CoRide: Joint Order Dispatching and Fleet Management for Multi-Scale Ride-Hailing Platforms

How to optimally dispatch orders to vehicles and how to tradeoff between immediate and future returns are fundamental questions for a typical ride-hailing platform. We model ride-hailing as a large-scale parallel ranking problem and study the joint decision-making task of order dispatching and fleet management in online ride-hailing platforms. This task brings unique challenges in the following four aspects. First, to facilitate a huge number of vehicles to act and learn efficiently and robustly, we treat each region cell as an agent and build a multi-agent reinforcement learning framework. Second, to coordinate the agents from different regions to achieve long-term benefits, we leverage the geographical hierarchy of the region grids to perform hierarchical reinforcement learning. Third, to deal with the heterogeneous and variant action space for joint order dispatching and fleet management, we design the action as the ranking weight vector to rank and select the specific order or the fleet management destination in a unified formulation. Fourth, to achieve the multi-scale ride-hailing platform, we conduct the decision-making process in a hierarchical way where a multi-head attention mechanism is utilized to incorporate the impacts of neighbor agents and capture the key agent in each scale. The whole novel framework is named as CoRide. Extensive experiments based on multiple cities real-world data as well as analytic synthetic data demonstrate that CoRide provides superior performance in terms of platform revenue and user experience in the task of city-wide hybrid order dispatching and fleet management over strong baselines.Comment: CIKM 201

Numerical wave propagation for the triangular P1DGP1_{DG}-P2P2 finite element pair

Inertia-gravity mode and Rossby mode dispersion properties are examined for discretisations of the linearized rotating shallow-water equations using the $P1_{DG}$-$P2$ finite element pair on arbitrary triangulations in planar geometry. A discrete Helmholtz decomposition of the functions in the velocity space based on potentials taken from the pressure space is used to provide a complete description of the numerical wave propagation for the discretised equations. In the $f$-plane case, this decomposition is used to obtain decoupled equations for the geostrophic modes, the inertia-gravity modes, and the inertial oscillations. As has been noticed previously, the geostrophic modes are steady. The Helmholtz decomposition is used to show that the resulting inertia-gravity wave equation is third-order accurate in space. In general the \pdgp finite element pair is second-order accurate, so this leads to very accurate wave propagation. It is further shown that the only spurious modes supported by this discretisation are spurious inertial oscillations which have frequency $f$, and which do not propagate. The Helmholtz decomposition also allows a simple derivation of the quasi-geostrophic limit of the discretised $P1_{DG}$-$P2$ equations in the $\beta$-plane case, resulting in a Rossby wave equation which is also third-order accurate.Comment: Revised version prior to final journal submissio