I haven't seen a list of all of what Adam may be using on this tour. His rack has been under the stage for as long as I can remember so it's not always been easy to know what he's using, bar for the occasional picture or feature in a music magazine.
That said, you can see a few of his effects in the picture below. I've not taken the time to put it under the microscope to see exactly what is there.
[The yellow pedal appears to be a Boss SD-1. The pedal next to that appears to be a Voodoo Lab pedal, perhaps a Proctavia? The pedal to the right of that appears to be a Boss GE-7 EQ. The boss pedal below that appears to be a Boss digital delay; model uncertain.] -- all unconfirmed. I wish there was a better picture.
While Adam did use a Ground Control midi controller connected to a Skrydstrup R & D MR9 loop system, on Vertigo, I think he's actually using the whole Skyrstrup system now, trading out the Ground Control for a Skrydstrup SC-1.
On the Vertigo tour Adam used:
dbx 160a Compressor/Limiter
Line 6 Bass Pod Pro
Electro Harmonix Big Muff
Line 6 DM4 (Distortion Modeler)
All of that was operated by Digital Music Corp Ground Control midi controller connected to a Skrydstrup R & D MR9 loop system