Optimal Searching Strategies for Different Target Distributions

Abstract

Random search has gained increasing attention from researchers in increasingly many fields and many papers have shown that Lévy searching strategy achieves a higher searching efficiency when the targets are sparse in some area. However, we have to face the question that what is the relationship between the optimal searching strategy and the target distribution. In this paper, three different searching strategies, i.e., δ-distribution (fixed flight distance), Gaussian distribution, and Lévy distribution, and three different target distributions, i.e., uniform distribution, Gaussian-like distribution, and Lévy-like distribution, are considered. We optimize the searching efficiency for three different searching strategies theoretically, which can be used to tune the parameters in the later experiments. According to the experimental results, it is found that Lévy searching strategy achieves the highest efficiency for uniform-distributed targets, while Gaussian searching strategy performs the best for Gaussian-distributed and some specific Lévy -like distributed targets. This study validates that the optimal searching strategy is closely related to the target distribution.

Keywords: Optimal random search, target distribution, Lévy distribution, Gaussian distribution