Kuśmierz Łukasz, Toyoizumi Taro
RIKEN Brain Science Institute, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan.
Phys Rev Lett. 2017 Dec 22;119(25):250601. doi: 10.1103/PhysRevLett.119.250601. Epub 2017 Dec 18.
In natural foraging, many organisms seem to perform two different types of motile search: directed search (taxis) and random search. The former is observed when the environment provides cues to guide motion towards a target. The latter involves no apparent memory or information processing and can be mathematically modeled by random walks. We show that both types of search can be generated by a common mechanism in which Lévy flights or Lévy walks emerge from a second-order gradient-based search with noisy observations. No explicit switching mechanism is required-instead, continuous transitions between the directed and random motions emerge depending on the Hessian matrix of the cost function. For a wide range of scenarios, the Lévy tail index is α=1, consistent with previous observations in foraging organisms. These results suggest that adopting a second-order optimization method can be a useful strategy to combine efficient features of directed and random search.
在自然觅食过程中，许多生物体似乎会进行两种不同类型的移动搜索：定向搜索（趋性）和随机搜索。当环境提供线索以引导朝向目标的运动时，会观察到前者。后者不涉及明显的记忆或信息处理，并且可以通过随机游走进行数学建模。我们表明，这两种搜索类型都可以由一种共同机制产生，其中 Lévy 飞行或 Lévy 游走从基于二阶梯度的带有噪声观测的搜索中出现。不需要明确的切换机制——相反，根据代价函数的海森矩阵，定向运动和随机运动之间会出现连续过渡。对于广泛的场景，Lévy 尾部指数为α = 1，这与先前在觅食生物体中的观察结果一致。这些结果表明，采用二阶优化方法可能是一种结合定向搜索和随机搜索的有效特征的有用策略。
