  Topological sorting is an important technique in numerous practical
applications, such as information retrieval, recommender systems, optimization,
etc. In this paper, we introduce a problem of generalized topological sorting
with maximization of choice, that is, of choosing a subset of items of a
predefined size that contains the maximum number of equally preferable options
(items) with respect to a dominance relation. We formulate this problem in a
very abstract form and prove that sorting by k-Pareto optimality yields a valid
solution. Next, we show that the proposed theory can be useful in practice. We
apply it during the selection step of genetic optimization and demonstrate that
the resulting algorithm outperforms existing state-of-the-art approaches such
as NSGA-II and NSGA-III. We also demonstrate that the provided general
formulation allows discovering interesting relationships and applying the
developed theory to different applications.
