Verified Methods for Computing Pareto Sets: General Algorithmic Analysis

Abstract

Verified Methods for Computing Pareto Sets: General Algorithmic AnalysisIn many engineering problems, we face multi-objective optimization, with several objective functionsf1, …,fn. We want to provide the user with the Pareto set—a set of all possible solutionsxwhich cannot be improved in all categories (i.e., for whichfj(x') ≥fj(x) for alljandfj(x') >fj(x) for somejis impossible). The user should be able to select an appropriate trade-off between, say, cost and durability. We extend the general results about (verified) algorithmic computability of maxima locations to show that Pareto sets can also be computed.