<p>Variation operators have great impact on the performance of evolutionary algorithms (EAs) because they determine the way of EAs constructing the new solutions during the evolutionary process. However, finding efficient variation operator for various kinds of optimization problems is a very challenge task in the field of evolutionary computation. This paper proposes an adaptive variation operator EA with using reinforcement learning. Specifically, the proposed EA adaptively selects variation operator from a set of simple operators to generate the offspring individuals by using Q-learning method in each generation. Theoretical analyses on a set of Pseudo-Boolean functions show that the expected runtime of the proposed algorithm is better than or equivalent to that of the well-studied <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10489_2025_6687_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="89" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{(1+1)\;\textrm{EA}}\)</EquationSource> </InlineEquation>. These results show the potential of the proposed method for solving complex problems in real-world applications. Moreover, this paper defines a new Pseudo-Boolean function, called Singular Point problem, which is showed to be rather challenge for several classic variation operators in conventional EAs and can be served as benchmark functions for theory analysis of EAs in future research.</p>

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Runtime analysis of adaptive selection variation operators in evolutionary algorithm with reinforcement learning

  • Yang Tianyi,
  • Zhou Yuren

摘要

Variation operators have great impact on the performance of evolutionary algorithms (EAs) because they determine the way of EAs constructing the new solutions during the evolutionary process. However, finding efficient variation operator for various kinds of optimization problems is a very challenge task in the field of evolutionary computation. This paper proposes an adaptive variation operator EA with using reinforcement learning. Specifically, the proposed EA adaptively selects variation operator from a set of simple operators to generate the offspring individuals by using Q-learning method in each generation. Theoretical analyses on a set of Pseudo-Boolean functions show that the expected runtime of the proposed algorithm is better than or equivalent to that of the well-studied \(\varvec{(1+1)\;\textrm{EA}}\) . These results show the potential of the proposed method for solving complex problems in real-world applications. Moreover, this paper defines a new Pseudo-Boolean function, called Singular Point problem, which is showed to be rather challenge for several classic variation operators in conventional EAs and can be served as benchmark functions for theory analysis of EAs in future research.