Optimization problem

[mkPyVS]

I would suggest taking a look at the python package networkx. It is a
wonderfully created path optimization and presentation package which
has a fair amount of extensabilty.

Basic lowest cost path solutions should be able to solve your
algorithmic needs here in polynomial time (Typically N**P time..
compute time through path to the number of nodes power) which is
typically adequate for most functional needs ( < 1 sec for 20 nodes)
and presents a simple solution path unless the path you present has
many loop options or path costs which are mal-formed. Good Luck,