Like Flater says in the comments, I too cannot think of a case where "As of" (as used in the first example) works without a time/date – that doesn't guarantee there are no such cases, but your example isn't one of them.
"Like other..." could work, but I believe the best alternative would be "As in...":
As in other classical facility location problems, this problem considers only location-allocation decisions.
Essentially it is saying, "As [is the case] in other [similar] problems, this problem considers [a particular aspect]...".
In the second example, the phrase is used differently, and – I believe – correctly:
The author of this, as of other official histories of the Second World War, has been given free access to official documents.
Here, it is saying "The author of [a specific work] [who is also the author of other related works] has been given...".
As pointed out in a comment, there are valid uses of "As of..." that don't explicitly mention a time/date, e.g.:
As of version 5, the application now makes coffee.
As of Android Nougat, battery life is infinite.
As of my last physical, I'm under doctor's orders to start exercising.
However, these all effectively establish a point-in-time: either through the chronology of product releases ("Version 5" and "Nougat" would have been released on specific dates) or life-events (the date of the speaker's last physical). They are thus just variants of the "As of [time/date]..." form.