Optimizely is based on jQuery and will use version 1.6.4 to run. By default, Optimizely will include a trimmed version of jQuery (only containing the code that is necessary to run Optimizely), but you can choose to either include the full jQuery lib or have Optimizely use your own jQuery lib (version 1.4.2 or higher).
You can find more detailed instructions on how to do this on our Learning Center: https://help.optimizely.com/hc/en-us/articles/200039655-How-can-I-use-Optimizely-with-my-own-copy-of-jQuery-
You can also find some more detailed explanation of how Optimizely avoids conflicts with existing Javascript libs in global scope on there: https://help.optimizely.com/hc/en-us/articles/200040385-Does-Optimizely-conflict-with-existing-javascript-libraries-like-jQuery-Prototype-or-MooTools-