  Ant Colony Optimization (ACO) has time complexity O(t*m*N*N), and its typical
application is to solve Traveling Salesman Problem (TSP), where t, m, and N
denotes the iteration number, number of ants, number of cities respectively.
Cutting down running time is one of study focuses, and one way is to decrease
parameter t and N, especially N. For this focus, the following method is
presented in this paper. Firstly, design a novel clustering algorithm named
Special Local Clustering algorithm (SLC), then apply it to classify all cities
into compact classes, where compact class is the class that all cities in this
class cluster tightly in a small region. Secondly, let ACO act on every class
to get a local TSP route. Thirdly, all local TSP routes are jointed to form
solution. Fourthly, the inaccuracy of solution caused by clustering is
eliminated. Simulation shows that the presented method improves the running
speed of ACO by 200 factors at least. And this high speed is benefit from two
factors. One is that class has small size and parameter N is cut down. The
route length at every iteration step is convergent when ACO acts on compact
class. The other factor is that, using the convergence of route length as
termination criterion of ACO and parameter t is cut down.
