Conquering the hard cases of Lennard-Jones clusters with simple recipes

Lennard-Jones clusters are the best-known benchmark for global cluster structure optimization. For a few cluster sizes, the landscape is deceptive, featuring several funnels, with the global minimum not being in the widest one. More than a decade ago, several non-deterministic global search algorithms were presented that could solve these cases, mostly using additional tools to ensure structural diversity. Recently, however, many publications have advertised new search algorithms, claiming efficiency but being unable to solve these harder benchmark cases. Here, we demonstrate that evolutionary algorithms can solve these hard cases efficiently, if enhanced with one of several very different diversity measures (niching) which were set up in an ad-hoc way, without extensive deliberation, testing or tuning. Hence, these hard benchmark cases should definitely be considered solvable. Additionally, these niching concepts offer insights into the different Lennard-Jones structural types, and into the way niching works in evolutionary algorithms. (C) 2016 Elsevier B.V. All rights reserved.