Modified particle swarm strategies in spatial public goods games

Particle swarm optimization (PSO) is a prominent swarm intelligence algorithm where each particle updates its position based on two key components, personal experience (its own historical best solution) and social learning (the best solution found by its neighbors or the swarm). In this study, we enhance both components to propose novel PSO variants. For the personal experience component, we model cognitive bias in self-experience by introducing a biased recollection of individual history, implemented via the Fermi function. Regarding social learning, we incorporate neighbor communication, utilizing either average or optimal neighbor information to guide collective updates. Our results demonstrate that these modifications significantly improve the level of cooperation compared to traditional PSO. By integrating noise-driven decision-making through the Fermi function and employing multi-swarm communication structures, our approach achieves more robust cooperation across diverse environments. These findings underscore the potential of adaptive swarm intelligence principles to foster enhanced cooperation in complex social systems.