Simple multicriteria optimization with Pareto layers

Chart: Three layers of Pareto sets
The red elements dominate over the green, the green over the blue, the blue over the unlayered rest.

Pareto set contains elements dominating over others.

From the optimization perspective, they contain elements that should be considered equal.

Often it is possible to establish layers of Pareto sets subordinate to the higher order sets.

Pareto sets and layers are interesting way of selecting elements characterized by multiple criteria.

One of the other methods is convolution.

There is a number of R packages for creating and analyzing  the Pareto frontier:

• http://cran.r-project.org/web/packages/TunePareto/index.html 
• http://cran.r-project.org/web/packages/mco/ 
• http://cran.r-project.org/web/packages/SPOT/index.html