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# 数学代写|随机过程Stochastic Porcesses代考|AMATH562 Other Methods

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## 数学代写|随机过程Stochastic Porcesses代考|

The described methods are examples of stochastic optimization strategies, but there are several other alternatives to solve optimization problems using meta-heuristic approaches. The GAs and DEs are methods based on the analysis of populations (or sets of solutions), where tabu search and simulated annealing are methods based on the analysis of single solutions. In this section, other stochastic optimization methods are mentioned and a brief description of each method is presented.

## 数学代写|随机过程Stochastic Porcesses代考|Ant Colony Optimization

Fixed Points and Root-Finding

The ant colony optimization method was developed by Dorigo and Gambardella (1997) and is inspired by the behavior of ant colonies. In general, the ants indicate the way from their nest to a food source by depositing pheromones on the ground. When various ants are taking different paths, the path representing the shortest distance will have a higher concentration of pheromones, thus most of the ants will be attracted to follow that route and will increase the concentration of pheromones even more. In the end, all the ants nearby will follow the shortest path. The ant colony optimization method emulates this behavior. Two parameters are of importance to the algorithm: the pheromone value and the age of a solution. The algorithm starts with a randomly generated set of solutions. Then, a local search procedure starts, where a simulated ant selects a solution, in terms of the pheromone values. Then, in terms of the age of the current solution, a new solution is selected. If the fitness function of the new solution is better than that of the previous solution, the new solution is selected. Otherwise, the previous solution remains. In both cases, the values of age and pheromone are modified. Then, a global search takes place and the pheromone values are updated to consider the phenomena of pheromone evaporation. The procedure continues until the CC is achieved (Jayaraman et al., 2010). This method has been used for applications such as the optimization of project scheduling (Merkle et al., 2002), the optimization of water distribution systems (Maier et al., 2003), and the scheduling of batch processes (Jayaraman et al., 2010). Nevertheless, to the best of the authors’ knowledge, there are only a few applications of this algorithm to the optimization of chemical processes.

## 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。