Why does Gurobi sometimes violate constraints during the solving process in order to achieve a better solution?

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di su

2025年04月22日 03:21

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Gurobi’ result violates the constraint S=max⁡{v_1,v_2} by always choosing v_1 to minimize the objective R. I suspect this happens because R is minimized when S always equals v_1（Conflict between objective function and constraints）. How can this situation be resolved?(Gurobi did not return 'infeasible' error)

The original problem is as follows:

min R
s.t.
S=max⁡{v_1,v_2}; R=(S+t)-v_1

t is a parameter, and x is a binary variable representing task assignment results. Gurobi returns x values as 0 or 1. However, S always equals v1 (regardless of the size of v1 and v2) no matter what constraints I apply.

I've tried four different approaches to solve the S value problem, also adding penalty terms to the objective function. However, the problem remains unsolved：

Method 1： v_1-v_2≤My; v_2-v_1≤M(1-y); S≥v_1; S≥v_2; S≤v_1+M(1-y); S≤v_2+My

Method 2： v_1-v_2≤My; v_2-v_1≤M(1-y); S≥v_1; S≥v_2; S=v_1 y+v_2 (1-y)

Method 3： We use the Gurobi function addGenConstrMax.

Method 4： v_1-v_2≤My; v_2-v_1≤M(1-y); S≤v_1+M(1-y); S≥v_1-M(1-y); S≤v_2+My; S≥v_2-My

0

• 

  Ahmed Azab

  • Gurobi Staff

  2025年04月22日 03:38

  Hi, 
  Where does the variable x appear in your model? Please provide more details.
  Regards
  -Ahmed

  0
• 

  Riley Clement

  • Gurobi Staff

  2025年04月22日 03:45

  Related: https://or.stackexchange.com/questions/13127/why-does-gurobi-sometimes-violate-constraints-during-the-solving-process-in-orde

  1
• 

  Gwyneth Butera

  • Gurobi Staff

  2025年04月22日 11:18

  Also, please see our KB article How do I diagnose a wrong solution? which provides a number of tips on how to troubleshoot this type of issue. - Gwyneth

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