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

## 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.

# 凸优化代考

## 数学代写|凸优化作业代写凸优化代考|针对

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