Monday, August 29, 2011

Which2 Multidimensional optimizer

Immediate results using the given multi-dimensional functions are poor, but promising

Fonseca data

All of our rules with 2-bin discretization using Which were in the tiny green square. However, the goal with fonseca is to minimize, so being in the top right corner is very bad. By comparison, with 8-bin, are rules were mostly in the top right blue square, but we had one rule with coordinates f1=0.2497 f2=0.9575.

In Kursawe

Our rules were all in the mass in the center left when I chose maximize to optimize. With 8-bin, the rules were spread out with than with 2-bin.

This is because 8-bin allows more detail than 2-bin. However, I posit once I am able to recurse this process, applying the constraints of the rules, that 2-bin will be better overall.

Further exploring these rules (by applying the rules as new constraints on the randomized input vectors on the data database) will involve a massive recoding. However, having done some manual constraints using the generated rules, the results improve in Round 2 (treating this as round 1). However, you cannot simply pick one rule to explore. Basically, your unconstrained start point is the head of an infinite tree, the branches from each node are the rules generated by each run of which using that node and all ancestor nodes to that node's rules as constraints on the input data. The rules can then be mapped to coordinates in the space of (f1, f2, ...fn). Ideally, these rules will approach the Pareto frontier.

Which is running through the data very quickly, but until I have further results which will take a massive reworking of code, can't say anything definitive about it's long term usefulness just yet.

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