Visualising high-dimensional Pareto relationships in two-dimensional scatterplots

Abstract. In this paper two novel methods for projecting high dimen-sional data into two dimensions for visualisation are introduced, which aim to limit the loss of dominance and Pareto shell relationships be-tween solutions to multi-objective optimisation problems. It has already been shown that, in general, it is impossible to completely preserve the dominance relationship when mapping from a higher to a lower dimen-sion – however, approaches that attempt this projection with minimal loss of dominance information are useful for a number of reasons. (1) They may represent the data to the user of a multi-objective optimi-sation problem in an intuitive fashion, (2) they may help provide in-sights into the relationships between solutions which are not immedi-ately apparent through other visualisation methods, and (3) they may offer a useful visual medium for interactive optimisation. We are con-cerned here with examining (1) and (2), and developing relatively rapid methods to achieve visualisations, rather than generating an entirely new search/optimisation problem which has to be solved to achieve the visualisation – which may prove infeasible in an interactive environment for real time use. Results are presented on randomly generated data, and the search population of an optimiser as it progresses. Structural insights into the evolution of a set-based optimiser that can be derived from this visualisation are also discussed