Coevolutionary Particle Swarm Optimization with Bottleneck Objective Learning Strategy for Many-Objective Optimization

Xiao-Fang LIU, Zhi-Hui ZHAN, Ying GAO, Jie ZHANG, Sam KWONG, Jun ZHANG

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

211 Citations (Scopus)


The application of multiobjective evolutionary algorithms to many-objective optimization problems often faces challenges in terms of diversity and convergence. On the one hand, with a limited population size, it is difficult for an algorithm to cover different parts of the whole Pareto front in a large objective space. The algorithm tends to concentrate only on limited areas. On the other hand, as the number of objectives increases, solutions easily have poor values on some objectives, which can be regarded as poor bottleneck objectives that restrict solutions’ convergence to the Pareto front. Thus, we propose a coevolutionary particle swarm optimization with a bottleneck objective learning strategy for many-objective optimization. In the proposed algorithm, multiple swarms coevolve in distributed fashion to maintain diversity for approximating different parts of the whole Pareto front, and a novel bottleneck objective learning strategy is developed to improve convergence on all objectives. In addition, we develop a solution reproduction procedure with both an elitist learning strategy and a juncture learning strategy to improve the quality of archived solutions. The elitist learning strategy helps the algorithm to jump out of local Pareto fronts, and the juncture learning strategy helps to reach out to the missing areas of the Pareto front that are easily missed by the swarms. The performance of the proposed algorithm is evaluated using two widely used test suites with different numbers of objectives. Experimental results show that the proposed algorithm compares favorably with six other state-of-the-art algorithms on many-objective optimization.
Original languageEnglish
Pages (from-to)587-602
JournalIEEE Transactions on Evolutionary Computation
Issue number4
Early online date11 Oct 2018
Publication statusPublished - Aug 2019
Externally publishedYes

Bibliographical note

This work was supported in part by the Outstanding Youth Science Foundation under Grant 61822602, in part by the National Natural Science Foundations of China under Grant 61772207 and Grant 61332002, in part by the Natural Science Foundations of Guangdong Province for Distinguished Young Scholars under Grant 2014A030306038, in part by the Project for Pearl River New Star in Science and Technology under Grant 201506010047, in part by the GDUPS in 2016, and in part by the Fundamental Research Funds for the Central Universities.


  • Bottleneck objective learning (BOL)
  • coevolution
  • many-objective optimization problems (MaOPs)
  • particle swarm optimization (PSO)


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