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Yes sorry, dominant means strictly better in some sense, but may be equal in many objectives. > Every solution in the Pareto front set dominates every solution
by speedstyle 1mo ago
Yes sorry, dominant means strictly better in some sense, but may be equal in many objectives.
> Every solution in the Pareto front set dominates every solution not in that set
Not quite – for each solution not in the set, there exists a solution in the set that dominates it. For instance a front with (0,2) (1,1) (2,0) would not have (1,0). While (0,2) doesn't dominate (1,0), something else does.
- kazinator 1mo agoYes; it is not relevant whether the dominating solution is in the set or not. It is a fact that the solutions in the front dominate all those not in the front, but the weakest statement we can make is that if a for a given solution B, we find another one A which is a dominant of B, then B is not in the front (regardless of whether or not A is). Anyway, a couple of hours ago, I fixed up the informal wording in the article, which had misleading interpretations.