MIP Relative Optimality Tolerance

1. Mathematical Program Identifier is set to MIP
2. changing the MIP Relative Optimality Tolerance in the Options Tree
3. and lastly:

solve MathProg where MIP_Relative_Optimality_Tolerance := 0.1;

1. Mathematical Program Identifier is set to MIP
2. changing the MIP Relative Optimality Tolerance in the Options Tree
3. and lastly:

solve MathProg where MIP_Relative_Optimality_Tolerance := 0.1;

1. In the progress window, what exactly is means by (Gap = 0.04%)? is it 0.04% of optimality gap, or 4% of optimality gap, or something else?
2. and if it is 4% of optimality gap, does it means that 96% of it is the best solution, meanwhile 4% of it is the less best solution?

Hi@Zahidah Mohd Zaulir.

In the progress window, what exactly is means by (Gap = 0.04%)? is it 0.04% of optimality gap, or 4% of optimality gap, or something else?

I think it is 0.04% of optimality gap.

@Zahidah Mohd Zaulir 

Gap is defined as below

[ |Incumbent - bestbound| / |Incumbent| ]*100

where Incumbent is the objective value of the current integer solution found and bestbound is the objective value of the LP relaxation. It is an indication of how far off is the integer solution from the relaxed solution. 

Based on the progress window, your model is quite large and it would be unusual for the very first incumbent to be at gap 0%. Your math program should have terminated based on the stop criteria you used. However, you can do a simple experiment using callback functions to get the data you want. The below code will retrieve the gap of the math program every 10 seconds. 

First, create a set and parameter as below. 

Set sIntervals {
    Index: iInterval;
    Parameter: epInterval;
}

Parameter pGap {
    IndexDomain: iInterval;
}

Now create a procedure as below. 

Procedure prTimeCallback {
    Body: {
        !will dynamically create elements in set sIntervals
        SetElementAdd(
            Setname : sIntervals , 
            Elempar : epInterval , 
            Newname : FormatString("%n s", MathProgram.SolutionTime ));
        
        !calculate the gap and store in pGap. Retrieves Incumbent and bestbound value
        pGap(epInterval) := (abs(MathProgram.Incumbent - MathProgram.bestbound)/$abs(MathProgram.Incumbent)) * 100;
    }
}

Now, edit your solve statement as below. 

!sets interval as every 10 seconds, change this value for more or less frequency

option progress_time_interval := 10;

!sets prTimeCallback as the procedure to be executed every 10 seconds
MathProgram.CallbackTime := 'prTimeCallback';

solve MathProgram;

Replace MathProgram with the name of your mathematical program, in your case it would be UniversityCourseTimetabling. As your solve took ~200 seconds, you should get 20 values showing how the gap is changing with time. 

If you want to do this every time an incumbent is found instead of every 10 seconds, use MathProgram.Callbackincumbent instead of MathProgram.Callbacktime

In situations like this where you want to find out what CPLEX is doing during the solve you should print the CPLEX status file which can be done by setting the folllowing options:

• Solvers General option 'Solver listing messages' to 'All'
• CPLEX option 'MIP display' to 'Display each nth node'

The CPLEX status file will be printed in the log folder. It will tell you exactly which incumbent solutions it found and the corresponding gap. Please attach the CPLEX status file here if you find it difficult to interpret it.

@mateusarakawa noted. thank you Mateus.

Hi @mohansx ,

Attached together is the screenshot of the latest progress window for this request:

For your information, CPLEX still give me the result of 0.0% gap.

I will try the coding that you share to see the result.

Hi @Marcel Hunting ,

Can you please interpret the file for me? Thank you in advance. 

Hi @Marcel Hunting ,

Noted. Thanks for your help. 

Hi @mohansx , 

When the CPLEX is done running, where can I see the values?

@Zahidah Mohd Zaulir

When the CPLEX is done running, where can I see the values?

You can see those values in the data of parameter pGap.

However, from your log file and Marcel’s comments - it seems like CPLEX is finding only one incumbent solution, which is at gap 0%. So, doing this experiment might not be helpful to you.

You could replace Mathprogram.Incumbent with Mathprogram.objective in the definition of gap, but I expect that to not be helpful either.

Noted. Thank you for the help, Mohan.