Confusion about MILP log: "best objective" not part of solutions, gap doesn't match
Ongoing
Hello,
I try to minimze an MILP problem of which I know that the optimal solution is 0. I formulated the problem in Matlab 2020b using the latest version of YALMIP as interface and Gurobi v9.1.1. However, the termination doesn't seem to work and the log is inconsistent. Below, I'm reporting some logs and my observations
1. I was puzzled that the solver doesn't report a gap and hence doesn't terminate although an optimal heuristic objective was found
Root relaxation: objective 0.000000e+00, 18016 iterations, 4.16 seconds
Total elapsed time = 11.89s
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 0.00000 0 10 - 0.00000 - - 12s
H 0 0 0.0000000 0.00000 - - 14s
0 0 0.00000 0 7 0.00000 0.00000 - - 21s
[shortened]
120067 18163 0.00000 293 3 0.00000 0.00000 - 16.9 1686s
Interrupt request received
120683 18175 - 289 0.00000 0.00000 - 16.9 1691s
Explored 121075 nodes (2087179 simplex iterations) in 1691.73 seconds
Thread count was 4 (of 32 available processors)
Solution count 1: 1.39698e-09
No other solutions better than 5.33873e-10
Solve interrupted
Best objective 0.000000000000e+00, best bound 0.000000000000e+00, gap 0.0000%
Already noticeable: the best objective is not part of the solutions presented with "Solution count" which I attributed to the solve interruption.
Regarding the gap: my assumption was that the best bound is perfect 0, i.e. the gap can only be 100% or 0% (taking gap = (incumbent-bestBound)/incumbent).
2. To avoid the 0% gap problem, I added a constant offset of 1e-5 to the objective function. Gurobi could solve the problem as expected, but the log is still inconstitent
Root relaxation: objective 9.998679e-06, 54585 iterations, 14.42 seconds
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 0.0000100 0.00001 0.00% - 18s
Explored 0 nodes (54585 simplex iterations) in 18.21 seconds
Thread count was 4 (of 32 available processors)
Solution count 1: 9.98937e-06
Optimal solution found (tolerance 5.00e-04)
Warning: max constraint violation (1.8059e-04) exceeds tolerance
Best objective 1.000000000000e-05, best bound 9.989365935326e-06, gap 0.1063%
Optimization completed in 25.35 s
Again, the best objective reported (1.00e-5) doesn't agree with the solution reported (9.99e-6). In addition, the final gap reported (0.1063%) doesn't match the 0.00% gap shown in the B&C log.
At this point, I'm not sure if there is a fundamental problem or if I'm just misreading the logs. Hope somebody can help here.
Best,
Lukas
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Hi Lukas,
Could you share the Problem statistics reported in the first ~30 lines of an optimization run? Is it possible for you to share an instance of the problem to make an investigation easier? You can share files as described in Posting to the Community Forum.
Best regards,
Jaromił0
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