For TSP(Traveling Salesman Problem) solving by ACO(Ant Colony Optimization), I've read something like Ant Colonies for traveling salesman problem, The Ant Colony Optimization Meta Heustic, aco2004.prn.pdf etc. I've got something about ACO including intuitive understanding and simple implementation, but math part.
In almost all the examples introduced, there is a function of Dij, prepresenting distance between vetex i and j, working as cost function. And this cost funtion is used in both η and τ in each iteration. Can I use different distance functions or cost functions for η and τ? For example, in a problem of searching shortest route in a special network, an assumption has been introduced as: the more out-spanning ports, the more probability of the router that would be in the shortest path. So, can I use the function of f(d, m){d: distance between vertexes, m: outspanning ports} for η and f(d){d: distance between vertexes} for τ?
In my mind, η is just a heuristic function to inject some bias in search, it could be any function valid. Is that right? I am also wondering if it (differenct cost function for η and τ) imposed some effections on validation of properties of ACO, like convergence, lower bounder etc.
Thank you very much!