Cyber-physical logistics system-based vehicle routing optimization
Mingyong Lai Hongming Yang Songping Yang Junhua Zhao Yan Xu
Journal of Industrial & Management Optimization 2014, 10(3): 701-715 doi: 10.3934/jimo.2014.10.701
Vehicle routing problem is a classic combinational optimization problem, which has been attracting research attentions in logistics and optimization area. Conventional static vehicle routing problem assumes the logistics information is accurate and timely, and does not take into account the uncertainties, which is therefore inadequate during practical applications. In this paper, a vehicle initial routing optimization model considering uncertainties is proposed, the vehicle capacity, customer time-window, and the maximum travelling distance as well as the road capacity are considered. In the cyber-physical logistics system background, a routing adjustment model is proposed to minimize the total distribution cost considering the road congestion, and the static and dynamic models are proposed for traffic information transmission network to quantitatively analyse the impact of the traffic information transmission delay on the vehicle routing optimization. The learnable genetic algorithm is adopted to solve the initial routing optimization model and the routing adjustment model. The simulation results have verified its effectiveness.
keywords: communication delay road congestion Vehicle routing problem learnable genetic algorithm. routing adjustment cyber-physical logistics system
Efficient time discretization for local discontinuous Galerkin methods
Yinhua Xia Yan Xu Chi-Wang Shu
Discrete & Continuous Dynamical Systems - B 2007, 8(3): 677-693 doi: 10.3934/dcdsb.2007.8.677
In this paper, we explore three efficient time discretization techniques for the local discontinuous Galerkin (LDG) methods to solve partial differential equations (PDEs) with higher order spatial derivatives. The main difficulty is the stiffness of the LDG spatial discretization operator, which would require a unreasonably small time step for an explicit local time stepping method. We focus our discussion on the semi-implicit spectral deferred correction (SDC) method, and study its stability and accuracy when coupled with the LDG spatial discretization. We also discuss two other time discretization techniques, namely the additive Runge-Kutta (ARK) method and the exponential time differencing (ETD) method, coupled with the LDG spatial discretization. A comparison is made among these three time discretization techniques, to conclude that all three methods are efficient when coupled with the LDG spatial discretization for solving PDEs containing higher order spatial derivatives. In particular, the SDC method has the advantage of easy implementation for arbitrary order of accuracy, and the ARK method has the smallest CPU cost in our implementation.
keywords: local discontinuous Galerkin method additive Runge-Kutta method higher order spatial derivatives. Spectral deferred correction method exponential time differencing method

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