as with any advanced javascript-based solution (which beaver builder clearly is), you'll have to find the right JS to exclude from optimization.
chances are beaver-builder loads wordpress' native media manager to access the media library. i've been looking into what the media manager adds (a huge amount of JS, inline and external) and how to optimize that, but I haven't been able to tame that monster yet. so if beaver builder uses media manager api, my advise would be exclude that entire page from optimization using the autoptimize_filter_noptimize-filter (see autoptimize_helper.php_example for an example of how to exclude a page based on the URL).
frank