### 数学代写|优化算法作业代写optimisation algorithms代考| Problematic and Beneficial

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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
• 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|优化算法作业代写optimisation algorithms代考|Problematic and Beneficial

Redundancy in the context of global optimization is a feature of the genotypephenotype mapping and means that multiple genotypes map to the same phenotype, i.e., the genotype-phenotype mapping is not injective. The role of redundancy in the genome is as controversial as that of neutrality [230]. There exist many accounts of its positive influence on the optimization process. Shackleton et al $[194,197]$, for instance, tried to mimic desirable evolutionary properties of RNA folding [106]. They developed redundant genotypephenotype mappings using voting (both, via uniform redundancy and via a non-trivial approach), Turing machine-like binary instructions, Cellular automata, and random Boolean networks [114]. Except for the trivial voting mechanism based on uniform redundancy, the mappings induced neutral networks which proved beneficial for exploring the problem space. Especially the last approach provided particularly good results $[194,197]$. Possibly converse

effects like epistasis (see Section 6 ) arising from the new genotype-phenotype mappings have not been considered in this study.

Redundancy can have a strong impact on the explorability of the problem space. When utilizing a one-to-one mapping, the translation of a slightly modified genotype will always result in a different phenotype. If there exists a many-to-one mapping between genotypes and phenotypes, the search operations can create offspring genotypes different from the parent which still translate to the same phenotype. The optimizer may now walk along a path through this neutral network. If many genotypes along this path can be modified to different offspring, many new solution candidates can be reached $[197]$. The experiments of Shipman et al $[198,196]$ additionally indicate that neutrality in the genotype-phenotype mapping can have positive effects.
Yet, Rothlauf [182] and Shackleton et al [194] show that simple uniform redundancy is not necessarily beneficial for the optimization process and may even slow it down. There is no use in introducing encodings which, for instance, represent each phenotypic bit with two bits in the genotype where 00 and 01 map to 0 and 10 and 11 map to $1 .$

## 数学代写|优化算法作业代写optimisation algorithms代考|Summary

Different from ruggedness which is always bad for optimization algorithms, neutrality has aspects that may further as well as hinder the process of finding good solutions. Generally we can state that degrees of neutrality $\nu$ very close to 1 degenerate optimization processes to random walks. Some forms of neutral networks $[14,15,27,105,208,222,223,237]$ accompanied by low (nonzero) values of $\nu$ can improve the evolvability and hence, increase the chance of finding good solutions.

Adverse forms of neutrality are often caused by bad design of the search space or genotype-phenotype mapping. Uniform redundancy in the genome should be avoided where possible and the amount of neutrality in the search space should generally be limited.

## 数学代写|优化算法作业代写optimisation algorithms代考|Epistasis

In biology, epistasis is defined as a form of interaction between different genes [163]. The term was coined by Bateson [16] and originally meant that one gene suppresses the phenotypical expression of another gene. In the context of statistical genetics, epistasis was initially called “epistacy” by Fisher [74]. According to Lush [132], the interaction between genes is epistatic if the effect on the fitness of altering one gene depends on the allelic state of other genes. This understanding of epistasis comes very close to another biological

expression: Pleiotropy, which means that a single gene influences multiple phenotypic traits [239]. In global optimization, such fine-grained distinctions are usually not made and the two terms are often used more or less synonymously.

Definition 3 (Epistasis). In optimization, Epistasis is the dependency of the contribution of one gene to the value of the objective functions on the allelic state of other genes $[4,51,153]$.

We speak of minimal epistasis when every gene is independent of every other gene. Then, the optimization process equals finding the best value for each gene and can most efficiently be carried out by a simple greedy search [51]. A problem is maximally epistatic when no proper subset of genes is independent of any other gene $[205,153]$. Examples of problems with a high degree of epistasis are Kauffman’s NK fitness landscape $[113,115]$, the p-Spin model $[6]$, and the tunable model of Weise et al [232].

## 有限元方法代写

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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。