  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.
