N-Dimensional Optimization

I wrote an algorithm that models interference between multiple iterations of the same path. The basic idea is simple: you have a random path, and you generate it some number of times. However, once you traverse a particular location in the path, that point becomes more likely. As a consequence, over time, the probabilities become non-uniform (obviously they start out uniform). When I articulated this, I noted that this is plainly an optimization algorithm, since you can update the probabilities of a given point (treated as a domain value) with the distance to some goal state (in the range). This can done in N-dimensions, by simply having N paths all doing exactly this. Moreover, you can vectorize many of the steps for this N-dimensional case easily in Octave. Here’s the two dimensional code (on dropbox).

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