Parallel peaks: A visualization method for benchmark studies of multimodal optimization

Cheng RAN, Miqing LI, Xin YAO

Research output: Book Chapters | Papers in Conference ProceedingsConference paper (refereed)Researchpeer-review

7 Citations (Scopus)


Multimodal optimization has attracted increasing interest recently. Despite the emergence of various multimodal optimization algorithms during the last decade, little work has been dedicated to the development of benchmark tools. In this paper, we propose a visualization method for benchmark studies of multimodal optimization, called parallel peaks. Inspired by parallel coordinates, the proposed parallel peaks method is capable of visualizing both distribution information and convergence information of a given candidate solution set inside a 2D coordinate plane. To the best of our knowledge, this is the first visualization method in the multimodal optimization area. Our empirical results demonstrate that the proposed parallel peaks method can be robustly used to visualize candidate solutions sets with a range of properties, including high-accuracy solutions sets, high-dimensional solution sets and solution sets with a large number of optima. Additionally, by visualizing the populations obtained during the optimization process, it can also be used to investigate search behaviors of multimodal optimization algorithms. © 2017 IEEE.
Original languageEnglish
Title of host publication2017 IEEE Congress on Evolutionary Computation, CEC 2017 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages8
ISBN (Print)9781509046010
Publication statusPublished - Jun 2017
Externally publishedYes

Bibliographical note

The authors would like to thank Dr. Michael Epitropakis and Dr. Xiaodong Li for providing the code for generating true global optima of test functions in the IEEE CEC’2013 benchmark test suite. This work was supported by grants from EPSRC, Projects EP/K001523/1 and EP/J017515/1.


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