﻿ Domination Rank

# Domination Rank

The domination rank of solutions is reported when you specify a multi-objective search (when you check multiple objectives as the search criteria).

Lower ranks are better.  A solution has domination rank 1 if no other solutions are either equal to or better than it on all of the search objectives.  To illustrate, the graphic below shows four possible solutions (A-D) plotted in terms of Profit on the X-axis and Share of Preference on the Y-axis.

Solution B has both higher share and higher profit than solution A.  Thus, A is dominated by solution B on both dimensions.  Solution C has higher profit than solution B, but lower share.  Neither B nor C is dominated (or equaled) on both dimensions by any other solution.  Thus, the Pareto efficient frontier of non-dominated solutions is defined by the set indicated by blue markers {B, C}.  We call solutions B and C rank order 1 solutions, because they are dominated by no other solutions.  The set {A, D} indicated by brown markers are rank order 2 solutions, because they each are dominated by exactly one other solution.  Rank-order 3 solutions are dominated by exactly 2 other solutions, etc.  We compute the rank-order for all solutions in this manner and remove any ranks that have no solutions (renumbering the ranks from 1 to n in successive integers).

Consider a multi-objective search for which we asked the software to report the top 50 solutions.  A graphic is reported where solutions of the same rank order are labeled with a common marker and color.  The blue circles in this graphic are rank order one solutions.

If you hover your pointer over a marker, the solution number (Result #287 in the example above) is reported so you can investigate the details (e.g. attribute level composition) of that solution in the table report.  In the table below, you see the metrics and attribute composition of Result Index #287 (the fifth result listed in the report).