Ferreira J, Raposo E P, Araújo H A, da Luz M G E, Viswanathan G M, Bartumeus F, Campos D
Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife-PE, 50670-901, Brazil.
Departamento de Matemática, Universidade Federal de Pernambuco, Recife-PE, 50670-901, Brazil.
Phys Rev E. 2021 Feb;103(2-1):022105. doi: 10.1103/PhysRevE.103.022105.
Information on the relevant global scales of the search space, even if partial, should conceivably enhance the performance of random searches. Here we show numerically and analytically that the paradigmatic uninformed optimal Lévy searches can be outperformed by informed multiple-scale random searches in one (1D) and two (2D) dimensions, even when the knowledge about the relevant landscape scales is incomplete. We show in the low-density nondestructive regime that the optimal efficiency of biexponential searches that incorporate all key scales of the 1D landscape of size L decays asymptotically as η_{opt}∼1/sqrt[L], overcoming the result η_{opt}∼1/(sqrt[L]lnL) of optimal Lévy searches. We further characterize the level of limited information the searcher can have on these scales. We obtain the phase diagram of bi- and triexponential searches in 1D and 2D. Remarkably, even for a certain degree of lack of information, partially informed searches can still outperform optimal Lévy searches. We discuss our results in connection with the foraging problem.
关于搜索空间相关全局尺度的信息，即使是部分信息，理论上也应该能提高随机搜索的性能。在此我们通过数值和解析方法表明，在一维（1D）和二维（2D）中，即使关于相关景观尺度的知识不完整，有信息的多尺度随机搜索也能优于典型的无信息最优 Lévy 搜索。我们在低密度无损区域表明，包含大小为 L 的一维景观所有关键尺度的双指数搜索的最优效率渐近衰减为 η_{opt}∼1/√[L]，这超越了最优 Lévy 搜索的 η_{opt}∼1/(√[L]lnL) 的结果。我们进一步刻画了搜索者在这些尺度上所能拥有的有限信息水平。我们得到了一维和二维中双指数和三指数搜索的相图。值得注意的是，即使在一定程度的信息缺失情况下，部分有信息的搜索仍然可以优于最优 Lévy 搜索。我们结合觅食问题讨论我们的结果。
