Coordinated Adaptation of Reference Vectors and Scalarizing Functions in Evolutionary Many-Objective Optimization

It is highly desirable to adapt the reference vectors to unknown Pareto fronts (PFs) in decomposition-based evolutionary many-objective optimization. While adapting the reference vectors enhances the diversity of the achieved solutions, it often decelerates the convergence performance. To address th...

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Bibliographic Details
Published in:IEEE transactions on systems, man, and cybernetics. Systems Vol. 53; no. 2; pp. 763 - 775
Main Authors: Liu, Qiqi, Jin, Yaochu, Heiderich, Martin, Rodemann, Tobias
Format: Journal Article
Language:English
Published: New York IEEE 01.02.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptation
Algorithms
Convergence
Deceleration
Evolutionary many-objective optimization
irregular Pareto fronts (PFs)
Mathematical analysis
Multiple objective analysis
Optimization
Problem solving
reference vector
scalarizing function
Shape
Sociology
Solids
Stars
Statistics
ISSN:2168-2216, 2168-2232
Online Access:Get full text
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Summary:It is highly desirable to adapt the reference vectors to unknown Pareto fronts (PFs) in decomposition-based evolutionary many-objective optimization. While adapting the reference vectors enhances the diversity of the achieved solutions, it often decelerates the convergence performance. To address this dilemma, we propose to adapt the reference vectors and the scalarizing functions in a coordinated way. On the one hand, the adaptation of the reference vectors is based on a local angle threshold, making the adaptation better tuned to the distribution of the solutions. On the other hand, the weights of the scalarizing functions are adjusted according to the local angle thresholds and the reference vectors' age, which is calculated by counting the number of generations in which one reference vector has at least one solution assigned to it. Such coordinated adaptation enables the algorithm to achieve a better balance between diversity and convergence, regardless of the shape of the PFs. Experimental studies on MaF, DTLZ, and DPF test suites demonstrate the effectiveness of the proposed algorithm in solving problems with both regular and irregular PFs.
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ISSN:2168-2216
2168-2232
DOI:10.1109/TSMC.2022.3187370