Yottaa Site Speed Optimizer supports HTTPS websites. During preview mode, you can get a "preview" of the HTTPS support for your site. (Read more about preview mode here.)
HTTP and HTTPS: Same domain, or a different domain?
Note, if you serve HTTP traffic on one domain (e.g. http://www.mysite.com), and serve HTTPS traffic on a different domain or subdomain (e.g. https://secure.mysite.com), then you set up the sites independently in Site Speed Optimizer. In other words, activating Optimizer for your HTTPS site won't impact your HTTP site if they're on different domains. However, if you use the same domain for both HTTP and HTTPS (e.g. http://www.mysite.com and https://www.mysite.com) then you only need to set up one site in your Yottaa dashboard.
HTTPS on the same subdomain? Set up HTTPS before making any DNS changes!
Finally, a note about activating Site Speed Optimizer (going live) for sites that support HTTPS and HTTP on the same subdomain: it is very important to set up HTTPS with Yottaa before you make the DNS change to go live. If you were to activate www.mysite.com without first setting up your SSL Certificate with Yottaa, your HTTP traffic would be fine but your HTTPS users would all see scary warnings about a missing SSL Certificate. So, if you are activating a domain that supports HTTPS, make sure you let us know when you're going through the (easy) Optimizer activation wizard. We've made it really easy to provision an SSL Cert for your HTTPS site. Note you'll still need to maintain your current SSL certificate to encrypt the connection between Yottaa's network and your origin servers.
You may want to read more about HTTPS and Yottaa Optimizer here.