2D P colony for vicinity search optimisation

Abstract P colony is a formal computational model suitable for modelling behaviour of simple agents acting in a shared environment. It builds on the framework of membrane systems, where both the environment and agents contain abstract discrete objects and formal rules acting upon them. Adding a 2D geometrical structure and an evolution of the environment results in the model of 2D evolving P colonies. The model is suitable for the simulation of phenomena like stigmergy, hence also for the implementation of multi-agent optimisation strategies. The main motivation lies in the use of P colonies as a high-level description language for optimisation tasks, reconfigurable without programming, and ready for a highly parallel and efficient implementation by existing GPU libraries for P systems. In this paper, we use a 2D P colony to implement an ant colony-inspired optimisation algorithm. The agents—ants—search the environment for food representing the extrema of an objective function. The search is oriented with the help of pheromone trails left by previous agents. The trails are subject to a decay and can eventually vanish. In our previous research, we implemented via a 2D P colony a classical formulation of the ant algorithm where ants immediately collect found food in the nest. Here we introduce an improved 2D P colony implementation inspired by variants of ACO algorithms with local search. We call this variant a vicinity search and we demonstrate experimentally that it greatly improves the search results. Furthermore, the new solution decreases asymptotically the complexity of programs in agents.