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Spatial evolution character of multi-objective evolutionary algorithm based on self-organized criticality theory

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  • Li, Jun-fang
  • Zhang, Bu-han
  • Liu, Yi-fang
  • Wang, Kui
  • Wu, Xiao-shan

Abstract

This paper analyzes the spatial evolution character of multi-objective evolutionary algorithms using self-organized criticality theory. The spatial evolution character is modeled by the statistical property of crowding distance, which displays a scale-free feature and a power-law distribution. We propose that the evolutional rule of multi-objective optimization algorithms is a self-organized state transition from an initial scale-free state to a final scale-free state. The target is to get close to a critical state representing the true Pareto-optimal front. Besides, the anti-Matthew effect is the internal incentive factor of most strategies. The final scale-free state reflects the quality of the final Pareto-optimal front. The speed of the state transition reflects the efficiency of the algorithm. We simulate the spatial evolution characters of three typical multi-objective evolutionary algorithms representing three fields, i.e., Genetic Algorithm, Differential Evolution and the Artificial Immune System algorithm. The results prove that the model and the explanation are effective for analyzing the evolutional rule of multi-objective evolutionary algorithms.

Suggested Citation

  • Li, Jun-fang & Zhang, Bu-han & Liu, Yi-fang & Wang, Kui & Wu, Xiao-shan, 2012. "Spatial evolution character of multi-objective evolutionary algorithm based on self-organized criticality theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5490-5499.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:22:p:5490-5499
    DOI: 10.1016/j.physa.2012.06.032
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    References listed on IDEAS

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    1. Hu, Mao-Bin & Jiang, Rui & Wu, Qing-Song & Wu, Yong-Hong, 2007. "Simulating the wealth distribution with a Richest-Following strategy on scale-free network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 467-472.
    2. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    3. Gong, Maoguo & Ma, Lijia & Zhang, Qingfu & Jiao, Licheng, 2012. "Community detection in networks by using multiobjective evolutionary algorithm with decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 4050-4060.
    4. Zhang, Qunzhi & Sornette, Didier, 2011. "Empirical test of the origin of Zipf’s law in growing social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4124-4130.
    5. Campos, Paulo R.A & de Oliveira, Viviane M, 2003. "Scale-free networks in evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(3), pages 570-576.
    6. Wu, Jieyu & Shao, Xinyu & Li, Jinhang & Huang, Gang, 2012. "Scale-free properties of information flux networks in genetic algorithms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1692-1701.
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