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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| Veröffentlicht in: | IEEE transactions on evolutionary computation Jg. 25; H. 6; S. 1028 - 1048 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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New York
IEEE
01.12.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1089-778X, 1941-0026 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Wang, Handing Srinivasan, Dipti Ishibuchi, Hisao Nan, Yang He, Linjun Trivedi, Anupam |
| Author_xml | – sequence: 1 givenname: Linjun orcidid: 0000-0002-4255-2538 surname: He fullname: He, Linjun email: this.helj@gmail.com organization: Department of Computer Science and Engineering, Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation, Southern University of Science and Technology, Shenzhen, China – sequence: 2 givenname: Hisao orcidid: 0000-0001-9186-6472 surname: Ishibuchi fullname: Ishibuchi, Hisao email: hisao@sustech.edu.cn organization: Department of Computer Science and Engineering, Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation, Southern University of Science and Technology, Shenzhen, China – sequence: 3 givenname: Anupam orcidid: 0000-0002-3066-5578 surname: Trivedi fullname: Trivedi, Anupam email: eleatr@nus.edu.sg organization: Department of Electrical and Computer Engineering, National University of Singapore, Singapore – sequence: 4 givenname: Handing orcidid: 0000-0002-4805-3780 surname: Wang fullname: Wang, Handing email: hdwang@xidian.edu.cn organization: School of Artificial Intelligence, Xidian University, Xi'an, China – sequence: 5 givenname: Yang orcidid: 0000-0001-8396-294X surname: Nan fullname: Nan, Yang email: nany@mail.sustech.edu.cn organization: Department of Computer Science and Engineering, Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation, Southern University of Science and Technology, Shenzhen, China – sequence: 6 givenname: Dipti orcidid: 0000-0003-4877-3478 surname: Srinivasan fullname: Srinivasan, Dipti email: dipti@nus.edu.sg organization: Department of Electrical and Computer Engineering, National University of Singapore, Singapore |
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| Snippet | A real-world multiobjective optimization problem (MOP) usually has differently scaled objectives. Objective space normalization has been widely used in... |
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| SubjectTerms | 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 |
| Title | A Survey of Normalization Methods in Multiobjective Evolutionary Algorithms |
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