Physarum启发的多商品流动动力学
Physarum-Inspired Multi-Commodity Flow Dynamics
摘要：
在湿实验室实验中，黏菌多头绒泡菌（Physarum polycephalum）已经证明了它解决最短路径问题和设计高效网络的能力。对于最短路径问题，可获得用于粘液演化的数学模型，并且在计算机实验中和通过数学分析表明，动力学解决了最短路径问题。在本文中，我们介绍了一个动态的网络设计问题。我们制定网络设计的问题，构建一个网络，有效地支持多商品流的问题。我们调查的动态计算机模拟和分析。仿真结果表明，该动力学能够构建高效和优雅的网络。在理论部分中，我们表明，动态最小化的目标相结合的网络成本和通过网络的路由需求的成本。我们还给出了最优解的替代表征。
英文摘要：
In wet-lab experiments, the slime mold Physarum polycephalum has demonstrated its ability to solve shortest path problems and to design efficient networks. For the shortest path problem, a mathematical model for the evolution of the slime is available and it has been shown in computer experiments and through mathematical analysis that the dynamics solves the shortest path problem. In this paper, we introduce a dynamics for the network design problem. We formulate network design as the problem of constructing a network that efficiently supports a multi-commodity flow problem. We investigate the dynamics in computer simulations and analytically. The simulations show that the dynamics is able to construct efficient and elegant networks. In the theoretical part we show that the dynamics minimizes an objective combining the cost of the network and the cost of routing the demands through the network. We also give alternative characterization of the optimum solution.
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