Use of Piecewise Linear and Nonlinear Scalarizing Functions in MOEA/D
Use of Piecewise Linear and Nonlinear Scalarizing Functions in MOEA/D
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DOI：
10.1007/978-3-319-45823-6_47
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
H. Ishibuchi;Ken Doi;Y. Nojima
中科院分区：
文献类型：
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作者：
H. Ishibuchi;Ken Doi;Y. Nojima
使用MOEA/D（基于分解的多目标进化算法）框架，已经提出了许多基于权向量的算法用于多目标优化。这些算法的特点是使用均匀分布的归一化权重向量，也称为参考向量、参考线和搜索方向。他们的共同想法是最小化到理想点的距离（即收敛）和到参考线的距离（即均匀性）。每种算法都有其自己的实现收敛一致性平衡的机制。在带有 PBI（基于惩罚的边界交叉）功能的原始 MOEA/D 中，这种平衡是通过惩罚参数来处理的。在本文中，我们首先讨论为什么适当指定惩罚参数是困难的。接下来，我们建议 MOEA/D 中标量函数的轮廓线的所需形状。然后我们提出了修改PBI功能的两个想法。所提出的想法生成分段线性和非线性轮廓线。最后，我们检查了所提出的想法对 MOEA/D 多目标测试问题性能的有效性。
A number of weight vector-based algorithms have been proposed for many-objective optimization using the framework of MOEA/D (multi-objective evolutionary algorithm based on decomposition). Those algorithms are characterized by the use of uniformly distributed normalized weight vectors, which are also referred to as reference vectors, reference lines and search directions. Their common idea is to minimize the distance to the ideal point (i.e., convergence) and the distance to the reference line (i.e., uniformity). Each algorithm has its own mechanism for striking a convergence-uniformity balance. In the original MOEA/D with the PBI (penalty-based boundary intersection) function, this balance is handled by a penalty parameter. In this paper, we first discuss why an appropriate specification of the penalty parameter is difficult. Next we suggest a desired shape of contour lines of a scalarizing function in MOEA/D. Then we propose two ideas for modifying the PBI function. The proposed ideas generate piecewise linear and nonlinear contour lines. Finally we examine the effectiveness of the proposed ideas on the performance of MOEA/D for many-objective test problems.