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Indicator Based Search in Variable Orderings: Theory and Algorithms

Indicator Based Search in Variable Orderings: Theory and Algorithms

Published: 2013

Buchtitel: in EMO 2013
Nummer: in press„in press“ ist keine Zahl.
Reihe: LNCS
Verlag: Springer

Referierte Veröffentlichung


Various real world problems, especially in financial applications, medical engineering and game theory, involve solving a multi-objective optimization problem with a variable ordering structure. This means that the ordering relation at a point in the (multi-)objective space depends on the point. This is a striking difference from usual multi-objective optimization problems, where the ordering is induced by the Pareto-cone and remains constant throughout the objective space. In addition to variability, in many applications (like portfolio optimization) the ordering is induced by a non-convex set instead of a cone. The main purpose of this paper is to provide theoretical and algorithmic advances for general set-based variable orderings. A hypervolume based indicator measure is also proposed for the first time, for such optimization tasks. Theoretical results are derived and properties of this indicator are studied. Moreover, the theory is also used to develop three indicator based algorithms for approximating the set of optimal solutions. Computational results show the niche of population based algorithms for solving multi-objective problems with variable orderings.


Effiziente Algorithmen


Evolutionäre Algorithmen, Multikriterielle Optimierung, Globale Optimierung