Clustering Algorithm for Paper Boys

Question

I need help selecting or creating a clustering algorithm according to certain criteria.

Imagine you are managing newspaper delivery persons.

• You have a set

Answer 1

• You have a set of street addresses, each of which is geocoded.
  • You want to cluster the addresses so that each cluster is assigned to a delivery person.
  • The number of delivery persons, or clusters, is not fixed. If needed, I can always hire more delivery persons, or lay them off.
  • Each cluster should have about the same number of addresses. However, a cluster may have less addresses if a cluster's addresses are more spread out. (Worded another way: minimum number of clusters where each cluster contains a maximum number of addresses, and any address within cluster must be separated by a maximum distance.)
  • For bonus points, when the data set is altered (address added or removed), and the algorithm is re-run, it would be nice if the clusters remained as unchanged as possible (ie. this rules out simple k-means clustering which is random in nature). Otherwise the delivery persons will go crazy.

As has been mentioned a Vehicle Routing Problem is probably better suited... Although strictly isn't designed with clustering in mind, it will optimize to assign based on the nearest addresses. Therefore you're clusters will actually be the recommended routes.

If you provide a maximum number of deliverers then and try to reach the optimal solution this should tell you the min that you require. This deals with point 2.

The same number of addresses can be obtained by providing a limit on the number of addresses to be visited, basically assigning a stock value (now its a capcitated vehicle routing problem).

Adding time windows or hours that the delivery persons work helps reduce the load if addresses are more spread out (now a capcitated vehicle routing problem with time windows).

If you use a nearest neighbour algorithm then you can get identical results each time, removing a single address shouldn't have too much impact on your final result so should deal with the last point.

I'm actually working on a C# class library to achieve something like this, and think its probably the best route to go down, although not neccesairly easy to impelement.