Evolutionary algorithms (EAs) are randomized search heuristics that solve problems successfully in many cases. Their behavior is often described in terms of strategies to find a high location on Earth's surface. Unfortunately, many digital elevation models describing it contain void elements. These are elements not assigned an elevation. Therefore, we design and analyze simple EAs with different strategies to handle such partially defined functions. They are experimentally investigated on a dataset describing the elevation of Earth's surface. The largest value found by an EA within a certain runtime is measured, and the median over a few runs is computed and compared for the different EAs. For the dataset, the distribution of void elements seems to be neither random nor adversarial. They are so-called semirandomly distributed. To deepen our understanding of the behavior of the different EAs, they are theoretically considered on well-known pseudo-Boolean functions transferred to partially defined ones. These modifications are also performed in a semirandom way. The typical runtime until an optimum is found by an EA is analyzed, namely bounded from above and below, and compared for the different EAs. We figure out that for the random model it is a good strategy to assume that a void element has a worse function value than all previous elements. Whereas for the adversary model it is a good strategy to assume that a void element has the best function value of all previous elements.

Evolutionary algorithms (EAs) are population-based randomized search heuristics that often solve problems successfully. Here the focus is on the possible effects of changing the parent population size in a simple, but still realistic, mutation-based EA. It preserves diversity by avoiding duplicates in its population. On the one hand its behavior on well-known pseudo-Boolean example functions is investigated by means of a rigorous runtime analysis. A comparison with the expected runtime of the algorithm's variant that does not avoid duplicates demonstrates the strengths and weaknesses of maintaining diversity. On the other hand, newly developed functions are presented for which the optimizer considered that even a decrease of the population size by a single increment leads from efficient optimization to enormous runtime and overwhelming probability. This is proven for all feasible population sizes and thereby this result forms a hierarchy theorem. In order to obtain all these results new methods for the analysis of the EA are developed.