Optimal random search using limited spatial memory

Lévy walks are known to be efficient movements because Lévy walkers search wide areas while restricting returns to previously visited sites. A self-avoiding walk (SAW) is a series of moves on a lattice that visit the same place only once. As such, SAWs can also be effective search algorithms. However, it is not realistic that foragers memorize many visited positions for a long time. In this work, we investigated whether foragers performed optimal searches when having limited memory. The agent in our model followed SAWs to some extent by memorizing and avoiding visited places. However, the agent lost its memory after a while. In that situation, the agent changed its reactions to visited patches by considering global trail patterns based on local memorized information. As a result, we succeeded in making the agent occasionally produce ballistic walks related to power-law tailed movements across some ranges.