Article

Adaptation of Scalarizing Functions in MOEA/D: An Adaptive Scalarizing Function-Based Multiobjective Evolutionary Algorithm

Authors:

Hisao Ishibuchi,

Noritaka Tsukamoto,

Yusuke NojimaAuthors Info & Claims

EMO '09: Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization

Pages 438 - 452

https://doi.org/10.1007/978-3-642-01020-0_35

Published: 21 April 2009 Publication History

Abstract

It is well-known that multiobjective problems with many objectives are difficult for Pareto dominance-based algorithms such as NSGA-II and SPEA. This is because almost all individuals in a population are non-dominated with each other in the presence of many objectives. In such a population, the Pareto dominance relation can generate no strong selection pressure toward the Pareto front. This leads to poor search ability of Pareto dominance-based algorithms for many-objective problems. Recently it has been reported that better results can be obtained for many-objective problems by the use of scalarizing functions. The weighted sum usually works well in scalarizing function-based algorithms when the Pareto front is convex. However, we need other functions such as the weighted Tchebycheff when the Pareto front is non-convex. In this paper, we propose an idea of automatically choosing between the weighted sum and the weighted Tchebycheff for each individual in each generation. The characteristic feature of the proposed idea is to use the weighted Tchebycheff only when it is needed for individuals along non-convex regions of the Pareto front. The weighted sum is used for the other individuals in each generation. The proposed idea is combined with a high-performance scalarizing function-based algorithm called MOEA/D (multiobjective evolutionary algorithm based on decomposition) of Zhang and Li (2007). Effectiveness of the proposed idea is demonstrated through computational experiments on modified multiobjective knapsack problems with non-convex Pareto fronts.

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Published In

cover image Guide Proceedings

EMO '09: Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization

April 2009

583 pages

ISBN:9783642010194

Editors:
Matthias Ehrgott
Department of Engineering Science, The University of Auckland, Auckland, New Zealand 1001
,
Carlos M. Fonseca
Faculty of Science and Technolgoy, Department of Electronic Engineering and Informatics, Universidade do Algarve, Faro, Portugal 8005-139
,
Xavier Gandibleux
Laboratoire d' Informatique de Nantes -LINA, UMR CNRS 6241, Université de Nantes, Nantes Cedex 03, France 44322
,
Jin-Kao Hao
LERIA, Faculty of Sciences, Université d'Angers, Angers Cedex 01, France 49045
,
Marc Sevaux
Université de Bretagne-sud - UEB CNRS, UMR 3192 - Lab-STICC, Centre de Recherche,, Lorient Cedex, France 56321

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 21 April 2009

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Tahernezhad-Javazm FRankin DCoyle D(2022)A Hybrid Multi-Objective Teaching Learning-Based Optimization Using Reference Points and R2 IndicatorProceedings of the 2022 6th International Conference on Intelligent Systems, Metaheuristics & Swarm Intelligence10.1145/3533050.3533053(19-23)Online publication date: 9-Apr-2022
https://dl.acm.org/doi/10.1145/3533050.3533053
Wang ZDeng JZhang QYang Q(2021)On the Parameter Setting of the Penalty-Based Boundary Intersection Method in MOEA/DEvolutionary Multi-Criterion Optimization10.1007/978-3-030-72062-9_33(413-423)Online publication date: 28-Mar-2021
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Nguyen BXue BAndreae PIshibuchi HZhang M(2020)Multiple Reference Points-Based Decomposition for Multiobjective Feature Selection in Classification: Static and Dynamic MechanismsIEEE Transactions on Evolutionary Computation10.1109/TEVC.2019.291383124:1(170-184)Online publication date: 1-Feb-2020
https://dl.acm.org/doi/10.1109/TEVC.2019.2913831
Gómez RCoello CBosman P(2017)A hyper-heuristic of scalarizing functionsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3071178.3071220(577-584)Online publication date: 1-Jul-2017
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Nguyen HXue BIshibuchi HAndreae PZhang M(2017)Multiple reference points MOEA/D for feature selectionProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3067695.3075985(157-158)Online publication date: 15-Jul-2017
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Pescador-Rojas MHernández Gómez RMontero ERojas-Morales NRiff MCoello Coello C(2017)An Overview of Weighted and Unconstrained Scalarizing Functions9th International Conference on Evolutionary Multi-Criterion Optimization - Volume 1017310.1007/978-3-319-54157-0_34(499-513)Online publication date: 19-Mar-2017
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Wang LZhang QZhou AGong MJiao L(2016)Constrained Subproblems in a Decomposition-Based Multiobjective Evolutionary AlgorithmIEEE Transactions on Evolutionary Computation10.1109/TEVC.2015.245761620:3(475-480)Online publication date: 1-Jun-2016
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Michalak K(2015)Using an outward selective pressure for improving the search quality of the MOEA/D algorithmComputational Optimization and Applications10.1007/s10589-015-9733-961:3(571-607)Online publication date: 1-Jul-2015
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Ma XLiu FQi YGong MYin MLi LJiao LWu J(2014)MOEA/D with opposition-based learning for multiobjective optimization problemNeurocomputing10.1016/j.neucom.2014.04.068146:C(48-64)Online publication date: 15-Oct-2014
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