computeDominanceRanking {ecr}

Ranking of approximation sets.

Description

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.

Usage

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.

Value

[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()