数学代写|凸优化作业代写Convex Optimization代考|ELEC4631

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数学代写|凸优化作业代写Convex Optimization代考|The Analysis of Exploratory Guess

The visualization applied to the available data gives a reason to guess the variable $x_2$ as the most significant variable defining a point on the Pareto front. However, the visual exploratory approach does not provide reliable conclusions, and a further analysis is necessary either to prove or reject this guess.

If the guess above is correct, a clearly expressed dependency between the value of $x_2$ and the position of the corresponding point on the Pareto front should exist. To indicate such a dependency in Figure 9.4a, the values of $x_2$ are shown depending on the index of a Pareto optimal solution where the latter are sorted according to the increase of $f_1\left(\mathbf{x}_i\right)$.

The linear dependency between $x_2$ and the index of a Pareto optimal decision is clearly seen in Figure 9.4a for the indices which belong to the interval $(20,170)$, which is much longer than the interval of interest indicated above. Since the points of the discrete representation are distributed over the Pareto front quite densely and uniformly, all characteristics of interest can be presented as functions of the index as an independent variable. However, such a parametric description of the problem data has a disadvantage: the independent variable has no interpretation in the engineering terms of problem formulation.

A variable $t$ varying along the line in Figure 9.4a seems well suited for use as an independent variable for parametric description of the data of interest. The value of $t$ can be interpreted as a value of $x_2$ smoothed along the Pareto front. The values of $t$ in the interval $0.15 \leq t \leq 0.4$ correspond to the kink of the Pareto front. The relationship between $f_1\left(\mathbf{x}_i\right), f_2\left(\mathbf{x}_i\right)$ and the corresponding value of $t$ is presented by Figure 9.4b. The graphs of $x_2(t)$ and $x_4(t) 0.15 \leq t \leq 0.4$ are presented in Figure 9.5a.

To highlight the location of the most interesting part of the Pareto optimal decisions corresponding to the kink of the Pareto front, the part of image of Figure $9.2$ is presented in Figure 9.5b. The images of the closest vertices are marked by 0 and 1 .

Before the visualization-based analysis, the engineers expected a different impact of the design variables to the trade-off between the Pareto optimal solutions. We refer to [263] where a priori opinion and the final conclusions are discussed in engineering terms.

数学代写|凸优化作业代写Convex Optimization代考|Multi-Objective Optimization Aided

Graphs are very popular models of many research subjects. Graphical presentation of a problem is advantageous for heuristic perception and understanding of relations between the objects considered. On the other hand, many efficient algorithmic techniques are available to attack mathematically stated graph problems. Therefore, graph models are especially useful where heuristic abilities of a human user in the formulation of a problem are combined with its algorithmic solution in the interactive mode. In the present chapter we consider the graph models of business processes which, in the literature on the management of business processes, are called business process diagrams (BPDs). To be more precise, a problem of drawing aesthetically pleasing layouts of BPDs is considered. The research of this problem was motivated by the fact that the aesthetic layouts are not only well readable but also most informative and practical [12].

The considered business process management methodology is oriented to managers and consultants either designing a new Small/Medium Enterprise (SME) or searching for the possibilities to improve an existing one. The Business Process Modeling Notation (BPMN) is accepted as a standard for drawing the business process diagrams [146]. The graph drawing aesthetics is comprehensively discussed, e.g., in $[15,171]$. Although the problem of graph drawing attracts many researchers, and plenty of publications are available, special cases of that problem frequently cannot be solved by straightforward application of the known methods and algorithms. We cite [172]: “Few algorithms are designed for a specific domain, and there is no guarantee that the aesthetics used for generic layout algorithms will be useful for the visualization of domain-specific diagrams.”

The original problem is reduced to a problem of the combinatorial multi-objective optimization. We start with the analysis of the attitude of the potential users of the supposed algorithms towards the relative importance of the widely acceptable criteria of aesthetics. The latter are used as the objectives of the multi-objective optimization problem which formalizes the problem of BPD drawing as an optimization problem.

General rules for drawing BPDs are defined by the standards of BPMN. These standards, however, leave sufficient freedom for choosing the techniques of BPD drawing that are most relévant to the supposed conditions of business processs management. We consider in the present chapter the methods for drawing BPDs aimed at the application by the business process management consultants who advise managers of small and medium enterprises planned to be established or undergoing the re-organization.

数学代写|凸优化作业代写Convex Optimization代考|ELEC4631

凸优化代考

数学代写|凸优化作业代写凸优化代考|探索性猜测的分析

.凸优化 .凸优化


应用于可用数据的可视化提供了猜测变量$x_2$作为定义帕累托前沿点的最重要变量的理由。然而,视觉探索性的方法并不能提供可靠的结论,需要进一步的分析来证明或否定这一猜测

如果上面的猜测是正确的,那么$x_2$的值和对应点在帕累托前沿的位置之间应该存在明显的依赖性。为了在图9.4a中表示这种依赖性,$x_2$的值取决于帕累托最优解的索引,后者是根据$f_1\left(\mathbf{x}_i\right)$的增加排序的 对于属于区间$(20,170)$的指数,$x_2$与帕累托最优决策的指数之间的线性依赖关系在图9.4a中可以清楚地看到,该区间远远长于上面表示的兴趣区间。由于离散表示的点分布在帕累托前沿相当密集和均匀,所有感兴趣的特征都可以表示为指数作为自变量的函数。然而,这种对问题数据的参数化描述有一个缺点:自变量在问题表述的工程术语中没有任何解释 沿着图9.4a中的直线变化的变量$t$似乎很适合用作感兴趣数据的参数描述的自变量。$t$的值可以被解释为沿着帕累托前沿平滑的$x_2$的值。区间$0.15 \leq t \leq 0.4$中$t$的值对应帕累托前沿的扭结。$f_1\left(\mathbf{x}_i\right), f_2\left(\mathbf{x}_i\right)$和$t$对应值之间的关系如图9.4b所示。$x_2(t)$和$x_4(t) 0.15 \leq t \leq 0.4$的图如图9.5a所示。


为了突出显示帕累托最优决策中与帕累托前弯相对应的最有趣部分的位置,图$9.2$的图像部分如图9.5b所示。最接近顶点的图像用0和1标记


在基于可视化的分析之前,工程师们预期设计变量对帕累托最优解之间权衡的不同影响。我们参考[263],其中先验意见和最终结论用工程术语进行讨论

数学代写|凸优化作业代写凸优化代考|多目标优化辅助


图是许多研究课题中非常流行的模型。问题的图形化表示有利于启发式感知和理解所考虑对象之间的关系。另一方面,许多有效的算法技术可用来解决数学表述的图问题。因此,当人类用户在制定问题时的启发式能力与交互式模式下的算法求解相结合时,图模型尤其有用。在本章中,我们考虑业务流程的图模型,在有关业务流程管理的文献中,这些图模型被称为业务流程图。更准确地说,本文考虑了如何绘制美观的bpd布局问题。这一问题的研究的动机是这样一个事实:美学布局不仅可读性好,而且信息量大,实用性强


经过深思熟虑的业务流程管理方法是面向经理和顾问设计一个新的中小型企业(SME)或寻找改进现有企业的可能性。业务流程建模符号(BPMN)被公认为绘制业务流程图的标准[146]。图形绘制美学是全面讨论的,例如,在$[15,171]$。尽管图的绘制问题吸引了许多研究人员,并且有大量的出版物可用,但该问题的特殊情况往往不能直接应用已知的方法和算法来解决。我们引用[172]:“很少有算法是为特定领域设计的,并且不能保证用于通用布局算法的美学将对特定领域图表的可视化有用。”


将原问题简化为一个组合多目标优化问题。我们首先分析假设算法的潜在用户对广泛接受的美学标准的相对重要性的态度。后者被用作多目标优化问题的目标,从而将BPD绘制问题形式化为优化问题


绘制bpd的一般规则由BPMN标准定义。然而,这些标准为选择BPD绘图技术留下了足够的自由,这些技术对于业务流程管理的假定条件最为relévant。在本章中,我们考虑了为计划成立或正在重组的中小企业的经理提供建议的业务流程管理顾问所使用的bpd的绘制方法.

数学代写|凸优化作业代写Convex Optimization代考

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