Sometimes in the Gurobi log, you might see an increase in the gap. In the example below, the gap increases from 113% up to 4171%, before it decreases again.
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
1503 1467 -283.00000 284 285 2160.99979 -285.00000 113% 609 127s
H 1968 1870 1858.0000000 -285.00000 115% 662 145s
[...]
4854 3038 -257.55772 357 368 13.00000 -285.00000 2292% 1044 919s
H 4924 2950 8.0000000 -285.00000 3662% 1050 919s
5130 3120 -246.16119 393 407 8.00000 -285.00000 3662% 1044 942s
H 5317 3172 7.0000000 -285.00000 4171% 1059 942s
5630 3377 infeasible 468 7.00000 -285.00000 4171% 1042 969s
5716 3420 -285.00000 21 472 7.00000 -285.00000 4171% 1058 993s
5937 3615 -284.00000 77 403 7.00000 -285.00000 4171% 1057 1024s
H 5938 3615 2.0000000 -285.00000 - 1057 1024s
[...]
8623 6061 -213.60040 141 748 2.00000 -285.00000 - 1219 1487s
H 8848 6207 -103.0000000 -285.00000 177% 1210 1487s
9149 6446 infeasible 191 -103.00000 -285.00000 177% 1199 1561s
9675 6904 -280.00000 114 725 -103.00000 -285.00000 177% 1182 1626s
[...]
H18133 14145 -118.0000000 -285.00000 142% 1015 3309s
18258 14238 -264.98878 195 590 -118.00000 -285.00000 142% 1020 3408s
18590 14461 -198.90509 211 630 -118.00000 -285.00000 142% 1027 3622s
H18749 815 -284.0000000 -285.00000 0.35% 1025 3622s
This is expected behavior in certain cases. The relative MIP gap is computed as
\[\frac{\left| \text{ObjBound} - \text{ObjVal} \right|}{\left| \text{ObjVal} \right|}\]
where ObjBound and ObjVal are the MIP objective bound (column BestBd) and incumbent solution objective, respectively.
If primal and dual bound have different signs, the interpretation of the MIP gap value may not make sense.
When the gap is larger than 9999%, Gurobi will not print it in the log in order to avoid formatting issues. In these cases a - is shown; note that- is also displayed for models without an incumbent solution.
It would be possible to add a constant to the objective function that is large enough to make sure that the objective is always positive. Doing this would, however, change the meaning of the gap.