678e+07    0   71 1.2950e+07 1.2678e+07  2.10%     -  244s
     0     0 1.2678e+07    0   76 1.2950e+07 1.2678e+07  2.10%     -  246s
     0     0 1.2678e+07    0   78 1.2950e+07 1.2678e+07  2.10%     -  248s
     0     0 1.2679e+07    0   69 1.2950e+07 1.2679e+07  2.09%     -  268s
     0     0 1.2680e+07    0   73 1.2950e+07 1.2680e+07  2.09%     -  281s
     0     0 1.2680e+07    0   72 1.2950e+07 1.2680e+07  2.09%     -  283s
     0     0 1.2680e+07    0   69 1.2950e+07 1.2680e+07  2.08%     -  297s

(the CPU is short because this is a small instance of the problem.)

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  • 3
    $\begingroup$ Before trying to adjust Gurobi parameter values, I suggest using the current version of Gurobi. Also, the magnitude of the objective value is quite large, which suggests poor numerical scaling of the problem; so you should try ti improve that. Some of the matrix and RHS values are quite large - perhaps your model has a very large value of Big M (which is not a good thing)? But the scaling problems go beyond Big M values. $\endgroup$ Commented Jun 25 at 15:35
  • 5
    $\begingroup$ Turning up the intensity of heuristics and cut generation is likely to cause the solver to spend more, not less, time on the root node. $\endgroup$
    – prubin
    Commented Jun 25 at 16:22
  • $\begingroup$ Try using the VarBranch parameter to disable strong branching, although I'm not sure that it will actually disable strong branching at the root node. And disabling cuts, or some of them, should help. $\endgroup$
    – Brannon
    Commented Jun 27 at 12:13

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