Soft Computing

, Volume 21, Issue 23, pp 7235–7249 | Cite as

An improved gradient-based NSGA-II algorithm by a new chaotic map model

Methodologies and Application


Gradient-based non-dominated sorting genetic algorithm II (G-NSGA-II) is successful for solving multi-objective optimization problems. However, the effectiveness of gradient-based hybrid operator is influenced by the distribution of individuals in the population. In order to solve the problem, based on the framework of G-NSGA-II, we propose an improved gradient-based NSGA-II algorithm by introducing a new chaotic map model named IG-NSGA-II. In this algorithm, a new hybrid chaotic map model is first established to initialize population for keeping the diversity of the initial population. Then, the substitution operation of chaotic population candidate is introduced to maintain the diversity and uniformity of the Pareto optimal solution set. Finally, the proposed algorithm is tested on several standard test problems and compared with other algorithms. The experimental results indicate that the proposed algorithm leads to better performance results in terms of the convergence to Pareto front or the diversity of the obtained non-dominated solutions.


Multi-objective evolutionary algorithm Gradient-based hybrid operator Hybrid chaotic map model Substitution operation of chaotic Non-dominated solutions 



This study was funded by the Key Project of the National Natural Science Foundation of China (61034005).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Information Science and EngineeringNortheastern UniversityShenyangChina
  2. 2.National Key Laboratory of Integrated Automation for Process IndustriesNortheastern UniversityShenyangChina

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