极值问题的动画视觉分析

极值问题的动画视觉分析(中文4000字,英文2800字)
摘  要
本文的结果在于建立了一种分析极值问题新方法的基础。发现了一种刻画极值问题的新现象。基于问题中目标函数观测集的交互性的知识发现，构造了动画视觉分析的方法。该分析的目的是在定义域中找到一个方向，从而最大化在该方向随机选择的两个点上的目标函数值的平均绝对差，或者（并且）最大化每个距离单元上该方向随机选择的两个点上的目标函数值的平均绝对差。提出的方法需要生成许多数据集合。有时这种生成是计算昂贵的。
因此，这篇文章讨论的的思想可以应用于侦查员不但想解决极值问题而且想得到更多信息的的情形。
关键字： 最优化;视觉分析;动画;数据分析;知识发现
 
1. 引言
     计算机辅助设计与控制的复杂问题来源于现代科技的快速发展。最优解的搜索在这有本质的意义，这个领域的研究有两个方向：新优化方法的发展和包含这些方法的各种实现手段的软件。关键是用最少的工作量去尽快地求解这些问题。当选择一种合适的优化策略后，极值问题的知识（目标函数，变量，约束条件）就显得很重要。在这些知识的基础上，我们选择具体的方法进行优化。对于需要优化的问题，极小化知识是经常用到得，也就是说，它是求解问题的必要条件（但不是最有效方法的必要条件）。利用提高最优化效率的观点，发展特别的方法和策略去得到最优化问题的知识发现时很有价值的。

Chapter 5
ANIMATED VISUAL ANALYSIS OF EXTREMAL
PROBLEMS
Gintautas Dzemyda
Institute of Mathematics and Informatics
Akademijos St. 4, 2600 Vilnius, Lithuania
dzemyda@ktl.mii.lt
Abstract The results presented in this paper make up the basis for a new way of analyzing extremal problems. A new phenomenon that characterizes an extremal problem has been discovered. The paper tries to reveal fields of application of this phenomenon. The method of animated visual analysis, based on the knowledge discovery in the set of observations of the objective function of the problem interactively, has been developed. The aim of analysis is to find a direction in the definition domain such that maximizes the mean absolute difference between two values of the objective function calculated at randomly selected points in this
direction, or (and) maximizes the mean absolute difference per distance unit of the objective function values calculated at two randomly selected points in this direction. The presented approach requires generating many data sets. Sometimes such a generation is very computation-expensive. Therefore, the ideas discussed in this paper may be applied in the case where the investigator wants not only to solve the extremal problem, but also to discover additional knowledge of it.
Keywords: Optimization, visual analysis, animation, data analysis, knowledge discovery