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Articulating User Preferences in Many-Objective Problems by Sampling the Weighted Hypervolume

Anne Auger 1 Johannes Bader 2 Dimo Brockhoff 1 Eckart Zitzler 2 
1 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : The hypervolume indicator has become popular in recent years both for performance assessment and to guide the search of evolutionary multiobjective optimizers. Two critical research topics can be emphasized with respect to hyper\-volume-based search: (i) the hypervolume indicator inherently introduces a specific preference and the question is how arbitrary user preferences can be incorporated; (ii) the exact calculation of the hypervolume indicator is expensive and efficient approaches to tackle many-objective problems are needed. In two previous studies, we addressed both issues independently: a study proposed the weighted hypervolume indicator with which user-defined preferences can be articulated; other studies exist that propose to estimate the hypervolume indicator by Monte-Carlo sampling. Here, we combine these two approaches for the first time and extend them, i.e., we present an approach of sampling the weighted hypervolume to incorporate user-defined preferences into the search for problems with many objectives. In particular, we propose weight distribution functions to stress extreme solutions and to define preferred regions of the objective space in terms of so-called preference points; sampling them allows to tackle problems with many objectives. Experiments on several test functions with up to 25 objectives show the usefulness of the approach in terms of decision making and search.
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Submitted on : Wednesday, November 11, 2009 - 3:15:51 PM
Last modification on : Sunday, June 26, 2022 - 11:50:50 AM
Long-term archiving on: : Thursday, June 17, 2010 - 6:02:17 PM

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Anne Auger, Johannes Bader, Dimo Brockhoff, Eckart Zitzler. Articulating User Preferences in Many-Objective Problems by Sampling the Weighted Hypervolume. Genetic and Evolutionary Computation Conference (GECCO 2009), Jul 2009, Montreal, Canada. pp.555-562, ⟨10.1145/1569901.1569979⟩. ⟨hal-00431271⟩

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