Monday, March 2, 2009

Cog Sci Project Idea

An idea springs forth from my new learnings! An integration of several high-falutin' things!

It seems that the Traveling Salesperson Problem can be applied to many different domains; the idea of minimizing the "cost" of connecting some set of things has broad application. Included are artificial neural networks, graph coloring, and whad'ya know... touring a bunch of cities.

How can the concept of "time value of money" be integrated into the TSP framework?
Perhaps if we're solving TSPs iteratively, and the parameters are changing?
For instance the, costs between any given vertices could change stochasticly (perhaps with an identifiable pattern (eg: cycle), perhaps not). The goal would be to find the set of TSP solutions that minimizes cost over time, given the uncertainty inherent in the changing connection costs. Further, the cost associated with implementing a TSP solution could be matched against the reward it brings to make a profit function. This, in turn, could be used over a series of iterations of the TSP (with the stochastic costs) to find an net present value.

I went further down the simulation road than I was intending there... ultimately I'm trying to tie the TSP framework back to forming abstractions (concepts) about the uncertain external world and strategies for acting on them. Here the TSP solution over time represents an uncertain (but hopefully useful) belief about the regular state of the domain. The NPV could then be interpreted as a measure of the value of that strategy, in other words how well the "concept" discovered captures the underlying structure of the environment.

I think that this idea may be generally applicable to agents on many levels; if so it would be a neat opportunity to integrate several feilds with some robust mathematical formalism.

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