The performance of Minima Hopping and Evolutionary Algorithms for cluster structure prediction

TL;DR

This paper compares Minima Hopping and Evolutionary Algorithms for cluster structure prediction, introducing new operators and improvements, and evaluates their effectiveness on various atomic clusters with different properties.

Contribution

It introduces a new average offspring recombination operator and enhancements to Minima Hopping, providing a comparative analysis of their performance on diverse cluster systems.

Findings

Minima Hopping performs well across all tested systems.

Evolutionary Algorithm is efficient for symmetric, compact clusters.

EA struggles with complex, asymmetric energy landscapes.

Abstract

We compare Evolutionary Algorithms with Minima Hopping for global optimization in the field of cluster structure prediction. We introduce a new {\em average offspring} recombination operator and compare it with previously used operators. Minima Hopping is improved with a {\em softening} method and a stronger feedback mechanism. Test systems are atomic clusters with Lennard-Jones interaction as well as silicon and gold clusters described by force fields. The improved Minima Hopping is found to be well-suited to all these homoatomic problems. The evolutionary algorithm is more efficient for systems with compact and symmetric ground states, including LJ$_{150}$, but it fails for systems with very complex energy landscapes and asymmetric ground states, such as LJ$_{75}$ and silicon clusters with more than 30 atoms. Both successes and failures of the evolutionary algorithm suggest ways for its improvement.