Is it permissible for a traveler to pray Asr before its prescribed time if he departs after Dhuhr and before the Adhan for Asr, and he prays Asr before leaving his house?

It is not permissible to combine and shorten prayers (jama' and qasr) except after departing from the populated area of the city. Therefore, it is not permissible for someone who intends to travel to combine Asr prayer with Dhuhr prayer before its time, while still at home.