树栖蚂蚁的最短路径问题分布式算法
Distributed Algorithms from Arboreal Ants for the Shortest Path Problem
AI总结：
本文提出一种基于增广随机游走的生物学合理模型，解释了树栖龟蚁通过信息素和双向流动解决最短路径问题及其变体的分布式算法，证明了收敛条件。
摘要：
树栖龟蚁的蚁群在热带森林的树冠中，由树枝和藤蔓形成的图上创建连接巢穴和食物源的道路网络。蚂蚁在遍历边时会在边上留下挥发性信息素。在每个顶点，根据当前信息素水平使用决策规则选择下一条要遍历的边。。网络中存在双向流动的蚂蚁。在一项实地研究中，Chandrasekhar等人（2021）观察到道路网络近似地最小化顶点数量，从而在无中心控制和最小计算资源下解决了了流行最短路径问题的变体。。我们提出了一种基于图上增强随机游走变体的生物学合理模型，解释了这一观察，并为最短路径问题及其变体提出了令人惊讶的算法。通过模拟和分析，我们展示了当蚂蚁流动速率不变时，动力学收敛到顶点数量最少的路径，与实地观察一致。当流动速率随时间增加时，动力学收敛到最短路径，因此蚁群仅通过增加流动速率就能解决最短路径问题。我们还展示了，为了确保收敛到最短路径，双向流动和按信息素水平比例分配流动的决策规则是必要的，但使用其他决策规则也可能收敛到近似最短路径。
英文摘要：
Colonies of the arboreal turtle ant create networks of trails that link nests and food sources on the graph formed by branches and vines in the canopy of the tropical forest. Ants put down a volatile pheromone on edges as they traverse them. At each vertex, the next edge to traverse is chosen using a decision rule based on the current pheromone level. There is a bidirectional flow of ants around the network. In a field study, Chandrasekhar et al. (2021) observed that the trail networks approximately minimize the number of vertices, thus solving a variant of the popular shortest path problem without any central control and with minimal computational resources. We propose a biologically plausible model, based on a variant of the reinforced random walk on a graph, which explains this observation and suggests surprising algorithms for the shortest path problem and its variants. Through simulations and analysis, we show that when the rate of flow of ants does not change, the dynamics converges to the path with the minimum number of vertices, as observed in the field. The dynamics converges to the shortest path when the rate of flow increases with time, so the colony can solve the shortest path problem merely by increasing the flow rate. We also show that to guarantee convergence to the shortest path, bidirectional flow and a decision rule dividing the flow in proportion to the pheromone level are necessary, but convergence to approximately short paths is possible with other decision rules.
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