Can the value of Big M change my results?

GAMS
1

Hi!
I have a multi objective NLP problem with Big M constraints.
I noticed that when I change the value of Big M the results of the variables included in my objective functions change. This happens when I run with MINOS or with BARON.
The values of the Big M are big enough, for example 1000 and 100000 (and the maximum logical value should be 60)

Is this logical? Why does this happen?

Thank you!

2

Hi,

The (global) optimal objective value should be the same. The solution itself can change. Many problems are degenerate and have multiple equally good solutions. If you change sth. (like your big M) the algorithm may find a different solution.
In general, it is recommend to choose big M sufficiently large but as small as possible. So if you no that a value of 60 is sufficient, you should choose that value.

I hope this helps!

Fred

3

Hi,

As per literature, you can use below equation in your model to find out value of bigM:
bigM = (x.UP - x.LO)*(y.UP - y.LO)

Regards,
ZAR