Visualising many-objective populations

Abstract

Optimisation problems often comprise a large set of objectives, and visualising the set of solutions to a problem can help with understanding them, assisting a decision maker. If the set of objectives is larger than three, visualising solutions to the problem is a difficult task. Techniques for visualising high-dimensional data are often difficult to interpret. Conversely, discarding objectives so that the solutions can be visualised in two or three spatial dimensions results in a loss of potentially important information. We demonstrate four methods for visualising many-objective populations, two of which use the complete set of objectives to present solutions in a clear and intuitive fashion and two that compress the objectives of a population into two dimensions whilst minimising the information that is lost. All of the techniques are illustrated on populations of solutions to optimisation test problems.