Adaptive population structure learning in evolutionary multi-objective optimization

  • Shuai Wang
  • Hu ZhangEmail author
  • Yi Zhang
  • Aimin Zhou
Methodologies and Application


Some recent research shows that in multi-objective evolutionary algorithms (MOEAs), mating with similar individuals can improve the quality of new solutions and accelerate the convergence of algorithms. Based on the above finding, some clustering-based mating restriction strategies are proposed. However, those clustering algorithms are not suitable for the population with non-convex structures. Therefore, it may fail to detect population structure in different evolutionary stages. To solve this problem, we propose a normalized hypervolume-based mating transformation strategy (NMTS). In NMTS, the population structure is detected by K-nearest-neighbor graph and spectral clustering before and after the mating transformation condition, respectively. And the parent solutions are chosen according to the founded population structure. The proposed algorithm has been applied to a number of test instances with complex Pareto optimal solution sets or Pareto fronts, and compared with some state-of-the-art MOEAs. The results have demonstrated its advantages over other algorithms.


Evolutionary algorithm Multi-objective optimization Mating restriction Population structure 



This study was found by National Natural Science Foundation of China (Grant numbers: 61703382, 51875053, 61673180) and China Ministry of Science and Technology Key Research and Development Program (Grant number: 2018YFC1903101).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringChangzhou UniversityChangzhouChina
  2. 2.Science and Technology on Complex System Control and Intelligent Agent Cooperation LaboratoryBeijing Electro-mechanical Engineering InstituteBeijingChina
  3. 3.Shanghai Key Laboratory of Multidimensional Information Processing, Department of Computer Science and TechnologyEast China Normal UniversityShanghaiChina

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