Fitness and distance based local search with adaptive differential evolution for multimodal optimization problems

Zi-Jia WANG, Zhi Hui ZHAN, Yun LI, Sam KWONG, Sang Woon JEON, Jun ZHANG

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

3 Citations (Scopus)


Local search has been regarded as a promising technique in multimodal algorithms to refine the accuracy of found multiple optima. However, how to execute the local search operations precisely on the found global optima and avoid the meaningless local search operations on local optima or found similar areas is still a challenge. In this paper, we propose a novel local search technique based on the individual information from two aspects, termed as fitness and distance based local search (FDLS). The fitness information can avoid the ineffective local search operations on the local optima, while the distance information can avoid the meaningless local search operations on the similar areas. These two kinds of information act in different roles and complement each other, which ensures that the local search is executed in different (ensured by distance information) and promising (ensured by fitness information) areas, leading to successful local search. Based on this, we design an adaptive DE (ADE) with adaptive parameters scheme and apply FDLS to ADE, termed as FDLS-ADE. Experimental results on the CEC2015 multimodal competition show the effectiveness and superiority of the FDLS-ADE, including comparisons with the winner of the CEC2015 multimodal competition. Furthermore, compared with other multimodal algorithms, the performance of the FDLS-ADE is seen relatively insensitive to niching parameters. Besides, experiments conducted also show that the FDLS can be applied to other multimodal algorithms easily and can further improve their performance. Finally, an application to a real-world nonlinear equations system further illustrates the applicability of the FDLS-ADE.
Original languageEnglish
Pages (from-to)684-699
Number of pages16
JournalIEEE Transactions on Emerging Topics in Computational Intelligence
Issue number3
Early online date19 Jan 2023
Publication statusPublished - Jun 2023
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported in part by the National Natural Science Foundations of China (NSFC) under Grants 62106055, 92270105, 62176094, and 61873097, in part by the Guangdong Natural Science Foundation under Grants 2022A1515011825, 2021B1515120078, and 2018B030312003, in part by the National Research Foundation of Korea under Grant NRF-2022H1D3A2A01093478, in part by the Hong Kong GRF-RGC General Research Fund under Grants 11209819 (CityU 9042816) and Grant 11203820 (CityU 9042598), and in part by the Hong Kong Innovation and Technology Commission through InnoHK Project CIMDA.

Publisher Copyright:
© 2017 IEEE.


  • Fitness and distance
  • differential evolution
  • evolutionary computation
  • local search
  • multimodal optimization problems


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