GTM: the generative topographic mapping
Neural Computation
A Spectral Algorithm for Seriation and the Consecutive Ones Problem
SIAM Journal on Computing
A general geometric construction of coordinates in a convex simplicial polytope
Computer Aided Geometric Design
Techniques for highly multiobjective optimisation: some nondominated points are better than others
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Heatmap visualization of population based multi objective algorithms
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
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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.