Initial population for a genetic algorithm from one individual
One nice thing about QAP is that local search methods can take advantage of incremental evaluation of modified solutions, and GAs typically can't. So a pure GA needs O(n^2) time for every fitness evaluation, but a local search can do many fitness calculations in O(1) time, and the rest in O(n).

What I've often done for QAP is to employ something like a tabu search method to do much of the search. See Eric Taillard's paper on Robust Tabu Search for a good example of how to apply it to QAP in particular, including how to do the incremental fitness update.

You can generate multiple good initial points by running multiple tabu searches from random starting points, or you can integrate it directly into the GA as a hybrid method.