Towards a 2-dimensional self-organized framework for structured population-based metaheuristics

This paper proposes a swarm intelligence framework for distributed population-based metaheuristics that uses stigmergy and similarity measures as basic modeling rules with a local range of action for structuring the neighborhood. The system - which can be described as a cellular automaton with short-term memory - displays complex and emergent behavior whose most visible trait is the self-organization of a population of particles into dynamic clusters. These clusters tend to gather similar particles (similarity here is measured as the algebraic difference between randomly assigned fitness values). During the execution of the algorithm, the particles move through a grid of nodes leaving a mark with the fitness value of the particle in each node they visit. When deciding where to move, the particles take into account the marks in the neighborhood and tend to travel to nodes with marks that minimize the difference between the particle's fitness and the mark's fitness. A kind of hierarchical behavior is also modeled by forcing the particles to move toward nodes with better fitness values. We show that these simple rules conduct the system to a critical state in which clusters are constantly created and broken, while maintaining a typical pattern of clusters and paths. In addition, we demonstrate that the system's variables display noise, which is one of the signatures of Self-Organized Criticality (SOC). Since it does not require the tuning of control parameters to precise values, we hypothesize that the proposed system converges to SOC.