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Visualizing multi-dimensional pareto-optimal fronts with a 3D virtual reality system

机译:用3D虚拟现实系统可视化多维帕肌架 - 最佳前端

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In multiobjective optimization, there are several targets that are in conflict, and thus they all cannot reach their optimum simultaneously. Hence, the solutions of the problem form a set of compromised trade-off solutions (a Pareto-optimal front or Pareto-optimal solutions) from which the best solution for the particular problem can be chosen. However, finding that best compromise solution is not an easy task for the human mind. Pareto-optimal fronts are often visualized for this purpose because in this way a comparison between solutions according to their location on the Pareto-optimal front becomes somewhat easier. Visualizing a Pareto-optimal front is straightforward when there are only two targets (or objective functions), but visualizing a front for more than two objective functions becomes a difficult task. In this paper, we introduce a new and innovative method of using three-dimensional virtual reality (VR) facilities to present multi-dimensional Pareto-optimal fronts. Rotation, zooming and other navigation possibilities of VR facilities make easy to compare different trade-off solutions, and fewer solutions need to be explored in order to understand the interrelationships among conflicting objective functions. In addition, it can be used to highlight and characterize interesting features of specific Pareto-optimal solutions, such as whether a particular solution is close to a constraint boundary or whether a solution lies on a relatively steep trade-off region. Based on these additional visual aids for analyzing trade-off solutions, a preferred compromise solution may be easier to choose than by other means.
机译:在多目标优化中,有几个在冲突中的目标,因此它们都无法同时达到最佳。因此,问题的解决方案形成了一组受损的折衷解决方案(帕累托 - 最佳前部或帕累托 - 最佳解决方案),可以选择特定问题的最佳解决方案。但是,发现最好的妥协解决方案不是人类思维的一件容易的任务。帕累托 - 最佳前端通常是为此目的而可视化的,因为以这种方式,解决方案之间的比较根据其位置在帕累托 - 最佳前部的位置变得有些更容易。当只有两个目标(或客观函数)时,可视化帕累托 - 最佳前端是简单的,但是以超过两个目标函数可视化前面成为一项艰巨的任务。在本文中,我们介绍了一种新的和创新的方法,使用三维虚拟现实(VR)设施呈现多维帕累托 - 最佳前端。 VR设施的旋转,缩放和其他导航可能性使得易于比较不同的权衡解决方案,并且需要探索更少的解决方案,以了解相互冲突的客观职能之间的相互关系。另外,它可用于突出显示特定帕累托 - 最佳解决方案的有趣特征,例如特定解决方案是否接近约束边界,或者解决方案是否在于相对陡峭的折衷区域。基于这些额外的视觉辅助装置来分析折衷解决方案,优选的折衷解决方案可能比其他方式更容易选择。

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