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.

翻译：树栖龟蚁的蚁群会在热带雨林冠层中由树枝与藤蔓构成的图上建立连接巢穴与食物源的路径网络。蚂蚁在行进时会在路径边沿释放挥发性信息素。在每个顶点处，蚂蚁根据当前信息素水平采用决策规则选择下一个行进边。网络中存在着蚂蚁的双向流动。在实地研究中，Chandrasekhar等人（2021）观察到该路径网络近似最小化顶点数量，从而在没有集中控制且计算资源极少的条件下解决了经典最短路径问题的变体。我们提出一种基于图上强化随机游走变体的生物合理模型，该模型解释了这一观测结果，并揭示了解决最短路径问题及其变体的新颖算法。通过仿真与分析，我们证明当蚂蚁流动速率不变时，该动力学过程收敛于包含最少顶点数的路径（与实地观察结果一致）；当流动速率随时间增加时，动力学过程收敛于最短路径——因此蚁群仅需提升流动速率即可解决最短路径问题。我们还证明：要保证收敛至最短路径，必须依赖双向流动与按信息素比例分配流量的决策规则，但采用其他决策规则时仍可实现近似最短路径的收敛。