Modelling Diversity of Solutions

Abstract: For many combinatorial problems, finding a single solution is not enough. This is clearly the case for multi-objective optimisation problems, as they have no single “best solution” and, thus, it is useful to find a representation of the non-dominated solutions (the Pareto frontier). However, it also applies to single objective optimisation problems, where one may be interested in finding several (close to) optimal solutions that illustrate some form of diversity. The same applies to satisfaction problems. This is because models usually idealise the problem in some way, and a diverse pool of solutions may provide a better choice with respect to considerations that are omitted or simplified in the model. This thesis describes a general framework for finding k diverse solutions to a combinatorial problem (be it satisfaction, single-objective or multi-objective), various approaches to solve problems in the framework, their implementations, and an experimental evaluation of their practicality.