Ibrahim Abdullahi Adinoyi, Muehlebach Michael, De Bacco Caterina
<a href="https://ror.org/04fq9j139">Max Planck Institute for Intelligent Systems</a>, Cyber Valley, Tübingen 72076, Germany.
Phys Rev Lett. 2024 Aug 2;133(5):057401. doi: 10.1103/PhysRevLett.133.057401.
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is limited by the lack of principled and flexible ways to incorporate realistic constraints. We propose a principled physics-based approach to impose constraints flexibly in optimal transport problems. Constraints are included in mirror descent dynamics using the D'Alembert-Lagrange principle from classical mechanics. This results in a sparse, local and linear approximation of the feasible set leading in many cases to closed-form updates.
在拥堵的网络中为多个交通需求找到最优轨迹是一项具有挑战性的任务。最优传输理论是一种有原则的方法，已成功用于研究各种交通问题。其应用受到缺乏纳入现实约束的有原则且灵活方法的限制。我们提出一种基于物理原理的方法，以便在最优传输问题中灵活施加约束。利用经典力学中的达朗贝尔 - 拉格朗日原理，将约束纳入镜像下降动力学中。这导致可行集的稀疏、局部和线性近似，在许多情况下可得到闭式更新。
