Visualizing Exact and Approximated 3D Empirical Attainment Functions
Table 1
Summarized properties of the presented visualization methods.
Slicing
MIP
DVR
Exact EAF values
+ Enables detailed analysis of the approximation sets − Visualizes only one slice at a time
− Not sensible to use since usually a large portion of the objective space has the maximum EAF value
− Not possible to use
Exact EAF differences
+ Enables detailed analysis of the approximation sets + Capable of simultaneously visualizing positive and negative differences without overlapping − Visualizes only one slice at a time
+ No parameters to set + Shows all values in a single image − No sense of depth − Feasible only for a limited number of cuboids (impractical)
− Not possible to use
Approximated EAF values
− No need to use it on the approximation as it works well for exact EAFs
− Not sensible to use since usually a large portion of the objective space has the maximum EAF value
+ Nice visualizations + Enables looking through the volume and preserves the sense of depth − Requires definition of the transfer function
Approximated EAF differences
− No need to use it on the approximation as it works well for exact EAFs
+ No parameters to set + Shows all values in a single image − No sense of depth
+ Nice visualizations + Enables looking through the volume and preserves the sense of depth − Requires definition of the transfer function