Gurobi MIP doesn't give optimal when under certain Start when Presolve is turned off.

[FANG Colin]

A simple MIP model (attached)

m = read_model("357.mps")



Gurobi Model:
    type   : LP (MIP)
    sense  : minimize
    number of variables             = 764
    number of linear constraints    = 639
    number of quadratic constraints = 0
    number of sos constraints       = 0
    number of non-zero coeffs       = 1796
    number of non-zero qp objective terms  = 0
    number of non-zero qp constraint terms = 0

If I don't specify a Start, it solves well with or without Presolve

Optimize a model with 639 rows, 764 columns and 1796 nonzeros
Coefficient statistics:
  Matrix range    [4e-01, 2e+04]
  Objective range [1e+00, 1e+00]
  Bounds range    [1e+00, 1e+04]
  RHS range       [6e-01, 1e+04]


MIP start did not produce a new incumbent solution
MIP start violates constraint R0 by 1.00


Variable types: 0 continuous, 764 integer (485 binary)
Found heuristic solution: objective -1.0000000


Root relaxation: objective -3.999789e+00, 213 iterations, 0.00 seconds


    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time


     0     0   -3.99979    0   56   -1.00000   -3.99979   300%     -    0s
Another try with MIP start
     0     0   -2.99821    0  118   -1.00000   -2.99821   200%     -    0s
     0     0   -2.99821    0  110   -1.00000   -2.99821   200%     -    0s
     0     0   -2.99821    0   62   -1.00000   -2.99821   200%     -    0s
H    0     0                      -3.0000000   -3.00000  0.00%     -    0s


Cutting planes:
  Learned: 4
  Gomory: 2
  Cover: 15
  Implied bound: 19
  Clique: 110
  MIR: 7
  Flow cover: 1


Explored 0 nodes (587 simplex iterations) in 0.04 seconds
Thread count was 1 (of 2 available processors)


Optimal solution found (tolerance 0.00e+00)
Best objective -3.000000000000e+00, best bound -3.000000000000e+00, gap 0.0%

If I specify a feasible Start, or it inherits from previous feasible solution with other objectives. The result is sub-optimal if Presolve is disabled.

Optimize a model with 639 rows, 764 columns and 1796 nonzeros
Coefficient statistics:
  Matrix range    [4e-01, 2e+04]
  Objective range [1e+00, 1e+00]
  Bounds range    [1e+00, 1e+04]
  RHS range       [6e-01, 1e+04]


Loaded MIP start with objective -1


Variable types: 0 continuous, 764 integer (485 binary)


Root relaxation: objective -3.999789e+00, 213 iterations, 0.00 seconds


    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time


     0     0   -3.99979    0   56   -1.00000   -3.99979   300%     -    0s
     0     0   -2.99821    0  118   -1.00000   -2.99821   200%     -    0s
H    0     0                      -2.0000000   -2.99821  49.9%     -    0s


Cutting planes:
  Cover: 3
  Implied bound: 10
  Clique: 127
  MIR: 1


Explored 0 nodes (544 simplex iterations) in 0.04 seconds
Thread count was 1 (of 2 available processors)


Optimal solution found (tolerance 0.00e+00)
Best objective -2.000000000000e+00, best bound -2.000000000000e+00, gap 0.0%

The example start is 

xx = [
    0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
    10000,10000,-10000,-10000,0,0,10000,10000,-10000,-10000,0,0,10000,10000,-10000,-10000,
    0,0,0,10000,10000,-10000,-10000,0,0,10000,10000,-10000,-10000,0,0,10000,10000,-10000,-10000,
    0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,
    1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,
    1,0,0,1,1,0,0,1,0,0,0,0,1,0,0,0,0,1,1,1,1,0,6,2,2,2,1,3,3,2,1,2,1,1,3,3,1,1,2,1,4,4,2,2,5,0,1,
    0,1,1,-1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,10000,10000,-10000,-10000,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,
    0,0,0,0,0,0,10000,10000,-10000,10000,0,0,0,0,1,0,0,5000,0,5000,0,1,0,10000,10000,-10000,10000,
    0,0,0,0,0,0,5000,0,5000,0,1,10000,10000,-10000,-10000,0,0,10000,10000,-10000,-10000,0,0,0,1,0,0,
    0,0,1,1,0,0,0,0,1,0,0,3,4,1,2,10000,0,10000,10000,-10000,0,0,0,0,1,0,0,5000,5000,0,1,0,1,0,0,0,0,
    0,0,1,0,1,0,0,0,0,1,0,1,4,2,3,0,0,10000,10000,-10000,-10000,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,
    0,0,10000,10000,-10000,-10000,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,10000,10000,-10000,-10000,0,
    10000,10000,-10000,-10000,0,0,0,0,0,1,1,0,0,0,1,0,0,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,
    0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,10000,10000,-10000,
    -10000,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,2,1,1,1,1,1,1,2,0,3,2,10003,3,10002,3,3,3,-9999,-1,10000,
    0,4,2,6,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10000,0,0,1,0,0,0,0,0,
    0,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0,0,0,1,0,0,0,10000,10000,-10000,0,0,0,0,0,5000,5000,
    0,0,0,10000,10000,-10000,-10000,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10000,10000,-10000,-10000,0,0,
    10000,10000,-10000,-10000,2,1,1,1,2,2,1,1,0,10002,2,1,1,10001,4,10002,-9999,0,-3,7,3,4,3,0,0,0,0,
    0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0,0,1,1,
    1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,0,1,1,-1,1,1,0,0,0,1,1,0,10000,10000,-10000,-10000
];

[Renan Garcia]

Can you please upgrade to the latest version of Gurobi (which is currently 7.0.1) to see if that resolves the issue?

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<357.mps>

[FANG Colin]

The issue occurred in v6.5.0

I don't have a license for v7.0.1 at the moment. Will test it as soon as I get the license.