# Search with home returns provides advantage under high uncertainty

## TL;DR

This paper develops a universal theoretical framework for search strategies involving home returns, showing that such strategies outperform free-range search under high uncertainty conditions.

## Contribution

It introduces a general, assumption-free model for search with home returns, linking it to free-range search solutions and revealing a universal phase diagram.

## Key findings

- Home returns improve search efficiency in high uncertainty environments.
- Theoretical framework applies to various search and return strategies.
- Universal phase diagram characterizes when home returns are advantageous.

## Abstract

Many search processes are conducted in the vicinity of a favored location, i.e., a home, which is visited repeatedly. Foraging animals return to their dens and nests to rest, scouts return to their bases to resupply, and drones return to their docking stations to recharge or refuel. Yet, despite its prevalence, very little is known about search with home returns as its analysis is much more challenging than that of unconstrained, free-range, search. Here, we develop a theoretical framework for search with home returns. This makes no assumptions on the underlying search process and is furthermore suited to treat generic return and home-stay strategies. We show that the solution to the home-return problem can then be given in terms of the solution to the corresponding free-range problem---which not only reduces overall complexity but also gives rise to a simple, and universal, phase-diagram for search. The latter reveals that search with home returns outperforms free-range search in conditions of high uncertainty. Thus, when living gets rough, a home will not only provide warmth and shelter but also allow one to locate food and other resources quickly and more efficiently than in its absence.