Visualization of Pareto-Sets in Evolutionary Multi-Objective Optimization
Visualization of Pareto-Sets in Evolutionary Multi-Objective Optimization
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DOI：
10.1109/his.2007.62
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发表时间：
2007-09
期刊：
影响因子：
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通讯作者：
M. Köppen;Kaori Yoshida
中科院分区：
文献类型：
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作者：
M. Köppen;Kaori Yoshida
本文提出了一种多目标进化优化（EMO）算法种群的可视化方法。这种方法的主要特点是尽可能好地保持个体之间的帕累托优势关系。它将表明，在一般情况下，从高维到低维空间的帕累托优势保持映射是不存在的。因此，要求是找到具有尽可能少的错误指示的支配关系的映射，这给出了除了诸如保持最近邻关系的其他映射目标之外的另一个目标。因此，这样的映射本身构成多目标优化问题，这也是由EMO算法（在这种情况下NSGA-II）处理。作为一个例子，所得到的映射显示为运行的NSGA-II版本的15个目标DTLZ 2问题。从这些图中，可以获得一些关于进化动力学的见解。
In this paper, a method for the visualization of the population of an evolutionary multi-objective optimization (EMO) algorithm is presented. The main characteristic of this approach is the preservation of Pareto-dominance relations among the individuals as good as possible. It will be shown that in general, a Pareto- dominance preserving mapping from higher- to lower- dimensional spaces does not exist. Thus, the demand is to find a mapping with as few wrongly indicated dominance relations as possible, which gives one more objective in addition to other mapping objectives like preserving nearest neighbor relations. Therefore, such a mapping poses a multi-objective optimization problem by itself, which is also handled by an EMO algorithm (NSGA-II in this case). The resulting mappings are shown for the run of a NSGA-II version on the 15 objective DTLZ2 problem as an example. From such plots, some insights into evolutionary dynamics can be obtained.