I have been experimenting with an algorithmic/mathematical approach to combine two melodies into a single, new melody and want to ask if there are other approaches to this problem.
I suggest looking into two things:
In "traditional", common practice music there is something called compound melody which is a single melodic line, but because the pitches get grouped into high/low regions, or through other devices, the single line seems to be a counterpoint of two separate lines. In some ways this is just a "trick." If you take two basic lines in counterpoint - for example, something in simple quarter notes - all you need to do is displace the notes of each line with quarter rests so the notes alternate back and forth between the two. It's a way to get a melodic instrument like a flute to sound like it's playing harmony.
In modern serial music you can have a series of pitches - a melody - and the series, sometimes called a row, can be permuted in various ways including breaking it up into smaller segments or recombining with itself in various counterpoints. This style is usually atonal. It's more math-ish treating all permutations are about equally viable.
Either of these could be described as some kind of multiple lines combined into, or derived from, a single line.
Oh, there's one other, really it technically fits into the serial stuff, but historically it's part of counterpoint and canon technique. The cancrizan, or crab canon. It's one melody played in counterpoint to itself played in retrograde, backwards. Since it's a separate term, I thought I should mention it.