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# 数学代写|线性规划代写Linear Programming代考|Multiobjective Optimization

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## 数学代写|线性规划代写Linear Programming代考|Multiobjective Optimization

In multi-criteria optimization, several opposing goal functions should be reduced to a minimum at the same time respecting the given restrictions:
$$\begin{array}{rlr} \text { Max.: } & Q(\mathbf{x})=\left{Q_1(\mathbf{x}), \ldots, Q_l(\mathbf{x})\right}, \quad \mathbf{x} \in \mathbf{R}^n \ \text { p.o.: } & f_i(\mathbf{x}) \leq 0, i=1, \ldots, m \ & h_i(\mathbf{x})=0, i=1, \ldots, k . \end{array}$$
It is possible to construct an interval (often called a constraint) in ( ref $M O O$ ); we simply denote by $\mathbf{X}$. Thus, the whole $\mathbf{X}$ is defined by $\mathbf{X}=\left{\mathbf{x} \mid f_i(\mathbf{x}) \leq 0, i=1, \ldots, m ; h_i(\mathbf{x})=0, i=1, \ldots, k\right}$.

As a consequence, the notation $\mathbf{x} \mathbf{X}$ will indicate that $\mathbf{x}$ satisfies the inequality and equality of boundaries in (1.0.1). With $\mathbf{x}_{\mathbf{j}}{ }^*$ we denote the point that maximizes the $j$-th function of the target depending on the constraint $\mathbf{x} \in \mathbf{X}$.

In general, there is no special point that maximizes all target functions at once. For these reasons, a possible point is constructed as optimal if there is no possible point with the same or goal function being estimated. So that the true increase has the minimum value of the target function. For the sake of completeness, we redefine the definitions of non-inferior solution (Pareto-optimal solution) and ideal (utopia) point from Refs. [12], [34], and [35].

## 数学代写|线性规划代写Linear Programming代考|Symbolic Transformations in Multi-Sector Optimization

The main details of multi-sector optimization that are specific to symbols and the expressions are described in the paper [57]. The implementation was performed in the software package MATHEMATICA. The method of weight coefficients, the main priority methods, and the method of target programming are discussed. The symbolic conversion of given goal functions and constraints into the corresponding problem of one goal function is treated in particular. Transformations from multiobjective to one-criteria problem u procedural programming languages are actually combinations of real values, and involve procedures that depend on the function of the goal. In our implementation, these transformations are performed in symbolic form by taking combinations of target functions, which include undefined symbols and unmarked variable prices.

We will suggest the following clear benefits that will result from the implementation problems of multiobjective optimization in the symbolic programming language MATHEMATICA, respect the traditional implementation in procedural programming languages.

Possibility to use arbitrary target functions and limitations (which are not defined by subroutines) during the execution of the implementation function. The main aspects of these advantages are:
(i) The problem of secretory optimization (1.0.1) is represented by a suitable in its form, whose elements can be used prices as formal parameters in the optimization software. Inside the dream form of the problem (1.0.1) is an edited triple
\begin{aligned} & \left{Q_1(\mathbf{x}), \ldots, Q_l(\mathbf{x})\right} \ & \left{f_1(\mathbf{x}) \leq 0, \ldots, f_m(\mathbf{x}) \leq 0, h_1(\mathbf{x})=0, \ldots, h_k(\mathbf{x})=0\right} \ & \left{x_1, \ldots, x_n\right} \end{aligned}
The first element of the inner form, denoted by $q$, is a list $\left{Q_1(\mathbf{x}), \ldots, Q_l(\mathbf{x})\right}$ whose elements indefinite expressions representing goal functions. The second element in (1.2.1) is the constraint list $f_i(\mathbf{x}) \leq 0, i=1, \ldots, m, h_i(\mathbf{x})=0, i=1, \ldots, k$. We will label this argument as constr. The third element, labeled var, is a generic list of variables $\left{x_1, \ldots, x_n\right}$, determined on the basis of $\mathbf{x}$. In this sense, it is allowed that some arguments in $\mathbf{x}$ can be defined in global environment MATHEMATICA kernela.
(ii) If $f$ is the objective function of the one-criteria optimization problem obtained from (1.2. 1), we can calculate its maximum using the standard function Maximize:
Maximize [f, constr, var] .
The possibility of software to process arbitrary target functions at arbitrary constraints enables the application of all optimization models.

Possibility to use arrays of functions, whose elements can be select and later apply to the given arguments. These structures are not inherent in procedural programming languages.

## 数学代写|线性规划代写Linear Programming代考|Multiobjective Optimization

$$\begin{array}{rlr} \text { Max.: } & Q(\mathbf{x})=\left{Q_1(\mathbf{x}), \ldots, Q_l(\mathbf{x})\right}, \quad \mathbf{x} \in \mathbf{R}^n \ \text { p.o.: } & f_i(\mathbf{x}) \leq 0, i=1, \ldots, m \ & h_i(\mathbf{x})=0, i=1, \ldots, k . \end{array}$$

## 数学代写|线性规划代写Linear Programming代考|Symbolic Transformations in Multi-Sector Optimization

(i)分泌优化问题(1.0.1)用一个合适的形式表示，其元素可以在优化软件中使用价格作为形式参数。在问题(1.0.1)的梦想形式中是一个编辑过的三元组
\begin{aligned} & \left{Q_1(\mathbf{x}), \ldots, Q_l(\mathbf{x})\right} \ & \left{f_1(\mathbf{x}) \leq 0, \ldots, f_m(\mathbf{x}) \leq 0, h_1(\mathbf{x})=0, \ldots, h_k(\mathbf{x})=0\right} \ & \left{x_1, \ldots, x_n\right} \end{aligned}

(ii)若$f$为式(1.2)求得的单准则优化问题的目标函数。1)，我们可以使用标准函数Maximize计算其最大值:

## 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。