Tea Tušar: Seeing 4D Approximation Sets

Talk on Seeing 4D Approximation Sets given by Tea Tušar.

In multiobjective optimization, the result produced by an optimizer is usually a set of nondominated solutions approximating the Pareto optimal front. Visualization of this approximation set can help assess its quality as well as present various features of the problem. Most often, scatter plots are used to visualize 2D and 3D approximation sets, while no scatter plot equivalent exists for visualization in higher dimensions.
We present a method for visualizing 4D approximation sets which performs dimension reduction using prosections (projections of a section). The method yields a prosection matrix—a matrix of intuitive 3D scatter plots that well reproduce the shape, range and distribution of vectors in the observed approximation set. The performance of visualization with prosections is analyzed theoretically and demonstrated on two examples with approximation sets of state-of-the-art test optimization problems.