遗传算法中的选择方法分析

N. Gulayeva, Artem Ustilov
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摘要

本文对代遗传算法中使用的选择方法进行了全面的综述。首先简要介绍了适应度比例选择方法,包括轮盘选择(RWS)及其修正、带替换的随机剩余选择(SRSWR)、剩余随机独立选择(RSIS)和随机普遍选择(SUS);排名选择方法包括线性排名和非线性排名;比赛选择方法,包括确定性和随机比赛以及有和没有替换的比赛;精英和截断选择方法;健身统一选择方案(FUSS)。其次,给出了选择方法性质的基本理论表述。特别考虑了选择噪声、选择压力、生长速率、繁殖速率和计算复杂度。为了说明选择方法的性质,在不使用其他遗传算子的情况下,对使用唯一选择方法的遗传算法进行了多次运行,并计算了所分析性质的数值特征。具体来说,通过计算接管时间和选择强度来估计选择压力;为了估计生长率,计算两个连续种群中最佳个体拷贝的比率;为了估计选择噪声,通过对特定适应度函数进行实验,分析算法的收敛速度,并为所有个体分配相同的适应度值。第三,研究了选择方法对种群适应度分布的影响。为此,进行了遗传算法运行,从二项分布的初始种群开始。结果表明,大多数选择方法使分布接近原始分布,从而增加了分布的平均值,而其他选择方法(如破坏性RWS、指数排序、截断和FUSS)则显著改变了分布。所得结果用表格和直方图加以说明。
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Analysis of Selection Methods Used in Genetic Algorithms
This paper offers a comprehensive review of selection methods used in the generational genetic algorithms.Firstly, a brief description of the following selection methods is presented: fitness proportionate selection methods including roulette-wheel selection (RWS) and its modifications, stochastic remainder selection with replacement (SRSWR), remainder stochastic independent selection (RSIS), and stochastic universal selection (SUS); ranking selection methods including linear and nonlinear rankings; tournament selection methods including deterministic and stochastic tournaments as well as tournaments with and without replacement; elitist and truncation selection methods; fitness uniform selection scheme (FUSS).Second, basic theoretical statements on selection method properties are given. Particularly, the selection noise, selection pressure, growth rate, reproduction rate, and computational complexity are considered. To illustrate selection method properties, numerous runs of genetic algorithms using the only selection method and no other genetic operator are conducted, and numerical characteristics of analyzed properties are computed. Specifically, to estimate the selection pressure, the takeover time and selection intensity are computed; to estimate the growth rate, the ratio of best individual copies in two consecutive populations is computed; to estimate the selection noise, the algorithm convergence speed is analyzed based on experiments carried out on a specific fitness function assigning the same fitness value to all individuals.Third, the effect of selection methods on the population fitness distribution is investigated. To do this, there are conducted genetic algorithm runs starting with a binomially distributed initial population. It is shown that most selection methods keep the distribution close to the original one providing an increased mean value of the distribution, while others (such as disruptive RWS, exponential ranking, truncation, and FUSS) change the distribution significantly. The obtained results are illustrated with the help of tables and histograms.
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