数学代写|凸优化作业代写Convex Optimization代考|MATH3204

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数学代写|凸优化作业代写Convex Optimization代考|Visualization of Sequence Flow

A special graph drawing problem, related to the visualization of business process diagrams, is stated as an optimization problem. It is requested to find aesthetically looking paths between the given pairs of vertices of a grid, where the vertices represent the business process flow objects, the paths represent the sequence flow, and the aesthetic criteria are formulated quantitatively. The sites of flow objects on the grid are fixed, and the sequence flow is defined. We state the problem as a problem of combinatorial multi-objective optimization, where the objectives correspond to the generally recognized criteria of aesthetics. To find a solution precisely, the algorithm of linear binary programming CPLEX was applied. For a fasterr solution, supposed for an interactive mode, a héuristic algorithm is developed. The experimental comparison of the mentioned algorithms is performed to substantiate the applicability of the latter.

To enable a user to completely percept the information presented by the observable part of the BPD, the sub-charts which comprise up to 30 shapes are drawn. A navigation tool aids a user to specify the sub-chart of interest. To denote the flow objects in the considered diagrams, the notation of BPMN, namely the rectangles, the rhombuses, and the circles, is used where these shapes represent the processes, the gateways, and the events correspondingly. The shapes are located in the pool lanes. The sequence flow is represented by the lines constituted of orthogonal straight line segments.

We assume that the location of geometric shapes, that represent business process objects, is fixed on a plane, and a sequence flow is defined. The lines, that represent the sequence flow, should be drawn aiming to obtain an aesthetically pleasing layout. For the general concept of aesthetic graph drawing we refer to $[12,15,100,171-173]$. Here we reduce this problem to a combinatorial multiobjective optimization.

As the main criteria of aesthetics considered in the literature, e.g., in $[12,100$, 173], are: the total length of connectors, the number of crossings, the number of bends, the uniformity of the distribution of shapes in the area of the drawing, and the compatibility of the process sub-flows with the generalized top-down and left-right direction. However, the influence of these criteria to the perception of the information presented by the considered BPD is different, and depends on the user of the BPD. To implement a visualization method, which ensures the effective perception of a BPD, the attitude of potential users towards the listed above criteria is important. The generalized attitude of a group of the potential users was elicited by means of a psychological experiment [93]. Subsequently, the elicited information is used in the statement of the multi-objective optimization problem the solution of which defines the considered sequence flow by the orthogonal connectors.

数学代写|凸优化作业代写Convex Optimization代考|A Brief Overview of Single-Objective Algorithms Aimed

Since we focus on the sequence flow visualization, the differences of the flow objects can be ignored, and a single rectangular shape can be used below to represent the flow objects. Visualization of the graphs, where vertices are drawn as rectangles connected by piecewise vertical and horizontal lines, is commonly used. As the examples, Entity Relationship and UML diagrams can be mentioned among others. The problem of drawing graphs, with the rectangular images of vertices, and with the edges composed of the pieces of vertical and horizontal lines, is considered in many papers. Depending on a supposed application area, the algorithms should satisfy different requirements. Some algorithms, efficient from the point of view of general complexity theory, are described in [117, 232]. A comprehensive review of algorithms oriented to the routing of paths to interconnect the pins on the circuit blocks or pads at the chip boundary is presented in [32]. The general purpose routing algorithms are classified in three groups, namely the maze, line-search, and $\mathrm{A}^*$-search groups. Different versions of these algorithms are proposed and investigated with the focus on the asymptotic complexity estimates and on the application in the chip design. However, from the point of view of the BPD drawing, the criteria of aesthetics prevail the criteria important in technological applications emphasized in [32]. In a recent paper [231] a brief review of the available algorithms and software, for the construction of orthogonal connectors, is presented. The experimental testing performed by these authors has shown that some of the available software packages, although provide the automatic orthogonal connector routing, produce the routes which may overlap other objects in the diagram. Popular software packages Microsoft Visio 2007 and Concept Draw Pro5 provide the object-avoiding orthogonal connector routing, but in both cases the aesthetic criteria, such as minimizing distance or number of segments, are not taken into account. We cite the conclusion made in the introduction of [231]: “in all current tools that we are aware of, automatic routing of orthogonal connectors uses ad-hoc heuristics that lead to aesthetically unpleasing routes and unpredictable behavior.” Agreeing with the latter conclusion as well as with the remarks cited in the introductory Section $10.1$ we find the developing of new domain-specific algorithms reasonable.

数学代写|凸优化作业代写Convex Optimization代考|MATH3204

凸优化代考

数学代写|凸优化作业代写凸优化代考|序列流可视化


一个与业务流程图可视化相关的特殊图形绘制问题被表述为一个优化问题。要求在给定的网格顶点对之间找到美观的路径,其中顶点表示业务流程流对象,路径表示序列流,并定量地表述美观标准。确定了流对象在网格上的位置,定义了序列流。我们将该问题描述为一个组合多目标优化问题,其中目标对应于公认的美学标准。为了精确求解,采用了线性二元规划CPLEX算法。为了更快的解决方案,假定为交互式模式,开发了héuristic算法。对上述算法进行了实验比较,以证实后者的适用性


为了使用户能够完全感知BPD的可观察部分所呈现的信息,绘制了包含多达30个形状的子图表。导航工具帮助用户指定感兴趣的子图。为了表示所考虑的图中的流对象,使用了BPMN的符号,即矩形、菱形和圆形,这些形状表示相应的流程、网关和事件。这些形状位于泳池的泳道上。序列流由正交直线段组成的线表示。


我们假设表示业务流程对象的几何形状的位置固定在平面上,并且定义了序列流。线,代表序列流,应该旨在获得一个美观的布局。关于美学图形绘制的一般概念,请参阅$[12,15,100,171-173]$。这里我们将这个问题简化为一个组合多目标优化问题

作为文献中考虑的主要美学标准,例如,在$[12,100$, 173],是:连接器的总长度,交叉的数量,弯曲的数量,形状分布在图纸区域的均匀性,以及工艺子流与广义的自上而下和左右方向的兼容性。但是,这些标准对被考虑的BPD所呈现的信息的感知的影响是不同的,并且取决于BPD的用户。要实现确保BPD有效感知的可视化方法,潜在用户对上面列出的标准的态度是重要的。一组潜在用户的广义态度是通过心理实验得到的[93]。然后,将所得到的信息用于多目标优化问题的表述中,该问题的解通过正交连接器定义了所考虑的序列流

数学代写|凸优化作业代写凸优化代考|针对

的单目标算法概述


由于我们关注的是序列流可视化,流对象的差异可以忽略,下面可以使用单个矩形形状来表示流对象。通常使用图形的可视化,其中顶点被绘制为由分段的垂直和水平线连接的矩形。作为例子,实体关系图和UML图可以被提及。许多论文都研究了用顶点的矩形图像和由垂直和水平的线段组成的边来绘制图形的问题。根据假设的应用领域,算法应该满足不同的要求。从一般复杂性理论的角度来看,一些有效的算法在[117,232]中得到了描述。[32]中全面回顾了面向路径路由的算法,以互连电路块上的引脚或芯片边界上的衬垫。通用路由算法分为三类,分别是maze、line-search和$\mathrm{A}^*$ -search。提出并研究了这些算法的不同版本,重点是渐近复杂度估计和在芯片设计中的应用。然而,从BPD制图的角度来看,美学标准占优势于[32]中强调的技术应用中重要的标准。在最近的一篇论文[231]中,简要回顾了用于构建正交连接器的现有算法和软件。这些作者所进行的实验测试表明,一些可用的软件包虽然提供了自动正交连接器路由,但产生的路由可能与图中的其他对象重叠。流行的软件包Microsoft Visio 2007和Concept Draw Pro5提供了避免对象的正交连接器路由,但在这两种情况下,没有考虑到美学标准,如最小化距离或段的数量。我们引用了[231]引言中的结论:“在我们所知的所有当前工具中,正交连接器的自动路由使用特殊的启发式,这会导致不美观的路由和不可预测的行为。”我们同意后一个结论以及在引言部分$10.1$中引用的注释,我们发现开发新的特定于领域的算法是合理的

数学代写|凸优化作业代写Convex Optimization代考

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