A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization

In evolutionary multiobjective optimization, maintaining a good balance between convergence and diversity is particularly crucial to the performance of the evolutionary algorithms (EAs). In addition, it becomes increasingly important to incorporate user preferences because it will be less likely to...

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Bibliographic Details
Published in:	IEEE transactions on evolutionary computation Vol. 20; no. 5; pp. 773 - 791
Main Authors:	Ran Cheng, Yaochu Jin, Olhofer, Markus, Sendhoff, Bernhard
Format:	Journal Article
Language:	English
Published:	IEEE 01.10.2016
Subjects:	Angle-penalized distance (APD) Convergence diversity Evolutionary computation evolutionary multiobjective optimization Linear programming many-objective optimization Pareto optimization preference articulation reference vector Sociology
ISSN:	1089-778X, 1941-0026
Online Access:	Get full text
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Abstract	In evolutionary multiobjective optimization, maintaining a good balance between convergence and diversity is particularly crucial to the performance of the evolutionary algorithms (EAs). In addition, it becomes increasingly important to incorporate user preferences because it will be less likely to achieve a representative subset of the Pareto-optimal solutions using a limited population size as the number of objectives increases. This paper proposes a reference vector-guided EA for many-objective optimization. The reference vectors can be used not only to decompose the original multiobjective optimization problem into a number of single-objective subproblems, but also to elucidate user preferences to target a preferred subset of the whole Pareto front (PF). In the proposed algorithm, a scalarization approach, termed angle-penalized distance, is adopted to balance convergence and diversity of the solutions in the high-dimensional objective space. An adaptation strategy is proposed to dynamically adjust the distribution of the reference vectors according to the scales of the objective functions. Our experimental results on a variety of benchmark test problems show that the proposed algorithm is highly competitive in comparison with five state-of-the-art EAs for many-objective optimization. In addition, we show that reference vectors are effective and cost-efficient for preference articulation, which is particularly desirable for many-objective optimization. Furthermore, a reference vector regeneration strategy is proposed for handling irregular PFs. Finally, the proposed algorithm is extended for solving constrained many-objective optimization problems.
AbstractList	In evolutionary multiobjective optimization, maintaining a good balance between convergence and diversity is particularly crucial to the performance of the evolutionary algorithms (EAs). In addition, it becomes increasingly important to incorporate user preferences because it will be less likely to achieve a representative subset of the Pareto-optimal solutions using a limited population size as the number of objectives increases. This paper proposes a reference vector-guided EA for many-objective optimization. The reference vectors can be used not only to decompose the original multiobjective optimization problem into a number of single-objective subproblems, but also to elucidate user preferences to target a preferred subset of the whole Pareto front (PF). In the proposed algorithm, a scalarization approach, termed angle-penalized distance, is adopted to balance convergence and diversity of the solutions in the high-dimensional objective space. An adaptation strategy is proposed to dynamically adjust the distribution of the reference vectors according to the scales of the objective functions. Our experimental results on a variety of benchmark test problems show that the proposed algorithm is highly competitive in comparison with five state-of-the-art EAs for many-objective optimization. In addition, we show that reference vectors are effective and cost-efficient for preference articulation, which is particularly desirable for many-objective optimization. Furthermore, a reference vector regeneration strategy is proposed for handling irregular PFs. Finally, the proposed algorithm is extended for solving constrained many-objective optimization problems.
Author	Sendhoff, Bernhard Olhofer, Markus Yaochu Jin Ran Cheng
Author_xml	– sequence: 1 surname: Ran Cheng fullname: Ran Cheng email: ranchengcn@gmail.com organization: Dept. of Comput. Sci., Univ. of Surrey, Guildford, UK – sequence: 2 surname: Yaochu Jin fullname: Yaochu Jin email: yaochu.jin@surrey.ac.uk organization: Dept. of Comput. Sci., Univ. of Surrey, Guildford, UK – sequence: 3 givenname: Markus surname: Olhofer fullname: Olhofer, Markus email: markus.olhofer@honda-ri.de organization: Honda Res. Inst. Eur., Offenbach, Germany – sequence: 4 givenname: Bernhard surname: Sendhoff fullname: Sendhoff, Bernhard email: bernhard.sendhoff@honda-ri.de organization: Honda Res. Inst. Eur., Offenbach, Germany
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Snippet	In evolutionary multiobjective optimization, maintaining a good balance between convergence and diversity is particularly crucial to the performance of the...
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SubjectTerms	Angle-penalized distance (APD) Convergence diversity Evolutionary computation evolutionary multiobjective optimization Linear programming many-objective optimization Pareto optimization preference articulation reference vector Sociology
Title	A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization
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