{"title":"分类紧凑遗传算法运行时间的尾边界","authors":"Ryoki Hamano, Kento Uchida, Shinichi Shirakawa, Daiki Morinaga, Youhei Akimoto","doi":"10.1162/evco_a_00361","DOIUrl":null,"url":null,"abstract":"<p><p>The majority of theoretical analyses of evolutionary algorithms in the discrete domain focus on binary optimization algorithms, even though black-box optimization on the categorical domain has a lot of practical applications. In this paper, we consider a probabilistic model-based algorithm using the family of categorical distributions as its underlying distribution and set the sample size as two. We term this specific algorithm the categorical compact genetic algorithm (ccGA). The ccGA can be considered as an extension of the compact genetic algorithm (cGA), which is an efficient binary optimization algorithm. We theoretically analyze the dependency of the number of possible categories K, the number of dimensions D, and the learning rate η on the runtime. We investigate the tail bound of the runtime on two typical linear functions on the categorical domain: categorical OneMax (COM) and KVAL. We derive that the runtimes on COM and KVAL are O(Dln(DK)/η) and Θ(DlnK/η) with high probability, respectively. Our analysis is a generalization for that of the cGA on the binary domain.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":" ","pages":"1-52"},"PeriodicalIF":4.6000,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Tail Bounds on the Runtime of Categorical Compact Genetic Algorithm.\",\"authors\":\"Ryoki Hamano, Kento Uchida, Shinichi Shirakawa, Daiki Morinaga, Youhei Akimoto\",\"doi\":\"10.1162/evco_a_00361\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>The majority of theoretical analyses of evolutionary algorithms in the discrete domain focus on binary optimization algorithms, even though black-box optimization on the categorical domain has a lot of practical applications. In this paper, we consider a probabilistic model-based algorithm using the family of categorical distributions as its underlying distribution and set the sample size as two. We term this specific algorithm the categorical compact genetic algorithm (ccGA). The ccGA can be considered as an extension of the compact genetic algorithm (cGA), which is an efficient binary optimization algorithm. We theoretically analyze the dependency of the number of possible categories K, the number of dimensions D, and the learning rate η on the runtime. We investigate the tail bound of the runtime on two typical linear functions on the categorical domain: categorical OneMax (COM) and KVAL. We derive that the runtimes on COM and KVAL are O(Dln(DK)/η) and Θ(DlnK/η) with high probability, respectively. Our analysis is a generalization for that of the cGA on the binary domain.</p>\",\"PeriodicalId\":50470,\"journal\":{\"name\":\"Evolutionary Computation\",\"volume\":\" \",\"pages\":\"1-52\"},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Evolutionary Computation\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1162/evco_a_00361\",\"RegionNum\":2,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Evolutionary Computation","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1162/evco_a_00361","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
摘要
离散领域进化算法的理论分析大多集中在二元优化算法上,尽管分类领域的黑盒优化有很多实际应用。在本文中,我们考虑一种基于概率模型的算法,将分类分布族作为其基础分布,并将样本量设为两个。我们将这种特定算法称为分类紧凑遗传算法(ccGA)。ccGA 可以看作是紧凑遗传算法(ccGA)的扩展,后者是一种高效的二进制优化算法。我们从理论上分析了可能的类别数 K、维数 D 和学习率 η 对运行时间的影响。我们研究了分类域中两个典型线性函数的运行时间尾界:分类 OneMax (COM) 和 KVAL。我们得出,COM 和 KVAL 的运行时间分别为 O(Dln(DK)/η) 和 Θ(DlnK/η),且概率很高。我们的分析是对二元域 cGA 分析的推广。
Tail Bounds on the Runtime of Categorical Compact Genetic Algorithm.
The majority of theoretical analyses of evolutionary algorithms in the discrete domain focus on binary optimization algorithms, even though black-box optimization on the categorical domain has a lot of practical applications. In this paper, we consider a probabilistic model-based algorithm using the family of categorical distributions as its underlying distribution and set the sample size as two. We term this specific algorithm the categorical compact genetic algorithm (ccGA). The ccGA can be considered as an extension of the compact genetic algorithm (cGA), which is an efficient binary optimization algorithm. We theoretically analyze the dependency of the number of possible categories K, the number of dimensions D, and the learning rate η on the runtime. We investigate the tail bound of the runtime on two typical linear functions on the categorical domain: categorical OneMax (COM) and KVAL. We derive that the runtimes on COM and KVAL are O(Dln(DK)/η) and Θ(DlnK/η) with high probability, respectively. Our analysis is a generalization for that of the cGA on the binary domain.
期刊介绍:
Evolutionary Computation is a leading journal in its field. It provides an international forum for facilitating and enhancing the exchange of information among researchers involved in both the theoretical and practical aspects of computational systems drawing their inspiration from nature, with particular emphasis on evolutionary models of computation such as genetic algorithms, evolutionary strategies, classifier systems, evolutionary programming, and genetic programming. It welcomes articles from related fields such as swarm intelligence (e.g. Ant Colony Optimization and Particle Swarm Optimization), and other nature-inspired computation paradigms (e.g. Artificial Immune Systems). As well as publishing articles describing theoretical and/or experimental work, the journal also welcomes application-focused papers describing breakthrough results in an application domain or methodological papers where the specificities of the real-world problem led to significant algorithmic improvements that could possibly be generalized to other areas.