Potential Numerical Bug in MIP Solving

Hi,

I have a small MIP instance in LP format:

\* seed *\
Minimize
OBJ: - 48.46 x0 - 25.81 x1
Subject To
_C1: 43.67 x0 - 65.24 x1 <= -2955.43
_C2: - 29.71 x0 - 3.98 x1 <= 2826.08
_C3: 42.8 x0 - 42.76 x1 <= 1744.85
_C4: 93.3 x0 + 68.89 x1 <= -2690.66
_C5: - 66.99 x0 + 21.22 x1 >= 1779.93
_C6: 0.45 x0 - 54.36 x1 <= 14.06
Bounds
 -200 <= x0 <= 200
 -200 <= x1 <= 200
Generals
x0
x1
End

Gurobi returns the correct answer with IntFeasTol=1e-9 or just by default:

Objective: 1593.3900000000003
x0 = -43.0
x1 = 19.0

But with IntFeasTol=1e-9, DualReductions=0 and CutPasses=0 (probably disable these two features), Gurobi returns with:

Objective: 1616.0400000000004
x0 = -44.0
x1 = 20.0

Is this consistency expected? Any suggestions or explanations are appreciated! Thanks.

I am using Gurobi 12.0.2 on Ubuntu 22.04 and macOS.

The log on mac:

$> gurobi_cl IntFeasTol=1e-9 DualReductions=0 CutPasses=0 seed.lp
Set parameter Username
Set parameter LicenseID to value 2670279
Set parameter IntFeasTol to value 1e-09
Set parameter CutPasses to value 0
Set parameter DualReductions to value 0
Set parameter LogFile to value "gurobi.log"
Using license file /Users/zxt/gurobi.lic
Academic license - for non-commercial use only - expires 2026-05-24

Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (mac64[arm] - Darwin 24.0.0 24A335)
Copyright (c) 2025, Gurobi Optimization, LLC

Read LP format model from file seed.lp
Reading time = 0.00 seconds
OBJ: 6 rows, 2 columns, 12 nonzeros

Using Gurobi shared library /Library/gurobi1202/macos_universal2/lib/libgurobi120.dylib

CPU model: Apple M2
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Non-default parameters:
IntFeasTol  1e-09
CutPasses  0
DualReductions  0

Optimize a model with 6 rows, 2 columns and 12 nonzeros
Model fingerprint: 0x91a7ebb9
Variable types: 0 continuous, 2 integer (0 binary)
Coefficient statistics:
  Matrix range     [5e-01, 9e+01]
  Objective range  [3e+01, 5e+01]
  Bounds range     [2e+02, 2e+02]
  RHS range        [1e+01, 3e+03]
Presolve removed 2 rows and 0 columns
Presolve time: 0.00s
Presolved: 4 rows, 2 columns, 8 nonzeros
Variable types: 0 continuous, 2 integer (0 binary)

Root relaxation: objective 1.575266e+03, 1 iterations, 0.00 seconds (0.00 work units)

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

     0     0 1575.26584    0    1          - 1575.26584      -     -    0s
H    0     0                    1619.2000000 1577.01435  2.61%     -    0s
H    0     0                    1616.0400000 1577.01435  2.41%     -    0s
     0     0 1577.01435    0    1 1616.04000 1577.01435  2.41%     -    0s

Explored 1 nodes (1 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1616.04 1619.2

Optimal solution found (tolerance 1.00e-04)
Best objective 1.616040000000e+03, best bound 1.616040000000e+03, gap 0.0000%

Ahmed Azab

Gurobi Staff

June 17, 2025 03:54

Hi Xintong,

I can reproduce this issue as well. Let us investigate this further and get back to you.

Regards
-Ahmed

Xintong Zhou

June 17, 2025 05:24

Hi Ahmed,

Thanks for your reply.

Best,

Xintong

July 16, 2025 06:09

Sorry, it has been a while. I will open a support ticket for you in our Help Center so that it will be easier to follow up on this. You will receive an email related to this shortly—please keep an eye on your junk/spam folders.

- Ahmed

July 16, 2025 06:19

Thanks for the update!

Gwyneth Butera

August 18, 2026 19:53

This is a numerical issue that arises due to the combination of nondefault parameters and the inability of floating point numbers to represent the entire number line (see Real numbers are not real and https://0.30000000000000004.com/ for more details if you are interested.

Potential Numerical Bug in MIP Solving

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