Analysis of Evolutionary Algorithms on Fitness Function with Time-Linkage Property

Weijie ZHENG, Huanhuan CHEN, Xin YAO

Research output: Journal PublicationsJournal Article (refereed)peer-review

10 Citations (Scopus)


In real-world applications, many optimization problems have the time-linkage property, that is, the objective function value relies on the current solution as well as the historical solutions. Although the rigorous theoretical analysis on evolutionary algorithms (EAs) has rapidly developed in recent two decades, it remains an open problem to theoretically understand the behaviors of EAs on time-linkage problems. This article takes the first step to rigorously analyze EAs for time-linkage functions. Based on the basic OneMax function, we propose a time-linkage function where the first bit value of the last time step is integrated but has a different preference from the current first bit. We prove that with probability $1-o(1)$ , randomized local search and (1 + 1) EA cannot find the optimum, and with probability $1-o(1)$ , $(\mu +1)$ EA is able to reach the optimum. © 1997-2012 IEEE.
Original languageEnglish
Article number9360867
Pages (from-to)696-709
Number of pages14
JournalIEEE Transactions on Evolutionary Computation
Issue number4
Early online date23 Feb 2021
Publication statusPublished - Aug 2021
Externally publishedYes

Bibliographical note

This work was supported in part by the Guangdong Basic and Applied Basic Research Foundation under Grant 2019A1515110177; in part by the Guangdong Provincial Key Laboratory under Grant 2020B121201001; in part by the Program for Guangdong Introducing Innovative and Enterpreneurial Teams under Grant 2017ZT07X386; in part by the Shenzhen Science and Technology Program under Grant KQTD2016112514355531; in part by the Program for University Key Laboratory of Guangdong Province under Grant 2017KSYS008; in part by the National Natural Science Foundation of China under Grant 61976111; and in part by the Science and Technology Innovation Committee Foundation of Shenzhen under Grant JCYJ20180504165652917.


  • Convergence
  • evolutionary algorithms (EAs)
  • running time analysis
  • time linkage


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