Exploring Structural Diversity in Evolutionary Algorithms

Optimization problems can either be single- or multi-objective. In the case of a single-objective problem, there is one solution or possibly a set of solutions that has the best objective value, whereas in the case of multi-objective problems with conflicting objectives, there is no single best solution, but a set of tradeoff solutions, the so-called Pareto-optimal front. Usually, the goal of optimizing algorithms is to find one or all of the best solutions in single-objective problems, and the whole Pareto-optimal front or a representative subset of it in multi-objective problems. This thesis considers the case that there are some uncertainties or simplifications in the optimization model, which make close-to-optimal solutions also interesting for the user who optimizes the problem. Moreover, we assume that the user is interested in a set of structurally diverse, close-to-optimal solutions. The present thesis (a) explores ways to generate such sets of solutions, and (b) provides methods to analyze the resulting sets of solutions. Finally, this thesis investigates the properties of the hypervolume indicator, which is a contemporary measure to quantify the quality of a set of solutions in terms of its objective values in multi-objective problems. We investigate the effectiveness of this indicator, which states whether an algorithm can reach a set of solutions of a certain size with the best hypervolume.