22078 articles – 15904 references  [version française]
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 Genetic and Evolutionary Computation Conference (GECCO 2009), Montreal : Canada (2009)
 Investigating and Exploiting the Bias of the Weighted Hypervolume to Articulate User Preferences
 Anne Auger 1, Johannes Bader 2
 (2009-07-08)
 Optimizing the hypervolume indicator within evolutionary multiobjective optimizers has become popular in the last years. Recently, the indicator has been generalized to the weighted case to incorporate various user preferences into hypervolume-based search algorithms. There are two main open questions in this context: (i) how does the specified weight influence the distribution of a fixed number of points that maximize the weighted hypervolume indicator? (ii) how can the user articulate her preferences easily without specifying a certain weight distribution function? In this paper, we tackle both questions. First, we theoretically investigate optimal distributions of $\mu$ points that maximize the weighted hypervolume indicator. Second, based on the obtained theoretical results, we propose a new approach to articulate user preferences within biobjective hypervolume-based optimization in terms of specifying a desired density of points on a predefined (imaginary) Pareto front. Within this approach, a new exact algorithm based on dynamic programming is proposed which selects the set of $\mu$ points that maximizes the (weighted) hypervolume indicator. Experiments on various test functions show the usefulness of this new preference articulation approach and the agreement between theory and practice.
 1: TAO (INRIA Saclay - Ile de France) INRIA – CNRS : UMR8623 – Université Paris XI - Paris Sud 2: Computer Engineering and Networks Laboratory (TIK) Swiss Federal Institute of Technology Zurich (ETH Zurich)
 Subject : Computer Science/Neural and Evolutionary ComputingMathematics/Optimization and Control
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 hal-00431274, version 1 http://hal.archives-ouvertes.fr/hal-00431274 oai:hal.archives-ouvertes.fr:hal-00431274 From: Dimo Brockhoff <> Submitted on: Wednesday, 11 November 2009 15:22:07 Updated on: Wednesday, 11 November 2009 22:09:56