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Convergence of stochastic search algorithms to finite size pareto set approximations
Ist Teil von
Journal of global optimization, 2008-08, Vol.41 (4), p.559-577
Ort / Verlag
Boston: Springer US
Erscheinungsjahr
2008
Link zum Volltext
Quelle
SpringerNature Journals
Beschreibungen/Notizen
In this work we investigate the convergence of stochastic search algorithms toward the Pareto set of continuous multi-objective optimization problems. The focus is on obtaining a finite approximation that should capture the entire solution set in a suitable sense, which will be defined using the concept of
ε
-dominance. Under mild assumptions about the process to generate new candidate solutions, the limit approximation set will be determined entirely by the archiving strategy. We propose and analyse two different archiving strategies which lead to a different limit behavior of the algorithms, yielding bounds on the obtained approximation quality as well as on the cardinality of the resulting Pareto set approximation.