A Rough-to-Fine Evolutionary Multiobjective Optimization Algorithm

This article presents a rough-to-fine evolutionary multiobjective optimization algorithm based on the decomposition for solving problems in which the solutions are initially far from the Pareto-optimal set. Subsequently, a tree is constructed by a modified <inline-formula> <tex-math notatio...

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Veröffentlicht in:IEEE transactions on cybernetics Jg. 52; H. 12; S. 13472 - 13485
Hauptverfasser: Gu, Fangqing, Liu, Hai-Lin, Cheung, Yiu-Ming, Zheng, Minyi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Piscataway IEEE 01.12.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Approximation algorithms
Complexity
Decomposition
Diversity reception
Empirical analysis
evolutionary algorithm
Evolutionary algorithms
Evolutionary computation
incremental
multiobjective optimization
Multiple objective analysis
Optimization
Optimization algorithms
Pareto optimization
Pareto optimum
Problem solving
Sociology
Sorting
Statistics
tree-like weight design
ISSN:2168-2267, 2168-2275, 2168-2275
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Zusammenfassung:This article presents a rough-to-fine evolutionary multiobjective optimization algorithm based on the decomposition for solving problems in which the solutions are initially far from the Pareto-optimal set. Subsequently, a tree is constructed by a modified <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>-means algorithm on <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> uniform weight vectors, and each node of the tree contains a weight vector. Each node is associated with a subproblem with the help of its weight vector. Consequently, a subproblem tree can be established. It is easy to find that the descendant subproblems are refinements of their ancestor subproblems. The proposed algorithm approaches the Pareto front (PF) by solving a few subproblems in the first few levels to obtain a rough PF and gradually refining the PF by involving the subproblems level-by-level. This strategy is highly favorable for solving problems in which the solutions are initially far from the Pareto set. Moreover, the proposed algorithm has lower time complexity. Theoretical analysis shows the complexity of dealing with a new candidate solution is <inline-formula> <tex-math notation="LaTeX">\mathcal {O}(M \log N) </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">M </tex-math></inline-formula> is the number of objectives. Empirical studies demonstrate the efficacy of the proposed algorithm.
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2021.3081357