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首页> 外文期刊>Evolutionary computation >Hyperplane-Approximation-Based Method for Many-Objective Optimization Problems with Redundant Objectives
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Hyperplane-Approximation-Based Method for Many-Objective Optimization Problems with Redundant Objectives

机译：具有超目标的多目标优化问题的基于超平面近似的方法

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摘要

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 sigma* 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 delta-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.
机译：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的Pareto前沿提出了两种新颖的目标约简算法。它们分别称为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估计PF的结构。这种方法与以前基于相关性或优势结构的客观约简算法完全不同。特别是在NLHA中，为了减小逼近误差，我们通过幂变换将非线性退化的Pareto前沿转换为几乎线性退化的Pareto前沿。另外，这里还提出了一个将幅度调整机制和性能指标sigma *集成在一起的客观简化框架。最后，为了证明所提出算法的性能，对三个基准问题DTLZ5（两个基于相关性的算法LPCA和NLMVUPCA以及两个基于支配结构的算法PCSEA和贪婪delta-MOSS进行了对比实验。 I，M），MAOP（I，M）和WFG3（I，M）。实验结果表明，该算法是有效的。

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