Analysis of the (1+1) EA on LeadingOnes with Constraints

IF 0.9 4区 计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING
Tobias Friedrich, Timo Kötzing, Aneta Neumann, Frank Neumann, Aishwarya Radhakrishnan
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引用次数: 0

Abstract

Understanding how evolutionary algorithms perform on constrained problems has gained increasing attention in recent years. In this paper, we study how evolutionary algorithms optimize constrained versions of the classical LeadingOnes problem. We first provide a run time analysis for the classical (1+1) EA on the LeadingOnes problem with a deterministic cardinality constraint, giving \(\Theta (n (n-B)\log (B) + nB)\) as the tight bound. Our results show that the behaviour of the algorithm is highly dependent on the constraint bound of the uniform constraint. Afterwards, we consider the problem in the context of stochastic constraints and provide insights using theoretical and experimental studies on how the (\(\mu \)+1) EA is able to deal with these constraints in a sampling-based setting.

带约束导联器的(1+1)EA分析
理解进化算法在约束问题上的表现近年来受到越来越多的关注。在本文中,我们研究了进化算法如何优化经典LeadingOnes问题的约束版本。我们首先对LeadingOnes问题上具有确定性基数约束的经典(1+1)EA进行运行时分析,给出\(\Theta (n (n-B)\log (B) + nB)\)作为紧界。结果表明,该算法的行为高度依赖于均匀约束的约束界。之后,我们在随机约束的背景下考虑这个问题,并通过理论和实验研究提供关于(\(\mu \) +1) EA如何能够在基于抽样的设置中处理这些约束的见解。
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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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