Optimize and pairing

Hi,

I have a bunch of subjects that I need to pair them up in a group of 2, but some subjects cannot be paired with some of them, the relationships between them is attached: The cells "FAIL" means that they cannot be paired together, e.g.: No6 and No3 cannot be paired together.

The subjects cannot be repeated in multiple pairs, i.e. if No7 is paired with No9, No7 cannot be paired with No1, No2, etc...

Are there any ways to optimize the pairing with the maximum number of pairs as an outcome?

Thank you so much!

Dexter