EE6227-遗传算法概要、优化策略及数学定理-优快云博客

本文详细介绍了遗传算法的基本原理，包括编码、适应度函数、选择、交叉和变异等操作。讨论了优化问题的全局最优与计算成本之间的平衡，并对比了连续参数进化算法的优势。此外，文章还探讨了非线性编程问题的解决方法，以及遗传算法的特性，如不需要搜索空间连续、不依赖梯度信息等。文中还提到了几种适应度缩放策略，以防止早熟收敛，并分析了不同改进策略对算法性能的影响。

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Involved Algorithms

GAs, PSO, Constraint Handling, Evolutionary Strategy, Differential Evolution, Multi-Objective Algorithms and multimodal optimization.

Principle of Evolutionary Algorithms

Proper encoding is necessary.
There is a certain index to quantify the fitness of every individual.
The selection of parents and the reproduction of parents is to some extend random.
The population of solutions will be better as the number of generations increases.

Introduction to Optimization

The problem can be described as:

$x∈ΩMinimize\,f(x)\,over\,x\in\Omega$

$constraints.\Omega\,is\,the\,permissible\,region\,of\,the\,decision\,variables,\,which\,is\,defined\,by\,constraints.$ Discrete solution can be considered as an approximate solution to the continuous problem. For example:

$−1≤x≤1Minimize\,f(x)=x^{2}\,where\,-1\leq x\leq1$

The value of x can be discretized for example using 32 bits plus a sign bit, so totally there are $2^{33}$ discrete solutions.

However, it is not efficient enough because the problems are likely to be a large numer of enumerations. Consequently, real-parameter evolutionary algorithms is much better.

Global Optimum v.s. Computational Cost

Due to the computational time, in most cases it is impossible and unnecessary to find the global solution. Algorithms such as the GA or simulated annealing can be used because these approaches make use of randomness to escape from local optimal solutions. However, no method can guarantee to produce the global optimal solution (especially for complex multimodal problems).

Nonlinear Programming Problems

Can be solved by using methods of calculus, but it is difficult to solve these problems analytically.
The most popular method is the sequential quadratic programming.
Iterative numerical algorithms are ideal ways to obtain acceptable solutions.

Properties of GAs

A simple way to obtain acceptable solutions.
Do not require the search spaceto be continuous or differentiable or unimodal.
Not deterministic rules so that it can escape from local opimal solutions.
Work with the objective function without gradie