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Optimizing random searches on three-dimensional lattices

Author

Listed:
  • Yang, Benhao
  • Yang, Shunkun
  • Zhang, Jiaquan
  • Li, Daqing

Abstract

Search is a universal behavior related to many types of intelligent individuals. While most studies have focused on search in two or infinite-dimensional space, it is still missing how search can be optimized in three-dimensional space. Here we study random searches on three-dimensional (3d) square lattices with periodic boundary conditions, and explore the optimal search strategy with a power-law step length distribution, p(l)∼l−μ, known as Lévy flights. We find that compared to random searches on two-dimensional (2d) lattices, the optimal exponent μopt on 3d lattices is relatively smaller in non-destructive case and remains similar in destructive case. We also find μopt decreases as the lattice length in z direction increases under high target density. Our findings may help us to understand the role of spatial dimension in search behaviors.

Suggested Citation

  • Yang, Benhao & Yang, Shunkun & Zhang, Jiaquan & Li, Daqing, 2018. "Optimizing random searches on three-dimensional lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 120-125.
    • Handle: RePEc:eee:phsmap:v:501:y:2018:i:c:p:120-125
    DOI: 10.1016/j.physa.2018.02.100
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    References listed on IDEAS

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    1. Jon M. Kleinberg, 2000. "Navigation in a small world," Nature, Nature, vol. 406(6798), pages 845-845, August.
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    Cited by:

    1. Jiang, Jianhua & Yang, Xi & Meng, Xianqiu & Li, Keqin, 2020. "Enhance chaotic gravitational search algorithm (CGSA) by balance adjustment mechanism and sine randomness function for continuous optimization problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    2. Jiang, Jianhua & Xu, Meirong & Meng, Xianqiu & Li, Keqin, 2020. "STSA: A sine Tree-Seed Algorithm for complex continuous optimization problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).

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