continuous time model
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Author(s):  
Aurélien Froger ◽  
Ola Jabali ◽  
Jorge E. Mendoza ◽  
Gilbert Laporte

Electric vehicle routing problems (E-VRPs) deal with routing a fleet of electric vehicles (EVs) to serve a set of customers while minimizing an operational criterion, for example, cost or time. The feasibility of the routes is constrained by the autonomy of the EVs, which may be recharged along the route. Much of the E-VRP research neglects the capacity of charging stations (CSs) and thus implicitly assumes that an unlimited number of EVs can be simultaneously charged at a CS. In this paper, we model and solve E-VRPs considering these capacity restrictions. In particular, we study an E-VRP with nonlinear charging functions, multiple charging technologies, en route charging, and variable charging quantities while explicitly accounting for the number of chargers available at privately managed CSs. We refer to this problem as the E-VRP with nonlinear charging functions and capacitated stations (E-VRP-NL-C). We introduce a continuous-time model formulation for the problem. We then introduce an algorithmic framework that iterates between two main components: (1) the route generator, which uses an iterated local search algorithm to build a pool of high-quality routes, and (2) the solution assembler, which applies a branch-and-cut algorithm to combine a subset of routes from the pool into a solution satisfying the capacity constraints. We compare four assembly strategies on a set of instances. We show that our algorithm effectively deals with the E-VRP-NL-C. Furthermore, considering the uncapacitated version of the E-VRP-NL-C, our solution method identifies new best-known solutions for 80 of 120 instances.


Author(s):  
Li-qiang Zhang ◽  
Long-yang Huang ◽  
Xiao-li Duan

AbstractPerson reidentification rate has become a challenging research topic in the field of computer vision due to the fact that person appearance is easily affected by lighting, posture and perspective. In order to make full use of the continuity of video data on the time line and the unstructured relationship of features, a video person reidentification algorithm combining the neural ordinary differential equation with the graph convolution network is proposed in this paper. First, a continuous time model is constructed by using the ordinary differential equation (ODE) network so as to capture hidden information between video frames. By simulating the hidden space of the hidden variables with the hidden time series model, the hidden information between frames that may be ignored in the discrete model can be obtained. Then, the features of the generated video frames are given to the graph convolution network to reconstruct them. Finally, weak supervision is used to classify the features. Experiments on PRID2011 datasets show that the proposed algorithm can significantly improve person reidentification performance.


2021 ◽  
Author(s):  
Li-qiang ZHANG ◽  
Long-yang HUANG ◽  
Xiao-li DUAN

Abstract Person reidentification rate has become a challenging research topic in the field of computer vision due to the fact that person appearance is easily affected by lighting, posture and perspective. In order to make full use of the continuity of video data on the time line and the unstructured relationship of features, a video person reidentification algorithm combining the neural ordinary differential equation with the graph convolution network is proposed in this paper. First, a continuous time model is constructed by using the ordinary differential equation (ODE) network so as to capture hidden information between video frames. By simulating the hidden space of the hidden variables with the hidden time series model, the hidden information between frames that may be ignored in the discrete model can be obtained. Then, the features of the generated video frames are given to the graph convolution network to reconstruct them. Finally, weak supervision are used to classify the features. Experiments on PRID2011 data sets show that the proposed algorithm can significantly improve person reidentification performance.


2021 ◽  
pp. 1-36
Author(s):  
Clemente De Rosa ◽  
Elisa Luciano ◽  
Luca Regis

ABSTRACT This paper provides a method to assess the risk relief deriving from a foreign expansion by a life insurance company. We build a parsimonious continuous-time model for longevity risk that captures the dependence across different ages in domestic versus foreign populations. We calibrate the model to portray the case of a UK annuity portfolio expanding internationally toward Italian policyholders. The longevity risk diversification benefits of an international expansion are sizable, in particular when interest rates are low. The benefits are judged based on traditional measures, such as the Risk Margin or volatility reduction, and on a novel measure, the Diversification Index.


2021 ◽  
Vol 31 (03) ◽  
pp. 2130008
Author(s):  
Ranchao Wu ◽  
Chuanying Zhang ◽  
Zhaosheng Feng

In this paper, we focus on a network system which describes spatiotemporal dynamics of single species population at different patches since species can have different features in various life stages and different behaviors in various spatial environments. With the effect of time delay and spatial dispersion, homogenous, periodic and spatiotemporally nonhomogeneous distributions are identified. The stability analysis is carried out for the discrete-space and continuous-time network on single species with time delay and the Hopf bifurcation of the single species population model in a network is explored. Formulas for determining the direction of Hopf bifurcation are derived by using the center manifold method and the normal form theorem. It is found that the network can generate spatial patterns only when time delay is present. Finally, numerical simulations are performed which agree well with our theoretical result, i.e. this discrete-space and continuous-time model admits regular temporal patterns since the delay induces Hopf bifurcations with network structure.


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