存在外部偏差时随机搜索过程的优化
Optimization of random search processes in the presence of an external bias
摘要：
我们研究的效率的随机搜索过程的基础上L{é}vy飞行与幂律分布的跳跃长度存在的外部漂移，例如，水下电流，气流，或简单的偏见的基础上先前的经验。当目标相对于起始点位于上游时，Lévy飞行被证明是有效的搜索过程，而在下游情况下，规则的布朗运动被证明是有利的。这是由L{é}vy航班的起飞引起的，由于L{é}vy航班通常超过一个点或小的间隔。扩展我们最近关于有偏LF搜索的工作[V. V. Palyulin，A. V. Chechkin和R. Metzler，Proc. Natl. Acad. Sci. USA，DOI：10.1073/pnas.1320424111]我们建立了当外部流和起始点与目标之间的初始距离的组合比常规布朗搜索更有利于L{é}vy飞行时的标准。与通常认为具有L{é}vy指数$α=1$的L{é}vy飞行（即，柯西飞行）是最佳的稀疏目标，我们发现，$α$的最佳值可以在整个区间$(1,2)$，并包括布朗运动作为整体最有效的搜索策略。
英文摘要：
We study the efficiency of random search processes based on L{é}vy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the bias of the searcher based on prior experience. While Lévy flights turn out to be efficient search processes when relative to the starting point the target is upstream, in the downstream scenario regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of L{é}vy flights, due to which L{é}vy flights typically overshoot a point or small interval. Extending our recent work on biased LF search [V. V. Palyulin, A. V. Chechkin, and R. Metzler, Proc. Natl. Acad. Sci. USA, DOI:10.1073/pnas.1320424111] we establish criteria when the combination of the external stream and the initial distance between the starting point and the target favors L{é}vy flights over regular Brownian search. Contrary to the common belief that L{é}vy flights with a L{é}vy index $α=1$ (i.e., Cauchy flights) are optimal for sparse targets, we find that the optimal value for $α$ may range in the entire interval $(1,2)$ and include Brownian motion as the overall most efficient search strategy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
