Understanding the Differences between MIP and RMIP Solvers

Hi all, I would like to seek clarification regarding the disparities between MIP (Mixed Integer Programming) and RMIP (Relaxed Mixed Integer Programming) solvers. While I understand that RMIP converts integer variables into continuous variables, I would like to explore any other significant dissimilarities between these two solvers.

Specifically, I am encountering fluctuations in the results of one of the variables when utilizing the MIP model as shown in the picture below. Despite the absence of any constraint-related issues, the values exhibit variability instead of remaining constant. 

Conversely, when employing the RMIP solver, the values remain consistent throughout (as presented in picture below). 

I am keen to understand the cause behind these fluctuations and any significant disparities between the MIP and RMIP solvers that could potentially explain this behavior. Any insights, explanations, or suggestions on how to address these fluctuations would be greatly appreciated too! 

Thank you in advance for your assistance!


Best answer by Marcel Hunting 26 May 2023, 10:31

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Hi @Marcel Hunting. I see! Your help is greatly appreciated. Thank you!

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Hi @Xinhui. Not much can be said based on the solution values of one variable. I assume that this variable interacts with other variables through constraints and in that case the other variables and the constraints also play a role.

Please note that if you have a constraint

b1 + b2 + b3 + b4 = 1

in which b1, b2, b3 and b4 are binary variables then in the MIP solution one of these binary variables will have a solution value of 1 and the other three will have a solution value of 0. A solution for the RMIP could be (0.25,0.25,0.25,0.25) or (0.1,0.1,0.1,0.7), etc. And these binary variables might impact other (continuous) variables.


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