The MIP log can be divided into three sections: the presolve section, the simplex progress section, and the summary 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
Presolve removed 0 rows and 3 columns Presolve time: 0.00s Presolved: 12 Rows, 148 Columns, 1615 NonzerosIn 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.
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 80811.127These 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 secondsTo 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 203266 12649 cutoff 30 40005.054 39756.344 0.62% 3.9 10sThis display is somewhat dense with information, but each column is hopefully fairly easy to understand. The
Nodessection (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
*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 (
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.
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
Gap) shows the relative gap between the two objective
bounds. When this gap is smaller than 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.
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
Optimaltermination status, since the achieved gap is smaller than the default MIPGap parameter value.