Nonzero gap at optimality?

I'm running Gurobi 9.5 through the python API to solve a small MIP and am noticing this strange behavior: my model is being solved to optimality but the results from model.objVal and model.ObjBound differ greater than my tolerance. I conjecture this is because a heuristic solution is being found, but would like some confirmation.

I can provide the exact model to replicate, but here's a snippet of code and the traceback I'm seeing:

model = call_model_optimize()
print('-' * 64)
print('Status: %s | ObjBound: %.03f | objVal %.03f' % (model.Status, model.ObjBound, model.objVal))

Which yields this traceback:

Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)

Thread count: 4 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 5 rows, 983 columns and 1967 nonzeros


Model fingerprint: 0xed05bdde

Variable types: 982 continuous, 1 integer (1 binary)

Coefficient statistics:

  Matrix range     [4e-10, 5e+00]

  Objective range  [8e-03, 4e-02]

  Bounds range     [6e-01, 6e+00]

  RHS range        [1e-06, 3e+00]

Presolve removed 1 rows and 961 columns

Presolve time: 0.00s

Presolved: 4 rows, 22 columns, 27 nonzeros

Variable types: 21 continuous, 1 integer (1 binary)

Found heuristic solution: objective -0.2150999



Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)

Thread count was 8 (of 8 available processors)



Solution count 1: -0.2151 



Optimal solution found (tolerance 1.00e-04)

Best objective -2.626314110670e-02, best bound -2.150998966824e-01, gap 719.0182%

----------------------------------------------------------------

Status: 2 | ObjBound: -0.215 | objVal -0.026

I should also note that I can compute this particular MIP in a closed-form way and can verify that the correct answer really should be the one returned by objVal.

Any insight here would be greatly appreciated!

Official comment

Simranjit Kaur

Gurobi Staff

November 16, 2025 23:44

This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.

Matt Jordan

February 16, 2022 17:06

Gurobi Support escalated this to a support ticket and we resolved these issues. To summarize:

>This unexpected behavior is caused by numerical issues during the solution process and turning off presolve (Presolve=0) or turning up Gurobi's numerical awareness (NumericFocus=2 or 3) solves the issue.

The root cause of my numerical issues came from many small coefficients that caused unexpected behavior. Increasing numerical focus works, but is ill-advised. It was recommended that I rescale my model, or follow other strategies listed here: https://www.gurobi.com/documentation/9.5/refman/guidelines_for_numerical_i.html

Nonzero gap at optimality?

Comments

Didn't find what you were looking for?