Swarm intelligence algorithms are designed to find approximate solutions to optimisation problems emerging from the individual contributions of members of a population, and hence they can be naturally interpreted within the framework of agent-based models. This paper takes a recently introduced numeric optimisation swarm method inspired in the foraging behaviour or urban pigeons and reports a reworking of the algorithm as an agent-based model. The practicality of the model is tested on a set of benchmarks suitably adapted to a discrete search landscape, and the impact of the model parameters is investigated by exhaustive empirical simulations. To further validate the model, we compared it to an existing agent-based model of the standard Particle Swarm Optimisation, a widely-known swarm intelligence method. Results indicate that effectiveness and efficiency of both models are comparable, and moreover, that the agent-based framework was useful to discover new insights about improving the behaviour of the pigeon-inspired method.