Documentation

MIP Logging

The MIP log can be divided into three sections: the presolve section, the simplex progress section, and the summary section.

Presolve Section

As with the simplex and barrier logs, the first section of the MIP log is the presolve section. Here is presolve output for MIPLIB model mas76:

Presolve removed 0 rows and 3 columns
Presolve time: 0.00s
Presolved: 12 Rows, 148 Columns, 1615 Nonzeros

In this example, presolve was able to remove 3 columns. The final line shows the size of the model that is passed to the branch-and-cut algorithm.

Progress Section

The next section in the MIP log tracks the progress of the branch-and-cut search. The search involves a number of different steps, so this section typically contains a lot of detailed information. The first thing to observe in the log for example mas76 is these lines:

Found heuristic solution: objective 93644.999
Found heuristic solution: objective 87658.484
Found heuristic solution: objective 80811.127

These indicate that the Gurobi heuristics found three integer feasible solutions before the root relaxation was solved.

The next thing you will see in the log is the root relaxation solution display. For a model where the root solves quickly, this display contains a single line:

Root relaxation: objective 3.889390e+04, 43 iterations, 0.00 seconds

For models where the root relaxation takes more time (MIPLIB model dano3mip, for example), the Gurobi solver will automatically include a detailed simplex log for the relaxation itself:

Root relaxation log...

Iteration    Objective       Primal Inf.    Dual Inf.      Time
    8370    5.6894789e+02   3.032449e+05   0.000000e+00      5s
   13770    5.6906050e+02   2.875568e+06   0.000000e+00     10s
   18758    5.6924158e+02   7.523521e+06   0.000000e+00     15s
   25649    5.7101828e+02   1.463095e+06   0.000000e+00     20s
   31400    5.7146225e+02   6.748823e+04   0.000000e+00     25s
   34230    5.7623162e+02   0.000000e+00   0.000000e+00     28s

Root relaxation: objective 5.762316e+02, 34230 iterations, 28.47 seconds

To be more precise, this more detailed log is triggered whenever the root relaxation requires more than the DisplayInterval parameter value (5 seconds by default).

The next section provides progress information on the branch-and-cut tree search:

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

     0     0  38893.904    0   11  80811.127  38893.904  51.9%     -    0s
H    0     0                       45476.147  38893.904  14.5%     -    0s
     0     0  38903.750    0   13  45476.147  38903.750  14.5%     -    0s
     0     0  38926.214    0   12  45476.147  38926.214  14.4%     -    0s
     0     0  38950.968    0   13  45476.147  38950.968  14.3%     -    0s
     0     0  38952.279    0   14  45476.147  38952.279  14.3%     -    0s
H    0     2                       43875.000  38952.279  11.2%     -    0s
H    0     2                       40005.054  38952.279  2.63%     -    0s
     0     2  38952.279    0   14  40005.054  38952.279  2.63%     -    0s
 96386 22115     cutoff   37       40005.054  39504.729  1.25%   4.0    5s
 153831 18491 infeasible   42       40005.054  39576.907  1.07%   4.0   10s
 203266 12649     cutoff   30       40005.054  39756.344  0.62%   3.9   15s

This display is somewhat dense with information, but each column is hopefully fairly easy to understand. The Nodes section (the first two columns) provides general quantitative information on the progress of the search. The first column shows the number of branch-and-cut nodes that have been explored to that point, while the second shows the number of leaf nodes in the search tree that remain unexplored. At times, there will be an H or * character at the beginning of the output line. These indicate that a new feasible solution has been found, either by a MIP heuristic (H) or by branching (*).

The Current Node section provides information on the specific node that was explored at that point in the branch-and-cut tree. It shows the objective of the associated relaxation, the depth of that node in the branch-and-cut tree, and the number of integer variables that have non-integral values in the associated relaxation.

The Objective Bounds section provides information on the best known objective value for a feasible solution (i.e., the objective value of the current incumbent), and the current objective bound provided by leaf nodes of the search tree. The optimal objective value is always between these two values. The third column in this section (Gap) shows the relative gap between the two objective bounds. When this gap is smaller than the MIPGap parameter, optimization terminates.

The Work section of the log provides information on how much work has been performed to that point. The first column shows the average number of simplex iterations performed per node in the branch-and-cut tree. The final column shows the elapsed time since the solve began.

By default, the Gurobi MIP solver prints a log line every 5 seconds (although the interval can sometimes be longer for models with particularly time-consuming nodes). The interval between log lines can be adjusted with the DisplayInterval parameter (see the Parameter section of this document for more information).

Note that the explored node count often stays at 0 for an extended period. This means that the Gurobi MIP solver is processing the root node. The Gurobi solver can often expend a significant amount of effort on the root node, generating cutting planes and trying various heuristics in order to reduce the size of the subsequent branch-and-cut tree.

Summary Section

The third section in the log provides summary information once the MIP solver has finished:

Cutting planes:
  Gomory: 6
  Cover: 5
  MIR: 8

Explored 226525 nodes (854805 simplex iterations) in 11.15 seconds
Thread count was 2 (of 2 available processors)

Optimal solution found (tolerance 1.00e-04)
Best objective 4.0005054142e+04, best bound 4.0001112908e+04, gap 0.0099%

In this example, the Gurobi solver required just over 11 seconds to solve the model to optimality, and it used two processors to do so (the processor count can be limited with the Threads parameter). The gap between the best feasible solution objective and the best bound is just under 0.01%, which produces an Optimal termination status, since the achieved gap is smaller than the default MIPGap parameter value.