  Population diversity is crucial in evolutionary algorithms to enable global
exploration and to avoid poor performance due to premature convergence. This
book chapter reviews runtime analyses that have shown benefits of population
diversity, either through explicit diversity mechanisms or through naturally
emerging diversity. These works show that the benefits of diversity are
manifold: diversity is important for global exploration and the ability to find
several global optima. Diversity enhances crossover and enables crossover to be
more effective than mutation. Diversity can be crucial in dynamic optimization,
when the problem landscape changes over time. And, finally, it facilitates
search for the whole Pareto front in evolutionary multiobjective optimization.
The presented analyses rigorously quantify the performance of evolutionary
algorithms in the light of population diversity, laying the foundation for a
rigorous understanding of how search dynamics are affected by the presence or
absence of population diversity and the introduction of diversity mechanisms.
