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Hyperplane-Approximation-Based Method for Many-objective Optimization Problems with Redundant Objectives
Evolutionary Computation ( IF 6.8 ) Pub Date : 2019-06-01 , DOI: 10.1162/evco_a_00223
Yifan Li 1 , Hai-Lin Liu 1 , E D Goodman 2
Affiliation  

For a many-objective optimization problem with redundant objectives, we propose two novel objective reduction algorithms for linearly and, nonlinearly degenerate Pareto fronts. They are called LHA and NLHA respectively. The main idea of the proposed algorithms is to use a hyperplane with non-negative sparse coefficients to roughly approximate the structure of the PF. This approach is quite different from the previous objective reduction algorithms that are based on correlation or dominance structure. Especially in NLHA, in order to reduce the approximation error, we transform a nonlinearly degenerate Pareto front into a nearly linearly degenerate Pareto front via a power transformation. In addition, an objective reduction framework integrating a magnitude adjustment mechanism and a performance metric σ* are also proposed here. Finally, to demonstrate the performance of the proposed algorithms, comparative experiments are done with two correlation-based algorithms, LPCA and NLMVUPCA, and with two dominance-structure-based algorithms, PCSEA and greedy δ-MOSS, on three benchmark problems: DTLZ5(I,M), MAOP(I,M), and WFG3(I,M). Experimental results show that the proposed algorithms are more effective.

中文翻译:

多目标多目标优化问题的基于超平面逼近的方法

对于具有冗余目标的多目标优化问题,我们针对线性和非线性退化帕累托前沿提出了两种新颖的目标约简算法。它们分别被称为 LHA 和 NLHA。所提出算法的主要思想是使用具有非负稀疏系数的超平面来粗略近似PF的结构。这种方法与之前基于相关性或优势结构的客观归约算法有很大不同。特别是在 NLHA 中,为了减少逼近误差,我们通过幂变换将非线性退化的帕累托前沿转化为近似线性退化的帕累托前沿。此外,这里还提出了一个集成了幅度调整机制和性能指标 σ* 的客观减少框架。最后,为了证明所提出算法的性能,使用两种基于相关性的算法,LPCA 和 NLMVUPCA,以及两种基于优势结构的算法,PCSEA 和贪婪的 δ-MOSS,在三个基准问题上进行了比较实验:DTLZ5(I, M)、MAOP(I,M) 和 WFG3(I,M)。实验结果表明,所提出的算法更有效。
更新日期:2019-06-01
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