Inquiry Regarding Better Solutions Found Using Warm Start for Linearized MIQCP Model

Awaiting user input

Chenhui Qu

• July 03, 2024 09:08

Dear All,

I am currently working on solving a Mixed-Integer Quadratically Constrained Program (MIQCP) and have opted to linearize the model for solving purposes. However, I have encountered an issue that I would appreciate your insight on.

Here is the situation:

1. I solved the linearized MIQCP model and obtained an optimal solution.
2. I then fixed the integer variables to their values from this optimal solution and re-input them into the linearized model. The result was consistent with the initial optimal solution.
3. Subsequently, I used the same integer values as a warm start for the linearized model. Surprisingly, the solution obtained in this case was better than the previously obtained optimal solution.

Upon comparing these two solutions, I noticed significant differences in the values of the linear variables. I am trying to understand the reasons behind this discrepancy. Is this difference possibly due to numerical errors, or are there other underlying factors at play?

Your guidance on this matter would be highly appreciated. Thank you for your time and assistance.

Best regards,

Chenhui

Related to

• MIQCP

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• 

  Jaromił Najman

  Gurobi Staff

  • July 04, 2024 09:06
  • Edited

  Hi Chenhui,

  Did you solve the linearized model to a 0% MIPGap? If not, then there is still room for improvement of the objective value, i.e., a better feasible point can be found, e.g., by providing an already very good warm start solution.

  Best regards, 
  Jaromił

  0

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