Does anyone know a good algorithm for quickly finding an approximate solution to the following problem?
Given two square matrices $A$ and $B$, minimize $\| P A P^\top - B \|$ over all permutation matrices $P$.
I have heard that there are several types of algorithms for these kinds of problems, like iterative improvement, simulated annealing, tabu search, genetic algorithms, evolution strategies, ant algorithms, and scatter search. I am looking for existing software.