Designing minimum-cost networks that are robust and avoid obstacles

该项目的目标是构建一个数学框架，用于设计鲁棒性和避免障碍的最小成本网络。通信、电力和运输所需的物理网络对我们的社会至关重要，但从经济和环境角度来看，成本高昂。需要数学优化工具来设计最低成本的网络，考虑到实际的考虑因素，如生存的本地连接故障和避免预先存在的障碍。这些被认为是数学上具有挑战性的问题。目前的方法采用限制性模型，无法捕捉现代基础设施网络的灵活性。这个项目的目的是开发几何设计方法，使用可变的“施泰纳点”，导致快速算法，最佳地解决这些问题。

The goal of this project is to construct a mathematical framework for the design of minimum-cost networks that are robust and avoid obstacles. Physical networks such as those required for communication, power and transportation are vital for our society, but are costly from economic and environmental viewpoints. There is a need for mathematical optimisation tools to design minimum-cost networks that take into account practical considerations such as surviving local connectivity failures and avoiding pre-existing obstacles. These are recognised as mathematically challenging problems. Current approaches employ restrictive models that do not capture the flexibility of modern infrastructure networks. This project aims to develop geometric design methods using variable ‘Steiner points’, leading to fast algorithms for optimally solving these problems.