I've been playing around with this Monte Carlo tree search (MCTS) code (if you need a short intro to MCTS click here). I want to learn how to use MCTS to optimise molecular properties so to get started I modified the code to minimise a very simple energy function that mimics a torsional potential.

$$E = \sum_i 1 + \cos(\phi_i) + \cos(3\phi_i)$$ It seems to work OK but in order to get some point of comparison for the efficiency I tested it against a genetic algorithm (GA). You can find the codes here and here.

More specifically, I tested for a function with 10-dihedral angles, each with three possible values (180.0, 60.0, and -60.0), meaning there are 59,049 possible combinations (i.e. "conformations"). Each 180 and ±60 angle contributes -1 and 0.5 to the energy so the global minimum is one in which all angles are 180 and has an energy of -10.

If you simply make 10 x 1000 random combinations of 10-dihedral angles and average the lowest energy found among each set of 1000 you get 0.35. This makes sense because the highest energy conformer has an energy of +5, but there more ways to make it, so the average should be around 0.

Using 1000 iterations (i.e. 1000 energy evaluation) the MCTS finds the global minimum 0 out of 10 times and gives an average energy of -7.6. In 4 cases the energy is -8.5 (i.e. it misses one dihedral) and -7 in the rest (i.e. it misses 2 dihedrals).

For comparison, the GA finds the global minimum 0 out of 10 times and gives an average energy of -6.85. In 2 cases the energy is -8.5, in 5 cases the energy is -7, and in the rest, -5.5. I use a population size of 50 and 20 generations, which also requires 1000 energy evaluations, and a mutation rate of 0.01. Using a population size of 20 and 50 generations results in an average energy of -6.7.

I'm actually a bit surprised that MCTS out-performs GA because I don't recall seeing MCTS being used for conformational search. One possible reason is that it's hard to see how to parallelise MCTS since energy evaluations are done sequentially, while they can be done in parallel for each generation for GA.

I did try running 10 100-iteration MCTSs, which could be done in parallel, and 1 of them managed to find a -8.5 conformer so maybe that's a possibility. Another way would to do a complete expansion of a terminal node and do the three energy evaluations in parallel. This might also be a better search strategy in any case. I am not quite sure how to implement this yet (recursion is not my strong suit) so any suggestions are welcome.

Also the reward function could probably be optimised. Currently it is simply 1 if the energy is lower than the current "global" minimum and 0 otherwise. Suggestions for other functions are most welcome.

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