here's the basic gist of the program i'm trying to make, but i have no idea how to approach it, if someone could shed some light, i would really appreciate it:


we have a linear sequence of connected energy rods, say like this /\/\/\/\/\/\/, and the rods are flexible and can move into various conformations such as /\/\/\/\/\_/ , or /\/\_/\/\/, each of the conformations can then move into further conformations like /\/\_/\/\_/, etc.There is one final conformation somewhere, that is the best conformation of all. In addition, some rods are more compact than others, so each conformation is associated with a score of some sort (lower score = more compact = good, I have a score function already). The ultimate goal is to find that conformation with the best score.

I'm thinking that I should implement a tree, and associate a compactness score with each node. Moreover, nodes that are a consequence of a merge, have a "goodness" factor that would somehow make it more favorable than other nodes (perhaps a greater search depth?)

In addition, nodes that revert back to the less compact stage are killed and discarded (no longer iterated).

As you move and wiggle around the \/\/\/\/\/\/, there are many paths to get to the final conformation that's the most compact. What would be the fastest way to find this final conformation?

How would I begin to make something like this?


(For those of you that know biology, I'm trying to solve the protein folding problem, realistically)

I don't see how you are associating depth within a tree to compactness, but then, you have thought about this problem longer than I have.

A more straight-forward algorithm would be to come up with an equation based on whatever parameters you want to describe a single rod's energy & collectively look for the minimum of the overall system. The Simplex method used in Operations Research is a standard algorithm for finding such minimums. Google "Simplex method" to find out the particulars. Implementing the algorithm is similar to Gaussian elimination performed on matrices, but determining pivot points is different.

As is true with any system of equations being solved with matrix algebra, you will need as many equations as you have variables to find a distinct minimum. Otherwise, you will only get a range based on several factors.

They're not really sticks of energy, they're more like sticks of complicated molecules connected together, the real score associated with each "conformation" is really an energy value and a compactness score.

In anycase, there isn't really an equation either, there's a very complicated function that can return the "energy" and "compactness" associated with any given conformation, but that's about it. The function performing this task is mostly based on heuristic evidence, making a real "equation" a bit difficult

In any case, i'll read up on the simplex method