Analysing Equilibrium States for Population Diversity

IF 0.9 4区 计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING
Johannes Lengler, Andre Opris, Dirk Sudholt
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Abstract

Population diversity is crucial in evolutionary algorithms as it helps with global exploration and facilitates the use of crossover. Despite many runtime analyses showing advantages of population diversity, we have no clear picture of how diversity evolves over time. We study how the population diversity of \((\mu +1)\) algorithms, measured by the sum of pairwise Hamming distances, evolves in a fitness-neutral environment. We give an exact formula for the drift of population diversity and show that it is driven towards an equilibrium state. Moreover, we bound the expected time for getting close to the equilibrium state. We find that these dynamics, including the location of the equilibrium, are unaffected by surprisingly many algorithmic choices. All unbiased mutation operators with the same expected number of bit flips have the same effect on the expected diversity. Many crossover operators have no effect at all, including all binary unbiased, respectful operators. We review crossover operators from the literature and identify crossovers that are neutral towards the evolution of diversity and crossovers that are not.

Abstract Image

分析种群多样性的平衡状态
种群多样性在进化算法中至关重要,因为它有助于全局探索和交叉的使用。尽管许多运行分析表明了种群多样性的优势,但我们并不清楚多样性是如何随时间演变的。我们研究了在((\mu +1)\)适合性中性的环境中,以成对汉明距离之和衡量的算法种群多样性是如何演变的。我们给出了种群多样性漂移的精确公式,并证明它会被驱动向均衡状态。此外,我们还限定了接近平衡状态的预期时间。我们发现,这些动态变化,包括均衡状态的位置,都不受令人惊讶的算法选择的影响。所有预期比特翻转次数相同的无偏突变算子对预期多样性都有相同的影响。许多交叉算子,包括所有二进制无偏、尊重算子,都没有任何影响。我们回顾了文献中的交叉算子,找出了对多样性进化中性的交叉算子和不中性的交叉算子。
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来源期刊
Algorithmica
Algorithmica 工程技术-计算机:软件工程
CiteScore
2.80
自引率
9.10%
发文量
158
审稿时长
12 months
期刊介绍: Algorithmica is an international journal which publishes theoretical papers on algorithms that address problems arising in practical areas, and experimental papers of general appeal for practical importance or techniques. The development of algorithms is an integral part of computer science. The increasing complexity and scope of computer applications makes the design of efficient algorithms essential. Algorithmica covers algorithms in applied areas such as: VLSI, distributed computing, parallel processing, automated design, robotics, graphics, data base design, software tools, as well as algorithms in fundamental areas such as sorting, searching, data structures, computational geometry, and linear programming. In addition, the journal features two special sections: Application Experience, presenting findings obtained from applications of theoretical results to practical situations, and Problems, offering short papers presenting problems on selected topics of computer science.
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