Visualisation and ordering of many-objective populations

We introduce novel methods of visualising and ordering multi-and many-objective populations. We compare individuals by the probability that one will beat another in a tournament on a randomly selected objective. This defines a weighted directed graph representing the population. We introduce a novel graphical representation of the many objective population based on Pareto shells. We examine leagues, Pareto shells, preference ordering, average rank, outflow, the stationary distribution and the power index for ordering the population finding that the average rank is equivalent to outflow and that these together with the power index are generally superior. Finally, we show how to seriate objectives to enhance the interpretability of heatmap visualisations.