Cyber-physical logistics system-based vehicle routing optimization
Mingyong Lai Hongming Yang Songping Yang Junhua Zhao Yan Xu
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
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
Continuity of the solution mappings to parametric generalized non-weak vector Ky Fan inequalities
Yangdong Xu Shengjie Li

In this paper, by using the nonlinear scalarization method and under some new assumptions, which do not involve any information on the solution set, we establish the continuity of solution mappings of parametric generalized non-weak vector Ky Fan inequality with moving cones. The results are new and improve corresponding ones in the literature. Some examples are given to illustrate our results.

keywords: Upper semicontinuity lower semicontinuity Ky Fan inequality nonlinear scalarization method
New structural properties of inventory models with Polya frequency distributed demand and fixed setup cost
Yanyi Xu Arnab Bisi Maqbool Dada

We study a stochastic inventory model with a fixed setup cost and zero order lead time. In a finite-horizon lost sales model, when demand has a Polya frequency distribution (P Fn), we show that there are no more than a pre-determined number of minima of the cost function. Consequently, depending on the relative cost of lost sales and inventory holding cost, there can be as few as one local minimum. These properties have structural implications for the optimal policies and cost functions. A necessary condition for the results to hold for the backordered model has been explained. We further conduct a numerical study to validate our structural results.

keywords: Inventory (s, S) policies P Fn distribution lost sales backorder
Performance evaluation of a power saving mechanism in IEEE 802.16 wireless MANs with bi-directional traffic
Shunfu Jin Wuyi Yue Xuena Yan
One of the most important ways for extending the battery lifetime of Mobile Stations (MSs) in a wireless Metropolitan Area Network (MAN) is to conserve the power consumption effectively. When a power saving mechanism with the sleep mode in IEEE 802.16-2009 is used, the system will be in a sleep state and the energy will be saved if both the Uplink (UL) and the Downlink (DL) are idle. In this paper, we present a new mathematical analysis for the system model with synchronous multiple vacations to capture the working principle of the Power Saving Class (PSC) type III in IEEE 802.16-2009 by taking into account the bi-directional traffic (the UL traffic and DL traffic together). By using the methods of a semi-Markov process and a two-dimensional embedded Markov chain, we derive the steady-state probability distribution of the system. Noting that the transmission of UL data frame will not be influenced by the sleep mode, but the sleep mode can be terminated by the arrival of UL data frames, we give the formula for the average delay of the DL data frames taking the bi-directional traffic into consideration. Moreover, we also present the expression for the energy saving ratio. Analytical results and simulation results are provided to investigate and validate the influence of the system parameters on the system performance. Finally, considering the trade-off between the average delay of data frames and the energy saving ratio, we develop a cost function to determine the optimal length of the sleep window in order to maximize the energy saving ratio while satisfying the Quality of Service (QoS) constraint on the average delay of data frames.
keywords: PSC type III bi-directional traffic Sleep mode synchronous multiple vacations IEEE 802.16-2009 semi-Markov process.
Bifurcations of multiple homoclinics in general dynamical systems
Yancong Xu Deming Zhu Xingbo Liu
By using the local active coordinates consisting of tangent vectors of the invariant subspaces, as well as the Silnikov coordinates, the simple normal form is established in the neighborhood of the double homoclinic loops with bellows configuration in a general system, then the dynamics near the homoclinic bellows is investigated, and the existence, uniqueness of the homoclinic orbits and periodic orbits with various patterns bifurcated from the primary orbits are demonstrated, and the corresponding bifurcation curves (or surfaces) and existence regions are located.
keywords: Silnikov coordinates. Homoclinic bellows Bifurcations
A fast patch-dictionary method for whole image recovery
Yangyang Xu Wotao Yin
Many dictionary based methods in image processing use dictionary to represent all the patches of an image. We address the open issue of modeling an image by its overlapping patches: due to overlapping, there are a large number of patches, and to recover these patches, one must determine an excessive number of their dictionary coefficients. With very few exceptions, this issue has limited the applications of image-patch methods to the ``local'' tasks such as denoising, inpainting, cartoon-texture decomposition, super-resolution, and image deblurring, where one can process a few patches at a time. Our focus is the global imaging tasks such as compressive sensing and medical image recovery, where the whole image is encoded together in each measurement, making it either impossible or very ineffective to update a few patches at a time.
    Our strategy is to divide the sparse recovery into multiple subproblems, each of which handles a subset of non-overlapping patches, and then the results of the subproblems are averaged to yield the final recovery. This simple strategy is surprisingly effective in terms of both quality and speed.
    In addition, we accelerate computation of the learned dictionary by applying a recent block proximal-gradient method, which not only has a lower per-iteration complexity but also takes fewer iterations to converge, compared to the current state-of-the-art. We also establish that our algorithm globally converges to a stationary point. Numerical results on synthetic data demonstrate that our algorithm can recover a more faithful dictionary than two state-of-the-art methods.
    Combining our image-recovery and dictionary-learning methods, we numerically simulate image inpainting, compressive sensing recovery, and deblurring. Our recovery is more faithful than those by a total variation method and a method based on overlapping patches. Our Matlab code is competitive in terms of both speed and quality.
keywords: non-convex optimization. Dictionary learning non-overlapping patches sparse representation whole-image recovery
Learning circulant sensing kernels
Yangyang Xu Wotao Yin Stanley Osher
In signal acquisition, Toeplitz and circulant matrices are widely used as sensing operators. They correspond to discrete convolutions and are easily or even naturally realized in various applications. For compressive sensing, recent work has used random Toeplitz and circulant sensing matrices and proved their efficiency in theory, by computer simulations, as well as through physical optical experiments. Motivated by recent work [8], we propose models to learn a circulant sensing matrix/operator for one and higher dimensional signals. Given the dictionary of the signal(s) to be sensed, the learned circulant sensing matrix/operator is more effective than a randomly generated circulant sensing matrix/operator, and even slightly so than a (non-circulant) Gaussian random sensing matrix. In addition, by exploiting the circulant structure, we improve the learning from the patch scale in [8] to the much large image scale. Furthermore, we test learning the circulant sensing matrix/operator and the nonparametric dictionary altogether and obtain even better performance. We demonstrate these results using both synthetic sparse signals and real images.
keywords: Compressive sensing dictionary learning. Toeplitz matrix circulant matrix sensing operator learning sensing kernel learning
Parallel matrix factorization for low-rank tensor completion
Yangyang Xu Ruru Hao Wotao Yin Zhixun Su
Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data reconstruction, and so on. We propose a new model to recover a low-rank tensor by simultaneously performing low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An alternating minimization algorithm is applied to solve the model, along with two adaptive rank-adjusting strategies when the exact rank is not known.
    Phase transition plots reveal that our algorithm can recover a variety of synthetic low-rank tensors from significantly fewer samples than the compared methods, which include a matrix completion method applied to tensor recovery and two state-of-the-art tensor completion methods. Further tests on real-world data show similar advantages. Although our model is non-convex, our algorithm performs consistently throughout the tests and gives better results than the compared methods, some of which are based on convex models. In addition, subsequence convergence of our algorithm can be established in the sense that any limit point of the iterates satisfies the KKT condtions.
keywords: low-rank tensor completion low-rank matrix completion alternating least squares non-convex optimization. Higher-order tensor

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