Posted on Categories:Integer Programming, 数学代写, 整数优化

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## 数学代写|整数优化代写Integer Programming代考|General integer model

The segment-search approach algorithm for the general integer model is summarized below.
Step 1: Solve the relaxed model (together with the useful additional constraints and slack/excess variable limits) and find an optimal solution.
Step 2: Is the continuous optimal solution integer?

• If yes, then go to Step 3.
• If no, then go to Step 4.
Step 3: Stop an optimal integer solution is available.
Step 4: From each of the two sub-problems determine $h_0$ and then go to Step 5.
Step 5: Search segments 1, 2, $3, \ldots, k$ until an integer optimal solution is obtained.
Segment 1: $\omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \leq h_0$
Segment 2: $\omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \geq h_0$ $\omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \leq h_0+h_1$
Segment 3: $\omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \geq h_0+h_1$ $\omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \leq h_0+h_1+h_2$
$\cdots$
Segment k: \begin{aligned}&\omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \geq h_0+h_1+h_2+\ldots+h_k \&\omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \leq h_0+h_1+h_2+\ldots+h_k+h_{k+1}\end{aligned}
The algorithm is also presented in Figure 1.3.

## 数学代写|整数优化代写Integer Programming代考|Mixed integer model

With the mixed integer model some of the variables are non-integer. As a result, we cannot use the same technique that we used for the general case. Only the integer restricted variables $\left(x_1, \chi_2, \ldots, x_r\right)$ are used to generate the variable sum constraint as is given in (1.25).

$$x_1+x_2+\ldots+x_r=\phi+f$$
The two sub-problems A and B.
Sub-problem A:
$$x_1+x_2+\ldots+x_r \leq \phi$$
Sub-problem B:
$$\chi_1+\chi_2+\ldots+\chi_r \geq \phi+1$$
The segments are searched in such a way that all the non-integer variables are ignored during the search. The segment-search approach for the mixed integer model is summarized below. The decrease in objective value $\left(h_0\right)$ is not necessarily integer.
Step 1: Solve the relaxed model (together with the useful additional constraints) to get an optimal solution.
Step 2: Is the continuous optimal solution satisfies integer requirement on integer restricted variables?

• If yes, then go to Step 3.
• If no, then go to Step 4.
Step 3: Stop as optimal mixed integer solution has been obtained.
Step 4: From each of the two sub-problems determine $h_0$ and then go to Step 5.
Step 5: Search segments $1,2,3, \ldots, k$ until the desired mixed integer solution is found,
Segment 1: $\omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \leq h_0$.
Segment 2: $\omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \geq h_0$ $\omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \leq h_0+h_1$
Segment 3: $\omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \geq h_0+h_1$ $\omega_1 s_1+\omega_2 s_2+::+\omega_n s_n \leq h_0+h_1+h_2$
Segment k: \begin{aligned}&\omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \geq h_0+h_1+h_2+\ldots+h_k \&\omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \leq h_0+h_1+h_2+\ldots+h_k+h_{k+1} .\end{aligned}
The algorithm is presented in Figure 1.4.

## 数学代写|整数优化代写Integer Programming代考|General integer model

$k: \quad \omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \geq h_0+h_1+h_2+\ldots+h_k \& \omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \leq h_0+h_1+h_2+\ldots+h_k+h_{k+1}$

## 数学代写整数优化代写Integer Programming代考|Mixed integer model

$$x_1+x_2+\ldots+x_r=\phi+f$$

$$x_1+x_2+\ldots+x_r \leq \phi$$

$$\chi_1+\chi_2+\ldots+\chi_r \geq \phi+1$$

$k: \quad \omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \geq h_0+h_1+h_2+\ldots+h_k \& \omega_1 s_1+\omega_2 s_2+\ldots+\omega_n s_n \leq h_0+h_1+h_2+\ldots+h_k+h_{k+1}$.

## 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。