On Scalable Multiobjective Test Problems With Hardly Dominated Boundaries

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...

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Bibliographic Details
Published in:IEEE transactions on evolutionary computation 2019-04, Vol.23 (2), p.217-231
Main Authors: Wang, Zhenkun, Ong, Yew-Soon, Ishibuchi, Hisao
Format: Article
Language:English
Subjects:
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Approximation algorithms
Boundaries
Decomposition
evolutionary algorithm
Evolutionary algorithms
Evolutionary computation
generalized decomposition
Genetic algorithms
hardly dominated boundaries
Linear programming
multiobjective optimization
Multiple objective analysis
Optimization
Pareto optimization
Pareto optimum
Search problems
Shape
test problems
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Summary: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
1941-0026
DOI:10.1109/TEVC.2018.2844286