A set packing inspired method for real-time junction train routing

Efficiently coordinating the often large number of interdependent, timetabled train movements on a railway junction, while satisfying a number of operational requirements, is one of the most important problems faced by a railway company. The most critical variant of the problem arises on a daily basis at major railway junctions where disruptions to rail traffic make the planned schedule/routing infeasible and rolling stock planners are forced to re-schedule/re-route trains in order to recover feasibility. The dynamic nature of the problem means that good solutions must be obtained quickly. In this paper we describe a set packing inspired formulation of this problem and develop a branch-and-price based solution approach. A real life test instance arising in Germany and supplied by the major German railway company, Deutsche Bahn, indicates the efficiency of the proposed approach by confirming that practical problems can be solved to within a few percent of optimality in reasonable time.     

Managing large fixed costs in vehicle routing and crew scheduling problems solved by column generation

We consider vehicle routing and crew scheduling problems that involve a lexicographic bi-level objective function (for instance, minimizing first the number of vehicles and second the operational costs) and can be solved by column generation where the subproblem is a resource constrained shortest path problem. Such problems are often modeled using a single-level objective function with a large fixed cost (weight) for ensuring the minimization of the primary objective. In this paper, we study the impact on the solution time of the fixed cost value. First, we present computational results which show that the solution time increases as the fixed cost value gets larger. Then, we develop an exact dynamic fixed cost procedure compatible with column generation that starts with a relatively small fixed cost value and increases it iteratively until optimality is reached. To prove optimality, a shortest path problem with resource constraints needs to be solved. Through a series of computational experiments on two types of problems, we show that this procedure can reduce solution times by up to 50% when compared to an approach relying on one very large fixed cost value.     

Scheduling strategies for master-slave tasking on heterogeneous processor platforms

We consider the problem of allocating a large number of independent, equal-sized tasks to a heterogeneous computing platform. We use a nonoriented graph to model the platform, where resources can have different speeds of computation and communication. Because the number of tasks is large, we focus on the question of determining the optimal steady state scheduling strategy for each processor (the fraction of time spent computing and the fraction of time spent communicating with each neighbor). In contrast to minimizing the total execution time, which is NP-hard in most formulations, we show that finding the optimal steady state can be solved using a linear programming approach and, thus, in polynomial time. Our result holds for a quite general framework, allowing for cycles and multiple paths in the interconnection graph, and allowing for several masters. We also consider the simpler case where the platform is a tree. While this case can also be solved via linear programming, we show how to derive a closed-form formula to compute the optimal steady state, which gives rise to a bandwidth-centric scheduling strategy. The advantage of this approach is that it can directly support autonomous task scheduling based only on information local to each node; no global information is needed. Finally, we provide a theoretical comparison of the computing power of tree-based versus arbitrary platforms.     

基于元强化学习的自动列车定速控制

本文考虑自动列车在路况变化下的定速控制问题. 由于铁路路况的复杂以及列车动力学的不确定性, 基于模型的控制器难以稳定、快速、精确地进行定速控制. 我们提出了一种无模型控制器, 其只需要很少的列车运行数据即可适应新的路况. 首先, 我们将列车的定速控制问题建模为一系列转移概率未知的静态连续马尔可夫过程. 然后, 我们应用元强化学习去求解该马尔可夫过程, 得到自适应神经网络控制器. 仿真说明该无模型控制器能够高效地进行定速控制, 并能迅速适应新的环境, 同时满足系统约束.     

Towards railway traffic management using switching Max-plus-linear systems

In this paper we present a railway traffic model and a model predictive controller for online railway traffic management of railway networks with a periodic timetable. The main aim of the controller is to recover from delays in an optimal way by changing the departure of trains, by breaking connections, by splitting joined trains, and - in the case of multiple tracks between two stations - by redistributing the trains over the tracks. The railway system is described by a switching max-plus-linear model. We assume that measurements of current running and dwell times and estimates of future running times and dwell times are continuously available so that they can be taken into account in the optimization of the system’s control variables. The switching max-plus-linear model railway model is used to determine optimal dispatching actions, based on the prediction of the future arrival and departure times of the trains, by recasting the dispatching problem as a Mixed Integer Linear Programming (MILP) problem and solving it. Moreover, we use properties from max-plus algebra to rewrite and reduce the model such that the MILP problem can be solved in less time. We also apply the algorithm to a model of the Dutch railway network.     

A dynamic programming based heuristic for locating stops in public transportation networks

The length of journey towards a bus stop or railway station greatly influences passenger satisfaction and, thus, the utilization of public transport offers. In this context, we investigate the maximum covering location problem in networks (MCLPN) where stops (or stations) are to be located in a given railway or bus network, such that the number of passengers reaching a stop within their particular coverage radius is maximized. Up to now, no specialized solution procedure directly addressing MCLPN exists, instead it is mainly referred to the well-known maximum covering location problem (MCLP), which, however, neglects the underlaying information of the given network structure. This paper exploits the network information, introduces a fast and efficient two-stage dynamic programming based heuristic specifically tailored to MCLPN, and compares it to existing procedures for MCLP. The results show that our heuristic delivers near optimal solutions, i.e., 87% of our test instances are solved to optimality, within a few seconds of computational time.     

Fast Nonlinear Least Squares Optimization of Large-Scale Semi-Sparse Problems

Many problems in computer graphics and vision can be formulated as a nonlinear least squares optimization problem, for which numerous off-the-shelf solvers are readily available. Depending on the structure of the problem, however, existing solvers may be more or less suitable, and in some cases the solution comes at the cost of lengthy convergence times. One such case is semi-sparse optimization problems, emerging for example in localized facial performance reconstruction, where the nonlinear least squares problem can be composed of hundreds of thousands of cost functions, each one involving many of the optimization parameters. While such problems can be solved with existing solvers, the computation time can severely hinder the applicability of these methods. We introduce a novel iterative solver for nonlinear least squares optimization of large-scale semi-sparse problems. We use the nonlinear Levenberg-Marquardt method to locally linearize the problem in parallel, based on its first-order approximation. Then, we decompose the linear problem in small blocks, using the local Schur complement, leading to a more compact linear system without loss of information. The resulting system is dense but its size is small enough to be solved using a parallel direct method in a short amount of time. The main benefit we get by using such an approach is that the overall optimization process is entirely parallel and scalable, making it suitable to be mapped onto graphics hardware (GPU). By using our minimizer, results are obtained up to one order of magnitude faster than other existing solvers, without sacrificing the generality and the accuracy of the model. We provide a detailed analysis of our approach and validate our results with the application of performance-based facial capture using a recently-proposed anatomical local face deformation model.     

Optimizing Train Network Routing Using Deterministic Search

In this paper, we use walk search strategy to solve the optimization problem of train routing on railway network. The proposed approach is a local search algorithm which explores the railway network by walker’s navigating through the network. Using some selection rules, walker can dynamically determine the optimal route of trains. In order to analyze and evaluate the proposed approach, we present two computational studies in which the search algorithm is tested on a part of railway network. The results demonstrate that the proposed approach is an effective tool for optimizing the train routing problem on railway network. Moreover, it can be executed with shorter computation time.     

基于MMC的RPC环流抑制策略

RPC能够对电气化铁路中产生的负序和无功进行就地综合补偿,适用于对高速铁路突出的负序和谐波问题进行综合治理,但RPC受到器件性能的限制难以增大其容量从而影响RPC未来的发展。针对这一问题,有学者提出基于单相MMC的RPC综合补偿装置（MRPC）,MRPC提高了应用的电压等级,有利于适应高压大功率场合。但MRPC中的环流增大了系统损耗,影响了系统稳定,严重时可能导致系统崩溃。针对这一问题,本文详细推导了MRPC的数学模型;分析了环流形成的机理;最后提出了一种环流抑制策略。仿真结果表明,所提出的控制策略可以抑制MRPC中的环流改善其的控制性能,有利于MRPC的实际应用。     

A Small Sphere and Large Margin Approach for Novelty Detection Using Training Data with Outliers

We present a small sphere and large margin approach for novelty detection problems, where the majority of training data are normal examples. In addition, the training data also contain a small number of abnormal examples or outliers. The basic idea is to construct a hypersphere that contains most of the normal examples, such that the volume of this sphere is as small as possible, while at the same time the margin between the surface of this sphere and the outlier training data is as large as possible. This can result in a closed and tight boundary around the normal data. To build such a sphere, we only need to solve a convex optimization problem that can be efficiently solved with the existing software packages for training nu-support vector machines. Experimental results are provided to validate the effectiveness of the proposed algorithm.