[Cbc] Cbc incorrect concludes integer infeasible for MIQP

[Jan-Willem Goossens]

Hi,

I’m using CBC 2.10.3 to solve the attached small MIQP (MIP with quad objective), but the solution is reported as “Integer infeasible”, which is not correct.

The actual solution is x1=1, x2=1, with obj value -7.5. Continuous relaxation solution is x1 = 0.66, x2 = 1.333  with obj value -8.22222. See https://www.inverseproblem.co.nz/OPTI/index.php/Probs/MIQP

The command I use is
cbc -import testmiqp.mps -minimize -solve -solution sol.txt

The output shows interesting lines:
                […]
Clp0000I Optimal - objective value -7.5
Cbc0012I Integer solution of -7.5 found by feasibility pump after 0 iterations and 0 nodes (0.00 seconds)
Cbc0001I Search completed - best objective -7.5, took 0 iterations and 0 nodes (0.00 seconds)
Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost
Clp0006I 0  Obj -7.5
Clp0000I Optimal - objective value -7.5
obj -7.5
Continuous objective value is -9 - 0.00 seconds
Testing OsiObject options 0
Cbc0006I The LP relaxation is infeasible or too expensive
[…]

So Feasibility Pump finds the integer solution with obj value -7.5, but then reported Continuous objective value of -9 seems incorrect.

How can I solve this MIQP with cbc?

Many thanks for any help.

Jan-Willem



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