Divergence of character is a cornerstone of natural evolution. On the contrary, evolutionary optimization processes are plagued by an endemic lack of population diversity: all candidate solutions eventually crowd the very same areas in the search space. The problem is usually labeled with the oxymoron “premature convergence” and has very different consequences on the different applications, almost all deleterious. At the same time, case studies from theoretical runtime analyses irrefutably demonstrate the benefits of diversity. This tutorial will give an introduction into the area of “diversity promotion”: we will define the term “diversity” in the context of Evolutionary Computation, showing how practitioners tried, with mixed results, to promote it. Then, we will analyze the benefits brought by population diversity in specific contexts, namely global exploration and enhancing the power of crossover. To this end, we will survey recent results from rigorous runtime analysis on selected problems. 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 diversity and the introduction of diversity mechanisms
