A Survey of Normalization Methods in Multiobjective Evolutionary Algorithms

A real-world multiobjective optimization problem (MOP) usually has differently scaled objectives. Objective space normalization has been widely used in multiobjective optimization evolutionary algorithms (MOEAs). Without objective space normalization, most of the MOEAs may fail to obtain uniformly d...

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Vydáno v:IEEE transactions on evolutionary computation Ročník 25; číslo 6; s. 1028 - 1048
Hlavní autoři: He, Linjun, Ishibuchi, Hisao, Trivedi, Anupam, Wang, Handing, Nan, Yang, Srinivasan, Dipti
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.12.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Dominance resistant solution (DRS)
Estimation
Evolutionary algorithms
Evolutionary computation
evolutionary multiobjective optimization (EMO)
Genetic algorithms
ideal point
Mopping
Multiple objective analysis
nadir point
objective space normalization
Optimization
Pareto optimization
Resistance
Search problems
ISSN:1089-778X, 1941-0026
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Shrnutí:A real-world multiobjective optimization problem (MOP) usually has differently scaled objectives. Objective space normalization has been widely used in multiobjective optimization evolutionary algorithms (MOEAs). Without objective space normalization, most of the MOEAs may fail to obtain uniformly distributed and well-converged solutions on MOPs with differently scaled objectives. Objective space normalization requires information on the Pareto front (PF) range, which can be acquired from the ideal and nadir points. Since the ideal and nadir points of a real-world MOP are usually not known a priori , many recently proposed MOEAs tend to estimate and update the two points adaptively during the evolutionary process. Different methods to estimate ideal and nadir points have been proposed in the literature. Due to inaccurate estimation of the two points (i.e., inaccurate estimation of the PF range), objective space normalization may deteriorate the performance of an MOEA. Different methods have also been proposed to alleviate the negative effects of inaccurate estimation. This article presents a comprehensive survey of objective space normalization methods, including ideal point estimation methods, nadir point estimation methods, and different methods based on the utilization of the estimated PF range.
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ISSN:1089-778X
1941-0026
DOI:10.1109/TEVC.2021.3076514