computeDominanceRanking function

Ranking of approximation sets.

Ranking is performed by merging all approximation sets over all algorithms and runs per instance. Next, each approximation set $C$ is assigned a rank which is 1 plus the number of approximation sets that are better than $C$. A set $D$ is better than $C$, if for each point $x in C$ there exists a point in $y in D$ which weakly dominates $x$. Thus, each approximation set is reduced to a number -- its rank. This rank distribution may act for first comparrison of multi-objecitve stochastic optimizers. See [1] for more details. This function makes use of parallelMap to parallelize the computation of dominance ranks.

computeDominanceRanking(df, obj.cols)

Arguments

• df: [data.frame]

  Data frame with columns at least prob , algorithm , repl and column names specified via parameter obj.cols.

• obj.cols: [character(>= 2)]

  Column names in df which store the objective function values.

Returns

[data.frame] Reduced df with columns prob , algorithm , repl

and rank .

Note

Since pairwise non-domination checks are performed over all algorithms and algorithm runs this function may take some time if the number of problems, algorithms and/or replications is high.

References

[1] Knowles, J., Thiele, L., & Zitzler, E. (2006). A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers. Retrieved from https://sop.tik.ee.ethz.ch/KTZ2005a.pdf

See Also

Other EMOA performance assessment tools: approximateNadirPoint(), approximateRefPoints(), approximateRefSets(), emoaIndEps(), makeEMOAIndicator(), niceCellFormater(), normalize(), plotDistribution(), plotFront(), plotScatter2d(), plotScatter3d(), toLatex()