I have so far assulted only AI.
I use this: Divide my force into 3 task forces. 1 and 2 will lead a small-sclae probing attacks on a wider front while focused on suspected soft spots (ie locations with poor LOS from other enemy positions). Once a softer spot is found, the TF making the probe begins to clean the mines and is ASAP accompanied bz the TF 3, a main strike force. I then try to clear waz ASAP using all available engineer equipment. After breaking through I rush to kill enemy arty and to take VH's, but I don't take VH's unless I have enough troops close to repel counterattacks. In the mean time, second probing force has already cleared atleast 1 hex wide passage so it can exploit enemy lines left bz counterattacking units, and usually it is able to join the main forces.
During all this, shelling with artillery any spot that seems fit to receive a group of heavy shells.
And in case you have to stop somewhere (for example minefield being too hard to clean), I tend to atleast scatter my troops as far as possible to soften the effect of arty.
NOTE: Damn that QWERTZ
If there is some "z" instead of "y", I apologise, but I tried to find them all.