Foraging in Particle Systems via Self-Induced Phase Changes

TL;DR

This paper introduces a novel stochastic foraging algorithm for particle systems that uses self-induced phase changes inspired by the Ising model, enabling autonomous, repeated search and gather behaviors based on local interactions.

Contribution

It presents the first algorithm leveraging self-induced phase transitions for autonomous foraging in particle systems, with a token passing mechanism ensuring effective dispersion and gathering.

Findings

Algorithm successfully induces phase changes to switch between search and gather modes.

Token passing mechanism guarantees dispersion wave outpaces compression wave.

Structured spiral gathering method effectively encloses food particles.

Abstract

The foraging problem asks how a collective of particles with limited computational, communication and movement capabilities can autonomously compress around a food source and disperse when the food is depleted or shifted, which may occur at arbitrary times. We would like the particles to iteratively self-organize, using only local interactions, to correctly gather whenever a food particle remains in a position long enough and search if no food particle has existed recently. Unlike previous approaches, these search and gather phases should be self-induced so as to be indefinitely repeatable as the food evolves, with microscopic changes to the food triggering macroscopic, system-wide phase transitions. We present a stochastic foraging algorithm based on a phase change in the fixed magnetization Ising model from statistical physics: Our algorithm is the first to leverage self-induced phase changes as an algorithmic tool. A key component of our algorithm is a careful token passing mechanism ensuring a dispersion broadcast wave will always outpace a compression wave. We also present a highly structured alternative algorithm that gathers by incrementally building a spiral tightly wrapped around the food particle.