Data-sets for the Visualisation of Multi-objective optimisation
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MooViz (Multi-objective optimisation Vizualisations) stores the objective values produced by Multi-Objective Evolutionary Algorithms. Visualisation is one of the great challenges for Muti-Objective Problems, specially when working with problems consisting of 4 or more objectives.

visualising the objective space

Organisation of repository

This repository is organised first into the number of dimensions (objectives), then into the problem being solved, then into the number of the sample. I.e., /objectives/problem/sample/sub-directories

The sub-directories are:

/lambda folder contains the candidate solutions up for consideration at each generation, i.e. they are competing to survive in the next generation and produce offspring.

/mu folder contains the parent solutions, these are solutions which have survived and will producing the lambda solutions.

/fig folder contains my own plots of the mu and lambda solutions. This has been omitted due to file size.

/gif folder contains my own ffmpeg GIF output of my /fig folder ffmpeg -i %d.png output.gif. Uploaded to gfycat too.

Each folder contains output at each iteration of the optimisation process.

Optimisation algorithm

The algorithm used to generate these results is CMA-PAES-HAGA. This is a many-objective optimisation algorithm. Open-access paper can be found here

  title={Covariance matrix adaptation pareto archived evolution strategy with hypervolume-sorted adaptive grid algorithm},
  author={Rostami, Shahin and Neri, Ferrante},
  journal={Integrated Computer-Aided Engineering},
  publisher={IOS Press}

The problem being solved is WFG9

  title={A scalable multi-objective test problem toolkit},
  author={Huband, Simon and Barone, Luigi and While, Lyndon and Hingston, Phil},
  booktitle={International Conference on Evolutionary Multi-Criterion Optimization},

Auxiliary information

The CMA-PAES-HAGA algorithm (used to generate these results) maintains additional parameters which describe a solution. Some of this data has also been stored in this repository to enhance your visualisations. E.g., you could make the markers indicating a solution smaller or larger depending on how much of the objective space they dominate explicitly.


There is a data file for each generation. This requires some explanation of the ordering of the lambda population at each generation:

  • The first 100 solutions are the mu (parent) population selected in the previous generation
  • The second 100 solutions are the offspring population created from the parent population.
  • Eeach solution in the mu population creates an offspring solution.
  • They are in order, such that in the lambda population, the solution at index 0 is the parent for the solution at index 100.

Column 1 of the data indicates which solution was this solutions parent. E.g., if the parent_id is 77, then the solution at index 77 is the parent. This ordering is maintained in all data-sets on this repository.

Column 2 of the data indicates if the solution is a parent. If it is a parent, you should ignore Column 1, as it will state the ID of the solution and not the parent. E.g. if the parent_id is 77, but column 2 is 1, you ignore it. However, if you see two solutions with parent_id, this indicates that both the parent and the offspring made it to the next generation. This can be interesting information.


There is a data file for each generation. This represents the adapted step-size for every solution in the selected mu population. The higher the sigma, the larger the steps when varying a solution. Higher sigma can indicate confidence in the direction of the evolution of solutions, lower sigma can indicate lower confidence in the direction (or maybe the solutions have converged).

dominance of solutions

In the mu population, the order of solutions indicates the explicit hypervolume of the objective space that they dominate. A solution at index 0 covers a greater area compared to the solution at index 1, when you're not considering the area which both of them overlap. This is in respect to a reference point.

This reference point is dynamically calculated at each generation:

ref = (lambda_pop.max(axis=0) * .1) + lambda_pop.max(axis=0)

where lambda_pop.max(axis=0) returns the largest (worst) value found in each column (objective).


If preference articulation has been used, whether it's a priori or progressive, the preferences will be stored for each generation.


The problem variables for each corresponding solution in mu/ are stored here. The minimum requirement is that the problem variables for the final population is stored.


This folder stores the current extreme (worst) objective values found at each generation.