Institute for Physics and Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany.
Proc Natl Acad Sci U S A. 2014 Feb 25;111(8):2931-6. doi: 10.1073/pnas.1320424111. Epub 2014 Feb 10.
It is generally believed that random search processes based on scale-free, Lévy stable jump length distributions (Lévy flights) optimize the search for sparse targets. Here we show that this popular search advantage is less universal than commonly assumed. We study the efficiency of a minimalist search model based on Lévy flights in the absence and presence of an external drift (underwater current, atmospheric wind, a preference of the walker owing to prior experience, or a general bias in an abstract search space) based on two different optimization criteria with respect to minimal search time and search reliability (cumulative arrival probability). Although Lévy flights turn out to be efficient search processes when the target is far from the starting point, or when relative to the starting point the target is upstream, we show that for close targets and for downstream target positioning regular Brownian motion turns out to be the advantageous search strategy. Contrary to claims that Lévy flights with a critical exponent α = 1 are optimal for the search of sparse targets in different settings, based on our optimization parameters the optimal α may range in the entire interval (1, 2) and especially include Brownian motion as the overall most efficient search strategy.
人们普遍认为，基于无标度、 Lévy 稳定跳跃长度分布（ Lévy 飞行）的随机搜索过程可以优化对稀疏目标的搜索。在这里，我们表明这种流行的搜索优势并不像人们通常假设的那样普遍。我们研究了在不存在和存在外部漂移（水下流、大气风、由于先前经验而导致的步行者偏好，或者在抽象搜索空间中的一般偏差）的情况下，基于两种不同的优化标准（最小搜索时间和搜索可靠性（累积到达概率）），基于 Lévy 飞行的最小搜索模型的效率。尽管 Lévy 飞行在目标远离起点或相对于起点在下游时，被证明是有效的搜索过程，但我们表明，对于近距离目标和下游目标定位，规则布朗运动是有利的搜索策略。与 Lévy 飞行的临界指数 α = 1 对不同环境中稀疏目标搜索是最优的说法相反，根据我们的优化参数，最优的 α 可能在整个区间（1，2）内变化，尤其是包括布朗运动作为整体最有效的搜索策略。
