Particle swarm optimization (PSO), a population-based optimization algorithm inspired by swarm behaviors, has been applied extensively to simulate social behaviors such as migration, urban planning, or resource utilization. It capitalizes on the inherent principles of social cooperation, adaptability and learning from peers to help individuals in a population search for optima. In this work, we propose a novel co-evolutionary game model in which individuals adapt their interaction radii by applying the PSO algorithm and study how the learning factor in the algorithm shapes the cooperation dynamics. We find that the adaptive interaction radii based on PSO could significantly enhance cooperation, especially in the scenario with strong social dilemma. By studying the snapshots of strategy pattern and the distributions of interaction radii in the population, we further reveal that the PSO-based adapting mechanism can protect cooperators by shrinking the interaction radii in a severe environment with an appropriate . Nevertheless, when cooperation is favorable, the adaptation leads to a relatively wide distribution of interaction radii to facilitate the spread of cooperation. The results of this work highlight the potential of the PSO algorithm to resolve social dilemmas when combined with the evolutionary dynamics.

中文翻译：

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粒子群智能通过调整协同进化博弈中的交互半径来促进合作

粒子群优化（PSO）是一种受群体行为启发的基于群体的优化算法，已广泛应用于模拟社会行为，例如迁移、城市规划或资源利用。它利用社会合作、适应性和向同伴学习的固有原则来帮助群体中的个体寻找最佳状态。在这项工作中，我们提出了一种新颖的协同进化博弈模型，其中个体通过应用 PSO 算法来调整其交互半径，并研究算法中的学习因素如何塑造合作动态。我们发现基于 PSO 的自适应交互半径可以显着增强合作，特别是在社交困境较强的场景中。通过研究策略模式的快照和群体中交互半径的分布，我们进一步揭示了基于 PSO 的适应机制可以通过在恶劣环境中以适当的 减小交互半径来保护合作者。然而，当合作有利时，适应会导致相互作用半径分布相对广泛，以促进合作的传播。这项工作的结果凸显了 PSO 算法与进化动力学相结合解决社会困境的潜力。