Evolutionary Multiobjective Optimization-Based Multimodal Optimization: Fitness Landscape Approximation and Peak Detection

Ran CHENG, Miqing LI, Ke LI, Xin YAO

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

97 Citations (Scopus)


Recently, by taking advantage of evolutionary multiobjective optimization techniques in diversity preservation, the means of multiobjectivization has attracted increasing interest in the studies of multimodal optimization (MMO). While most existing work of multiobjectivization aims to find all optimal solutions simultaneously, in this paper, we propose to approximate multimodal fitness landscapes via multiobjectivization, thus providing an estimation of potential optimal areas. To begin with, an MMO problem is transformed into a multiobjective optimization problem (MOP) by adding an adaptive diversity indicator as the second optimization objective, and an approximate fitness landscape is obtained via optimization of the transformed MOP using a multiobjective evolutionary algorithm. Then, on the basis of the approximate fitness landscape, an adaptive peak detection method is proposed to find peaks where optimal solutions may exist. Finally, local search is performed inside the detected peaks on the approximate fitness landscape. To assess the performance of the proposed algorithm, extensive experiments are conducted on 20 multimodal test functions, in comparison with three state-of-the-art algorithms for MMO. Experimental results demonstrate that the proposed algorithm not only shows promising performance in benchmark comparisons, but also has good potential in assisting preference-based decision-making in MMO. © 1997-2012 IEEE.
Original languageEnglish
Article number8038800
Pages (from-to)692-706
Number of pages15
JournalIEEE Transactions on Evolutionary Computation
Issue number5
Early online date15 Sept 2017
Publication statusPublished - Oct 2018
Externally publishedYes

Bibliographical note

This work was supported by the Engineering and Physical Sciences Research Council under Grant EP/K001523/1 and Grant EP/J017515/1. The work of X. Yao was supported by a Royal Society Wolfson Research Merit Award.


  • Decision-making
  • fitness landscape approximation
  • multimodal optimization (MMO)
  • multiobjective optimization
  • multiobjectivization
  • niching
  • peak detection
  • preference


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