Modelling Diversity of Solutions

For many combinatorial problems, finding a single solution is not enough. This is clearly the case for multi-objective optimization problems, as they have no single "best solution" and, thus, it is useful to find a representation of the nondominated solutions (the Pareto frontier). However, it also applies to single objective optimization 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 idealize 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 paper 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.