论文标题

基于图像的基准测试和可视化,以进行大规模全局优化

Image-Based Benchmarking and Visualization for Large-Scale Global Optimization

论文作者

Harrison, Kyle Robert, Bidgoli, Azam Asilian, Rahnamayan, Shahryar, Deb, Kalyanmoy

论文摘要

在优化的背景下,可视化技术对于理解优化算法的行为很有用,甚至可以提供一种促进与优化器相互作用的方法。为了实现这一目标,一个基于图像的可视化框架而没有缩小尺寸,该框架可视化图像时大规模全局优化问题的解决方案。在提出的框架中,像素可视化决策变量,而整个图像表示整体解决方案质量。该框架比现有的可视化技术提供了许多好处,包括增强的可伸缩性(就决策变量的数量而言),促进标准图像处理技术的促进,提供了几乎无限的基准案例以及与人类感知的明确一致性。此外,基于图像的可视化可用于实时可视化优化过程,从而允许用户在搜索过程中确定搜索过程的特征。据作者所知,这是一个具有维度可扩展的可视化框架的第一个实现,该框架嵌入了决策空间与目标空间之间的固有关系。所提出的框架在图像重建问题上使用了10种不同的映射方案,该方案包括连续,离散,二进制,组合,约束,动态和多目标优化。然后,在已知的Optima的任意基准问题上证明了所提出的框架。实验结果阐明了灵活性,并证明了如何通过拟议的可视化框架收集有关搜索过程的有价值信息。

In the context of optimization, visualization techniques can be useful for understanding the behaviour of optimization algorithms and can even provide a means to facilitate human interaction with an optimizer. Towards this goal, an image-based visualization framework, without dimension reduction, that visualizes the solutions to large-scale global optimization problems as images is proposed. In the proposed framework, the pixels visualize decision variables while the entire image represents the overall solution quality. This framework affords a number of benefits over existing visualization techniques including enhanced scalability (in terms of the number of decision variables), facilitation of standard image processing techniques, providing nearly infinite benchmark cases, and explicit alignment with human perception. Furthermore, image-based visualization can be used to visualize the optimization process in real-time, thereby allowing the user to ascertain characteristics of the search process as it is progressing. To the best of the authors' knowledge, this is the first realization of a dimension-preserving, scalable visualization framework that embeds the inherent relationship between decision space and objective space. The proposed framework is utilized with 10 different mapping schemes on an image-reconstruction problem that encompass continuous, discrete, binary, combinatorial, constrained, dynamic, and multi-objective optimization. The proposed framework is then demonstrated on arbitrary benchmark problems with known optima. Experimental results elucidate the flexibility and demonstrate how valuable information about the search process can be gathered via the proposed visualization framework.

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