Article

Quantifying the effects of objective space dimension in evolutionary multiobjective optimization

Authors:

Joshua Knowles,

David CorneAuthors Info & Claims

EMO'07: Proceedings of the 4th international conference on Evolutionary multi-criterion optimization

Pages 757 - 771

Published: 05 March 2007 Publication History

Abstract

The scalability of EMO algorithms is an issue of significant concern for both algorithm developers and users. A key aspect of the issue is scalability to objective space dimension, other things being equal. Here, we make some observations about the efficiency of search in discrete spaces as a function of the number of objectives, considering both uncorrelated and correlated objective values. Efficiency is expressed in terms of a cardinality-based (scaling-independent) performance indicator. Considering random sampling of the search space, we measure, empirically, the fraction of the true PF covered after p iterations, as the number of objectives grows, and for different correlations. A general analytical expression for the expected performance of random search is derived, and is shown to agree with the empirical results. We postulate that for even moderately large numbers of objectives, random search will be competitive with an EMO algorithm and show that this is the case empirically: on a function where each objective is relatively easy for an EA to optimize (an NK-landscape with K=2), random search compares favourably to a well-known EMO algorithm when objective space dimension is ten, for a range of inter-objective correlation values. The analytical methods presented here may be useful for benchmarking of other EMO algorithms.

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Published In

cover image Guide Proceedings

EMO'07: Proceedings of the 4th international conference on Evolutionary multi-criterion optimization

March 2007

953 pages

ISBN:9783540709275

Editors:
Shigeru Obayashi
Tohoku University, Sendai, Japan
,
Kalyanmoy Deb
Indian Institute of Technology, Kanpur, India
,
Carlo Poloni
University of Trieste, Trieste, Italy
,
Tomoyuki Hiroyasu
Doshisha University, Kyoto, Japan
,
Tadahiko Murata
Kansai University, Osaka, Japan

Sponsors

Kansai University
JAXA: Japan Aerospace Exploration Agency
Institute of Fluid Science
Graduate School of Information Sciences

In-Cooperation

Cd-Adapco Japan Co., Ltd.
Cray Japan Inc.
BESTSYSTEMS Co., Ltd.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 05 March 2007

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Cited By

Sun YYen GYi Z(2018)Improved Regularity Model-Based EDA for Many-Objective OptimizationIEEE Transactions on Evolutionary Computation10.1109/TEVC.2018.279431922:5(662-678)Online publication date: 1-Oct-2018
https://dl.acm.org/doi/10.1109/TEVC.2018.2794319
Sun YYen GYi Z(2017)Global view-based selection mechanism for many-objective evolutionary algorithms2017 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2017.7969343(427-434)Online publication date: 5-Jun-2017
https://dl.acm.org/doi/10.1109/CEC.2017.7969343
Yu GShen RZheng JLi MZou JLiu Y(2017)Binary search based boundary elimination selection in many-objective evolutionary optimizationApplied Soft Computing10.1016/j.asoc.2017.07.03060:C(689-705)Online publication date: 1-Nov-2017
https://dl.acm.org/doi/10.1016/j.asoc.2017.07.030
Liu RSong XFang LJiao L(2017)An r-dominance-based preference multi-objective optimization for many-objective optimizationSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-016-2098-x21:17(5003-5024)Online publication date: 1-Sep-2017
https://dl.acm.org/doi/10.1007/s00500-016-2098-x
Shen RZheng JLi MZou J(2017)Many-objective optimization based on information separation and neighbor punishment selectionSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-015-1842-y21:5(1109-1128)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1007/s00500-015-1842-y
Cuate ODerbel BLiefooghe ATalbi ESchütze O(2017)An Approach for the Local Exploration of Discrete Many Objective Optimization Problems9th International Conference on Evolutionary Multi-Criterion Optimization - Volume 1017310.1007/978-3-319-54157-0_10(135-150)Online publication date: 19-Mar-2017
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Zhu CXu LGoodman E(2016)Generalization of Pareto-Optimality for Many-Objective Evolutionary OptimizationIEEE Transactions on Evolutionary Computation10.1109/TEVC.2015.245724520:2(299-315)Online publication date: 1-Apr-2016
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Martí LGarcía JBerlanga AMolina J(2016)A stopping criterion for multi-objective optimization evolutionary algorithmsInformation Sciences: an International Journal10.1016/j.ins.2016.07.025367:C(700-718)Online publication date: 1-Nov-2016
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