A Self-Adjusting Algorithm for Driver Scheduling

Public transport driver scheduling is a world wide problem, which is NP-hard. Although some mathematically based methods are being used in the transport industry, there is still much scope for improvements. This paper presents a novel evolutionary approach that simulates the self-adjusting process on a single schedule. Five factors characterized by fuzzy membership functions are first aggregated to evaluate the shift structure. This evaluating function is incorporated into a constructing heuristic to make shift selection. A self-adjusting algorithm is then designed to guide the constructing heuristic to improve a given initial schedule iteratively. In each generation an unfit portion of the working schedule is removed. Broken schedules are repaired by the constructing heuristic until stopping condition is met. Experimental results on real-world driver scheduling problems has demonstrated the success of the proposed approach.     

The homogeneous projective transformation of general quadratic matrix equations

^** Email: vassilios.tsachouridis{at}ieee.org^*** Email: basil.kouvaritakis{at}eng.ox.ac.uk Algebraic quadratic equations are a special case of a singlegeneralized algebraic quadratic matrix equation (GQME). Hence,the importance of that equation in science and engineering isevident. This paper focus on the study of solutions of thatGQME and a unified framework for the characterization and identificationof solutions at infinity and of finite solutions of generalquadratic algebraic matrix equations is presented. The analysisis based on the concept of homogeneous projective transformationfor general polynomial systems (Morgan, 1986). In addition,a numerical error analysis for the computed solutions is providedfor the assessment of numerical accuracy, stability and conditioningof the computed solutions. The proposed framework is independentof any numerical method and therefore it can be used along withvarious possible numerical methods for the GQME solution, especiallymatrix flow-based algorithms (Chu, 1994) (e.g. continuation/homotopy,Morgan, 1989).     

Stopping criteria, forward and backward errors for perturbed asynchronous linear fixed point methods in finite precision

^** Email: pierre.spiteri{at}enseeiht.fr This paper deals with perturbed linear fixed point methods inthe presence of round-off errors. Successive approximationsas well as the more general asynchronous iterations are treated.Forward and backward error estimates are presented, and theseare used to propose theoretical stopping criteria for thesemethods. In the case of asynchronous iterations, macro-iterationsare used as a tool in order to obtain estimates.     

线阵CCD光积分时间的智能控制技术及其应用

本文提出了一种新型线阵ＣＣＤ驱动电路的设计方法，可以在不改变系统工作主频的情况下，连续地改变ＣＣＤ的光积分时间，并且可通过计算机接口实现智能调整，此项技术已成功应用于热扎线材外径的线检测仪中，控制效果极其理想。     

悬浮RDX炸药粉尘爆轰的数值模拟

用两相流模型对悬浮RDX炸药粉尘爆轰波进行了数值模拟。RDX炸药颗粒在爆轰波阵面后的高温高速气流中加速并升温,颗粒表面发生熔化。参考液滴在高速气流作用下剥离的效应,假设炸药熔化部分在高速气流的作用下发生剥离,破碎成极小的颗粒,瞬时发生分解反应,释放出能量支持爆轰波传播。数值模拟了在不同粒径和浓度的悬浮RDX炸药粉尘中爆轰波的发展与传播过程,得到了爆轰波流场中气-固两相的物理量分布,并确定了爆轰波参数。在较低的RDX粉尘浓度条件下,爆轰波阵面压力的峰值曲线出现振荡。当RDX粉尘浓度在80~150 g/m3时,数值模拟得到的爆轰波阵面压力峰值曲线的振荡是规则的;当RDX粉尘浓度为70 g/m3时,爆轰波阵面压力峰值曲线出现不规则振荡。     

基于CPLD工作模式可调的线阵CCD驱动电路设计

针对传统驱动电路一旦做出修改,则需对硬件或程序进行改变的缺点,以型号为TCD1707D的线阵CCD为例,介绍了一种工作模式可调的驱动方法.该方法是利用复杂可编程逻辑器件和控制外端结合,通过分别设置内外触发来实现的.在外触发模式下,利用外触发脉冲,可由用户控制CCD的曝光和信号输出时间;内触发时,可以调节CCD的积分时间和驱动频率.为提高信号输出质量,针对EMC问题给出了线阵CCD的外围驱动电路.实验结果表明,该方法调试方便、电路结构简单、集成度较高、输出信号可靠稳定、受干扰小,可配合多种用户需要,对高速精确测量及线阵推扫模式具有一定参考价值.     

Simulation of harmonic oscillators on the lattice

This work deals with the simulation of a two-dimensional ideal lattice having simple tetragonal geometry. The harmonic character of the oscillators give rise to a system of second-order linear differential equations, which can be recast into matrix form. The explicit solutions which govern the dynamics of this system can be expressed in terms of matrix trigonometric functions. For the derivation we employ the Lagrangian formalism to determine the correct solutions, which extremize the underlying action of the system. In the numerical evaluation we develop diverse state-of-the-art algorithms which efficiently tackle equations with matrix sine and cosine functions. For this purpose, we introduce two special series related to trigonometric functions. They provide approximate solutions of the system through a suitable combination. For the final computation an algorithm based on Taylor expansion with forward and backward error analysis for computing those series had to be devised. We also implement several MATLAB programs which simulate and visualize the two-dimensional lattice and check its energy conservation.     

Convergence rates for forward–backward dynamical systems associated with strongly monotone inclusions

We investigate the convergence rates of the trajectories generated by implicit first and second-order dynamical systems associated to the determination of the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz continuous one in a real Hilbert space. We show that these trajectories strongly converge with exponential rate to a zero of the sum, provided the latter is strongly monotone. We derive from here convergence rates for the trajectories generated by dynamical systems associated to the minimization of the sum of a proper, convex and lower semicontinuous function with a smooth convex one provided the objective function fulfills a strong convexity assumption. In the particular case of minimizing a smooth and strongly convex function, we prove that its values converge along the trajectory to its minimum value with exponential rate, too.     

A simple comparison between Skorokhod & Russo-Vallois integration for insider trading

We consider a simplified version of the problem of insider trading in a financial market. We approach it by means of anticipating stochastic calculus and compare the use of the Skorokhod and the Russo-Vallois forward integrals within this context. We conclude that, while the forward integral yields results with a clear financial meaning, the Skorokhod integral does not provide a suitable formulation for this problem.     

Existence of an optimal control for a coupled FBSDE with a non degenerate diffusion coefficient

We consider a controlled system driven by a coupled forward–backward stochastic differential equation with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential equation, at the initial time. Our goal is to find an optimal control which minimizes the cost functional. The method consists to construct a sequence of approximating controlled systems for which we show the existence of a sequence of feedback optimal controls. By passing to the limit, we establish the existence of a relaxed optimal control to the initial problem. The existence of a strict control follows from the Filippov convexity condition.