tools/resources on probabilistic inference and mixed-integer programming

#1
Hi there!

Here's the problem I'm trying to solve: Given a pool of gene ID and their read counts -- some genes are unique to one particular species while some are shared--what is the most likely combination of species that can be present in the sample and how to calculate their relative abundance?

It seems like this problem requires some form of probabilistic inference but I wasn't sure what tools there are out there.I also heard about mixed-integer programming might help in this...If anyone knows of any tools/resources on ways to solve this kind of problem, please let me know!

Thanks for your help!