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

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

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 22, 5490-5499

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.

Keywords: Spatial evolution character; Self-organized criticality; Scale-free characteristic; Power-law distribution; Multi-objective evolutionary algorithm; Matthew effect (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:22:p:5490-5499

DOI: 10.1016/j.physa.2012.06.032

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