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Title: On scalable multiobjective test problems with hardly dominated boundaries
Authors: Wang, Zhenkun
Ong, Yew-Soon
Ishibuchi, Hisao
Keywords: Engineering::Computer science and engineering
Issue Date: 2018
Source: Wang, Z., Ong, Y.-S., & Ishibuchi, H. (2019). On scalable multiobjective test problems with hardly dominated boundaries. IEEE Transactions on Evolutionary Computation, 23(2), 217-231. doi:10.1109/tevc.2018.2844286
Journal: IEEE Transactions on Evolutionary Computation 
Abstract: The DTLZ1-DTLZ4 problems are by far one of the most commonly used test problems in the validation and comparison of multiobjective optimization evolutionary algorithms (MOEAs). However, very recently, it has been pointed out that they have the following two special characteristics: 1) the regularly oriented Pareto front shape and 2) the single distance function. As a modification of them, this paper presents a new set of test problems mDTLZ1-mDTLZ4 to avoid the two special characteristics. Using these new test problems, we investigate the performance of three representative multiobjective evolutionary algorithms NSGA-II, MOEA/D-Tch, and SMS-EMOA. Experimental results indicate that the performance of NSGA-II and MOEA/D-Tch deteriorates on mDTLZ1-mDTLZ4. Subsequently, our analysis reveals that there exist the hardly dominated boundaries in each of mDTLZ1-mDTLZ4, which hinder the approximation of Pareto dominance-based algorithms and Tchebycheff-decomposition-based algorithms. Furthermore, we summarize that the hardly dominated boundary should be an often encountered problem feature in multiobjective optimization. Last but not least, we point out and validate some coping strategies for dominance-based algorithms and decomposition-based algorithms to overcome the challenges caused by the hardly dominated boundary.
ISSN: 1089-778X
DOI: 10.1109/TEVC.2018.2844286
Schools: School of Computer Science and Engineering 
Rights: © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at:
Fulltext Permission: open
Fulltext Availability: With Fulltext
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