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
| ObjBound - ObjVal | / | ObjVal |
where ObjBound and ObjVal are the MIP objective bound (column BestBd) and incumbent solution objective, respectively.
In the case that zero is a member of the interval between primal and dual bound, 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.