Homes, Herds, and Hunts: Toward Optimality in Collectives

Abstract

The patterns formed by interacting agents in nature have enthralled us for centuries. Despite much research in the past several decades, less attention has been devoted to the functional benefits of collective behavior, particularly when it comes to control and optimization. Given the practical and scientific value of understanding how collectives are affected by their environments in both active and passive ways, further effort ought to be devoted to the study of how collectives tend toward optimality. Here, I investigate three examples of optimization and control of a group of collective agents across the dimensions of time, number, and cooperation. First, I begin by examining how ecology, physiology, and number affect the shape and structure of a termite mound. Are there certain places, colony sizes, or species of termite that build particularly hospitable mounds? Second, I consider how a single shepherd can optimally guide a flock to a target in unconstrained environments. Third, I extend the simple model—herding with a single shepherd—by including constraints and multiple shepherds. How does the inclusion of walls and gates affect the transport problem? Fourth, I explore a simplified one dimensional for the study of pursuit and evasion in the wild to understand the tradeoff between agility and speed.