# Decision Optimization

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## Different optimal solution for same data set from MIP and CP

• #### 1.  Different optimal solution for same data set from MIP and CP

Posted Sun November 03, 2019 12:59 PM

Originally posted by: memop

Hi,

I have modeled my problem by using CPLEX (MIP Model) and CP (CP Model). My models consist of some logical constraints. So the MIP model has been established with indicator constraints. The models run and all constraints are satisfied in two models. But both models produce different optimum solutions for the same data set. The models are attached to the post. Do I have a problem with modeling logical constraints? Thank you in advance.

Regards.

• #### 2.  Re: Different optimal solution for same data set from MIP and CP

Posted Mon November 04, 2019 03:53 AM

You CP model gives an objective value of 55. For your MIP model already the initial LP relaxation gives a lower bound of 56.8, proving that this model cannot have an optimal solution of 55.

To debug this I suggest to take the solution found from CP and figure out why it is infeasible in MIP.

• #### 3.  Re: Different optimal solution for same data set from MIP and CP

Posted Mon November 04, 2019 05:50 AM

Originally posted by: memop

Thank you Daniel. The MIP model is established properly, is it true? The problem stems from the CP model. But when I checked the results obtained from CP model, all the constraints are satisfied and all assignments are proper. Where exactly should we look for the problem? Regards.

• #### 4.  Re: Different optimal solution for same data set from MIP and CP

Posted Mon November 04, 2019 04:13 PM

As Daniel suggested, take the solution from the CP model and fix the variables in the MIP model to those values (by setting lower bound = upper bound = value in CP solution). Then try to solve the MIP model. CPLEX should say it is infeasible. Assuming so, use the conflict refiner to identify a set of constraints that cannot be satisfied by your CP solution. If one or more of those constraints are expressed incorrectly, fix them. If they all are correct, then you have to ask yourself why the CP model allowed an apparently infeasible solution to be accepted. Go back to the CP model, identify where the constraints in the MIP conflict occur, and see if they are written correctly in the CP model.

• #### 5.  Re: Different optimal solution for same data set from MIP and CP

Posted Tue November 05, 2019 02:10 AM

Originally posted by: memop

Thank you PaulRubin. I will try your suggestion.

Regards.