[tannk11001]

If you have a good relationship with them and trust them: tell them as soon as possible -- even before you start receiving offers.

They'll respect your needs but will want to work with you to make a smooth transition to your replacement. That's going to take a while and they'll benefit from as much assistance and lead time as you can give them. You can work with them to make sure you have some paying work with them until you find a new job even once a new candidate is found.

If you're not completely burnt out, they might even try to address your concerns and make things more comfortable for you so that you don't have to look for a new job at all.