There is reference to Algorithms used by the ArcGIS Network Analyst extension—Help | ArcGIS for Desktop
Which for your case ... Algorithms used by the ArcGIS Network Analyst extension—Help | ArcGIS for Desktop
The location-allocation solver starts by generating an origin-destination matrix of shortest-path costs between all the facilities and demand point locations along the network. It then constructs an edited version of the cost matrix by a process known as Hillsman editing. This editing process enables the same overall solver heuristic to solve a variety of different problem types. The location-allocation solver then generates a set of semirandomized solutions and applies a vertex substitution heuristic (Teitz and Bart) to refine these solutions creating a group of good solutions. A metaheuristic then combines this group of ....
Since I knew I had heard this before and that the actual references weren't in the help.... this brought me back to a page that gives them from Jay Sandhu a more authoritive reference.
But I will copy a portion of his response for posterity.
Here is a reference to the original paper by Ed Hillsman:
Hillsman, E.L. (1984). The p-median structure as a unified linear model for location-allocation analysis. Environment and Planning A, 16 (3), 305-318
And here is another researcher using a similar approach: