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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|凸优化作业代写Convex Optimization代考|Description of the Problem

The problem of visualization of a sequence flow was posed as a problem of combinatorial multi-objective optimization in [93], where the objectives correspond to the aesthetic criteria. The results of a psychological experiment, described in [93], substantiate the selection of aesthetic criteria that are most important for the potential users. The stated problem was attacked in [93] by a metaheuristic ant colony optimization algorithm. The solutions, found by means of that algorithm in reasonable time, were assessed as acceptable for applications. Nevertheless, the following reason motivated a further investigation: usually a few non-dominated solutions were found. Therefore, a hypothesis seems likely that there exist other Pareto optimal solutions, but they were not found by the metaheuristic algorithm used. To test that hypothesis all the global optima of the criteria in question should be found with a guarantee. To this end, the corresponding single-objective optimization problems were stated in the form of binary-linear optimization, and the CPLEX algorithm [38] was applied to solve them. A combination of CPLEX with the scalarization technique is also used to solve the multi-objective optimization problem in question. However, such a combination, although well suitable to solve small size problems, fails in the case of larger problems because of long computing time. A heuristic algorithm was proposed applicable to the problems of size sufficient for applications.

An example of elementary BPD is presented in Figure 10.1a. In geometric terms, it is requested to draw paths that consist of horizontal and vertical line segments, and connect the given geometric shapes (circles, rhombuses, and rectangles) in the plane. The shapes are located in “swim lanes,” at the centers of cells of a rectangular grid, and the paths are requested to consist of horizontal and vertical segments with the ends at circle markers, located on the boarders between “swim lanes,” as shown in Figure 10.1b. In terms of the graph theory we are interested in the paths between the given vertices of a graph, defined by a rectangular grid [92] of the type presented in Figure 10.1b. We search here for the paths with the minimum total length, minimum total number of bends, and minimum neighborhood; we refer to [93] for a detailed discussion on the criteria of path desirability. The argumentation presented there substantiates the consideration of the problem of aesthetic drawing of BPDs by means of the methods for multi-objective graph optimization.

Although some similarity is obvious between the considered problem and the classical bi-objective path problem [64, 77], the known methods for the latter do not seem applicable to the former one. This remark also holds for the similarity of the considered problem with routing problems in electronic design [32].

## 数学代写|凸优化作业代写Convex Optimization代考|Binary-Linear Model

To state a multi-objective optimization problem mathematically, we have to introduce variables that define the considered (reduced) graph. Let $p$ denote the number of rows, and $n$ denote the number of columns. The pivot vertices are marked hy a double index $i j$ that indicates the crossing of the $i$-th row and $j$-thcolumn. The intermediate vertices are indicated by two neighboring pivot vertices. A path is defined by assigning value 1 to the indexed variable $x$, related to the edge which belongs to the path; the values of the variables related to edges not belonging to the path in question are equal to zero. The variable $x$ is indexed as follows: $\dot{x}{i j}$ and $x{i j}$ are related to the top and bottom adjacent edges of the vertex $i j$, respectively; see Figure 10.3. Similarly $\overleftarrow{x}{i j}$ and $\vec{x}{i j}$ are related to the right and left adjacent edges. The values of $z_{i j}$ mark the path as follows: $z_{i j}=1$, if the vertex $i j$ is on the path, and $z_{i j}=0$, if it is not on the path. The values of the introduced variables should satisfy the following equalities:
$$\begin{array}{r} \dot{x}{i j}-\dot{x}{i+1, j}=0, \overleftarrow{x}{i, j+1}-\vec{x}{i j}=0 \ \dot{x}{i j}+\dot{x}{i j}+\overleftarrow{x}{i j}+\vec{x}{i j}-2 z_{i j}=0 \ \overleftarrow{x}{i 1}=0, \vec{x}{i n}=0, \dot{x}{1 j}=0, \dot{x}{m j}=0 \ i=1, \ldots, p, j=1, \ldots, n \end{array}$$
Note that the zero length edges in (10.3) are redundant; but they are included into the model to unify the adjacency of all the pivot vertices.

A path is specified by the start and sink vertices, which are of the intermediate type; such vertices are presented in the mathematical model by the balance equalities as follows:
$$\dot{x}{i j}+\dot{x}{i+1, j}=1,$$
if the vertex is located on the $j$-th column between $i$ and $i+1$ rows, and
$$\overleftarrow{x}{i, j+1}+\vec{x}{i j}=1$$
if the vertex is located on the $i$-th row between $j$ and $j+1$ columns.

. quot

## 数学代写|凸优化作业代写凸优化代考|二元线性模型

$$\begin{array}{r} \dot{x}{i j}-\dot{x}{i+1, j}=0, \overleftarrow{x}{i, j+1}-\vec{x}{i j}=0 \ \dot{x}{i j}+\dot{x}{i j}+\overleftarrow{x}{i j}+\vec{x}{i j}-2 z_{i j}=0 \ \overleftarrow{x}{i 1}=0, \vec{x}{i n}=0, \dot{x}{1 j}=0, \dot{x}{m j}=0 \ i=1, \ldots, p, j=1, \ldots, n \end{array}$$

$$\dot{x}{i j}+\dot{x}{i+1, j}=1,$$
，如果顶点位于$i$和$i+1$行之间的$j$ -th列，
$$\overleftarrow{x}{i, j+1}+\vec{x}{i j}=1$$
，如果顶点位于$j$和$j+1$列之间的$i$ -th行

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师