I've always thought of harmonic/melodic modes as being modes the fall parallel to harmonic/melodic minor. I don't have any references, but I swear I've seen this corroborated in a few places.
Harmonic Minor: A-B-C-D-E-F-G#-A
Melodic Minor: A-B-C-D-E-F#-G#-A
Harmonic Major: C-D-E-F-G#-A-B-C
Melodic Major: C-D-E-F#-G#-A-B-C
Harmonic Dorian: D-E-F-G#-A-B-C-D
Melodic Dorian: D-E-F#-G#-A-B-C-D
This, however, creates some issues with Lydian and Mixolydian, in which the root notes are affected (F#-G#-A-B-C-D-E-F# and G#-A-B-C-D-E-F-G#, respectively), and, in general, kind of defeats the entire purpose of harmonic and melodic principals in the first place. Harmonic minor adds a strong V-i resolution, borrowed from major, back in, and melodic minor helps to blend out the sound of the raised 7th degree by also raising the 6th.
These same ideas can be applied to other modes to achieve similar results. Dorian, for example, lacks a V-i cadence, but we can achieve this by raising the 7th degree, just as in harmonic minor, but related to Dorian. The 6th, of course, is already raised, so there is no need for melodic dorian. Several other modes present similar issues, as notated below, but these, I feel, may be acceptable as they simply mean the harmonic/melodic function is already satisfied.
Harmonic Dorian: D-E-F-G-A-B-C#-D (borrowing the V-i cadence from major, instead of the II-v from harmonic minor)
Melodic Dorian: (unnecessary, 6th already major)
Harmonic Mixolydian: G-A-B-C-D-E-F#-G (wait a second...this is just major!)
Melodic Mixolydian: (6th already major)
Harmonic/Melodic Lydian: (6th and 7th already major)
Harmonic Phrygian: E-F-G-A-B-C-D#-E
Melodic Phrygian: E-F-G-A-B-C#-D#-E
So, is it really fair, or even appropriate to apply harmonic/melodic concepts, and then shift modes? Or should the mode be accounted for first, before applying harmonic/melodic adjustments, using them for the same purposes the are used in minor, but in relation to the current mode (ie, resolution and blending)?