On Scalable Multiobjective Test Problems With Hardly Dominated Boundaries
On Scalable Multiobjective Test Problems With Hardly Dominated Boundaries
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DOI：
10.1109/tevc.2018.2844286
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发表时间：
2019-04
影响因子：
14.3
通讯作者：
Zhenkun Wang;Y. Ong;H. Ishibuchi
中科院分区：
文献类型：
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作者：
Zhenkun Wang;Y. Ong;H. Ishibuchi
DTLZ 1-DTLZ 4问题是多目标优化进化算法验证和比较中最常用的测试问题之一。然而，最近有人指出，他们有以下两个特殊的特点：1）规则定向的帕累托前沿形状和2）单一的距离函数。作为对它们的改进，本文提出了一组新的测试问题mDTLZ 1-mDTLZ 4，以避免这两个特殊性。使用这些新的测试问题，我们研究了三个代表性的多目标进化算法NSGA-II，MOEA/D-Tch，和SMS-EMOA的性能。实验结果表明，NSGA-II和MOEA/D-Tch算法在mDTLZ 1-mDTLZ 4上性能恶化。分析表明，mDTLZ 1-mDTLZ 4都存在难支配边界，这阻碍了基于Pareto优势的算法和基于Tchebycheff分解的算法的逼近.此外，我们总结了几乎不支配边界应该是多目标优化中经常遇到的问题特征。最后，我们指出并验证了基于优势的算法和基于分解的算法的一些应对策略，以克服几乎没有优势的边界所带来的挑战。
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.