I have a sea of weighted nodes with edges linking clusters of nodes together. This graph follows the typical small world layout.
I wish to find a path finding algorithm, which isn't costly on processor power, to find a path along the best possible path where the nodes are the most favorably weighted, the fastest route is not the most important factor. This algorithm, also takes into consideration load bearing, and traffic rerouting.
(sidenote: could neural networks be used here?)
Thanks
I'm looking at ACO. Is there anything better than ACO for this kind of problem?
Right the A* algorithm finds the least cost or fastest route, without load balancing.
Lets say that the fastest or shortest route is not the most important route, what is more important is following a path where the weighted nodes have a certain value. no1.
no2. If using A* the traffic on that route gets overloaded then suddenly that path is redundant. So as cool as A* is, it doesnt have certain features that ACO ie inherent load balancing.
-- unless im mistaken and misunderstood A*
Then what beats ACO?
It really looks like a show down between ACO and A* , there has been so much positive talk about A* , I will certainly look deeper into it.
Firstly in response to David; I can run ACO simulation in the back ground and come up with the best path, so yes there is an initial startup cost but the startup luckily isnt essential. So i can afford to run a simulation multiple times. The one real trouble is finding connected source and destination nodes. Whereas it seems A* will be able to do this quite easily. Now what happens when this network get dreadfully large like in millions of nodes. Will A* be able to scale easily?
I will research A* further. But I leave you with a last question!
Will A* be able to scale as well as Antnet (ACO)?
Dijkstra's algorithm and it optimised variant A* find the path with "the" minimal cost through your graph. The important things are a) defining your graph correctly and b) defining an appropriate cost function.
In the face of a changing cost function Dijksta requires one to re-calculate the solution.
For load-balancing I would extend Dikstra to not only calculate the optimal path, but use some kind of flood-fill behaviour to create a set of possible paths (sorted by cost) to find alternatives. Only knowledge about the specific problem and cost function can answer whether and how this might work.
Ant Colony Optimisation on the other hand seems to be much more flexible in adapting to a changing cost function, by continuing the iteration after/while the cost function changes.
This depends very much on your problem domain. If you have a good heuristic (see the Complexity section of the A* article) and seldom cost changes then A*'s polynomial runtime might favour repeated re-calculations. ACO on the other hand has to iterate over and over again before converging on an approximate solution. If cost changes occur very frequently, continuing the iteration at a constant rate might be more efficient than updating the A*-solution, since information is retained within the state of the algorithm. ACO doesn't promise the optimal solution, though and probably has higher start-up costs before converging onto a "good" solution. Again that very much depends on your specific domain, graph and cost function as well as your requirements on optimality.