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What are the benefits or pitfalls in using a GA based optimizer for geometry optimization instead of a more traditional Hessian based algorithm?
It can be argued that performing single point energy calculations is much cheaper than calculating the approximate hessian at each point. The origin of this question is from this paper where the authors have used a GA based optimizer to obtain the stable structure for $C_{60}$ and $C_{20}$ molecules.
The paper you cite has certainly left a legacy, but it is by now almost 30 years old! I think its main insight is in applying physics-agnostic, information-theoretic ideas to atomistic coordinates. (You can guess where this will end up!)
While it's certainly been spiritually successful (for example, it's cited in the Materials Project paper), I think it would be difficult to naturally extend a GA approach to generic systems. How do you naturally "genotype" a configuration, so that "breeding" configurations yields a suitable descendant "phenotype"? The descendant must inherit the "traits" that made its parents strong -- while being a distinct enough to encourage exploration of configuration space.
The paper authors found a clever way to do this for carbon cluster coordinates (slicing a plane through configurations and then "gluing" parents together at the join), but it's not obvious that their methods could generalise to, say, optimising protein structures (or ligand docking) or liquid weak ordering or phase transitions in bulk metals or ...
It seems that, especially with today's increasing computational power, you could do better than GA in one of two directions: less information theory, or more information theory. In the less info-theory direction, why not calculate forces along with energies? Sure, they're expensive, but not that much more expensive. And once you have forces you have the full gradient of energy vs atomic coordinates. While you don't have the Hessian, you do now have plenty of Hessian-free optimisation methods available, especially conjugate gradient as a simple off-shelf method well suited to energy optimisation (since the energy of a bound state is nicely symmetric positive-definite). Plenty of molecular dynamics (MD) packages will do all this and more for you -- replica exchange, instead of simulated annealing, comes to mind as another method for encouraging phase space exploration.
In the more info-theory direction: machine learning! ML descriptors are a souped-up "genotype" for atomic configurations. They incorporate physical information about the system, while also being generically definable across a variety of systems and mathematically ready to be ingested by your favourite ML platform. Put differently, a genetic algorithm, in the process of evolving towards an optimal configuration, doesn't pick up how to calculate forces from positions (and thus it could run on 1995 computers). But an ML model trained to calculate energies can also calculate the derivatives of energy in the atomic descriptors -- and that gets you forces! So you get an MD force field into the bargain, opening up all kinds of follow-on calculation possibilities.
That's just what I think -- this was a fantastic paper for 1995, but these days you'd go either in the MD direction or the ML direction (which you could also hook up to subsequent MD simulations).
