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Examples include the use of trees to represent populations of solutions, such as the dominated trees and non-dominated tree structures proposed by and the non-dominated tree structure proposed in. Hierarchies are a convenient structure within evolutionary computation.
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Other methods avoid this loss of information by presenting the objective vectors in terms of the full set of objectives (e.g., ) or visualising relationships between solutions (for example, conveying which solutions are superior to others) and are constructed in terms of the full objective set (e.g., ). For example, in some methods the number of dimensions to be visualised is reduced so that a conventional visualisation can be employed (e.g., ). The information that can be extracted from such methods varies depending on the type of visualisation. In the past decade, much work has been focussed on the development of methods that can visualise many-objectives. The visualisation methods proposed herein are intended to aid the decision maker in this task. Presented with the solution set, the decision maker must select a single solution that can be implemented to solve the problem. In the case of any MaOEA the task of a decision maker is an important one as the result of executing the algorithm is a set of solutions, which are usually incomparable according to measures such as Pareto dominance. Thus, visualisation is a vital part of the optimisation process as it enables the non-expert user to better understand the results they are presented with. They are likely from an industrial or scientific background, and do not necessarily have a background in evolutionary computation. In this work the decision maker is considered to be the problem owner-the person who wishes to solve the optimisation problem.
![treemap chart counter-indicated when treemap chart counter-indicated when](http://www.maartenlambrechts.com/assets/exporttreemap.png)
The main motivation behind this work is to facilitate the decision maker’s selection of a final operating solution.
![treemap chart counter-indicated when treemap chart counter-indicated when](https://media.cheggcdn.com/comis/bb0/bb08e20e-28d8-43a8-be58-e4d329a14a4b/732950-MEM6-1IL1.png)
Visualising the objective vectors to such problems is a non-trivial problem because humans are not able to comprehend more than three spatial dimensions. At various stages during the process of solving a many-objective problem with a MaOEA it is desirable to visualise objective vectors.