Convex Normalizations in Lift-and-Project Methods for 0–1 Programming

Branch-and-Cut algorithms for general 0–1 mixed integer programs can be successfully implemented by using Lift-and-Project (L&P) methods to generate cuts. L&P cuts are drawn from a cone of valid inequalities that is unbounded and, thus, needs to be truncated, or normalized. We consider general normalizations defined by arbitrary closed convex sets and derive dual problems for generating L&P cuts. This unified theoretical framework generalizes and covers a wide group of already known normalizations. We also give conditions for proving finite convergence of the cutting plane procedure that results from using such general L&P cuts.     

CO2激光用于船体型线放样切割的研究及应用

用激光打标和激光切割方法,实现对船舶建造中船体型线样板箱制作材料的划线与下料的工艺步骤.介绍了由激光器、数控系统、机床构架和冷水机组、除尘与空气压缩机组等辅助设备组成的龙门式三维激光加工联合机床的设计配置与工作原理,并通过对机床的操作试验,选定对木制材料加工的主要工艺参数,并对影响加工质量的现象进行了分析.     

CO2激光切割质量的视觉检测(Ⅱ) 切割质量的评价方法及其视觉图像特征

提出了利用切割面下缘粗糙度作为评价切割面质量的方法.建立了侧面视觉检测系统,对激光切割过程中火花簇射行为进行分析.结果表明在一定工艺条件下,随着切割速度的变化,火花簇射喷射长度以具有极大值的倒U形曲线形式变化,最大的火花喷射长度(即火花簇射视觉图像不同亮度带像素数的极大值)对应于最低的切割面近下缘粗糙度.     

On a Primal-Dual Analytic Center Cutting Plane Method for Variational Inequalities

We present an algorithm for variational inequalities VI( , Y) that uses a primal-dual version of the Analytic Center Cutting Plane Method. The point-to-set mapping is assumed to be monotone, or pseudomonotone. Each computation of a new analytic center requires at most four Newton iterations, in theory, and in practice one or sometimes two. Linear equalities that may be included in the definition of the set Y are taken explicitly into account.We report numerical experiments on several well—known variational inequality problems as well as on one where the functional results from the solution of large subproblems. The method is robust and competitive with algorithms which use the same information as this one.     

Oxygen assisted laser cutting mechanism—a laminar boundary layer approach including the combustion process

The present study examines the combined effects of chemical reactions taking place between a gas jet and molten metal, the cooling effect of the jet and the evaporation of metal, during a CO₂ laser cutting process. A laminar boundary layer approach was used to develop a theoretical model for the oxygen gas jet laser cutting mechanism. An experiment was carried out to monitor the keyhole formation using a video recorder and detect the light emitted from the entrance and exist surfaces of the workpiece using a fibre-optic probe during the cutting process. The experimental study was extended to employ two different workpiece materials (stainless steel and mild steel) at two thicknesses, and varying oxygen assisting gas pressures. It is found that the theoretical model developed in the present study is valid for a cutting speed of about 30 mm s⁻¹ and all jet velocities up to sonic, since the effect of shock is excluded in the model.     

Embedding optimisation algorithms with Mosel

Algebraic modelling languages allow models to be implemented in such a way that they can easily be understood and modified. They are therefore a working environment commonly used by practitioners in Operations Research. Having once developed models, they need to be integrated inside the company information system. This step often involves embedding a model into a programming language environment: many existing algebraic modelling languages make possible to run parameterised models and subsequently retrieve their results, but without any facility for interacting with the model during the model generation or solution process.In this paper we show how to use the Mosel environment to implement complex algorithms directly in the modelling language.The Office cleaning problem is solved by a branch-and-cut algorithm, implemented entirely in the modelling language (including the definition of the callback function for the solver). Secondly, a cutting stock problem is solved by column generation, also implemented in the modelling language.AMS classification: 90Cxx, 65K05, 68N15     

碳化硼厚板的激光切割工艺及其机制

介绍了碳化硼陶瓷加工中存在的主要问题,将激光技术应用于加工碳化硼陶瓷上,研究出一种新型加工方法,设计出两种有效的激光切割方法并对碳化硼陶瓷进行切割。在实验基础上分析了激光加工参数对加工的影响,采用扫描电镜(SEM)对各种激光切割工艺的断口进行分析和讨论,提出激光加工碳化硼陶瓷的自行断裂机制。实验结果表明,在特定的功率下激光能够用来加工碳化硼陶瓷厚板。对于厚度为5.5 mm碳化硼陶瓷板,Nd∶YAG激光平均功率为130 W时,激光束沿同一位置重复走刀两次即可切断,最高切割速度可达到120 mm/min,可以做到无微裂纹切割。     

激光切割排样系统在硅钢板材加工中的应用

激光切割技术是当前世界上最先进的切割工艺之一，加之排样软件的应用，使板材的利用率得到了很大提高。为了填补扇片零件研究的不足，借鉴传统多边形顶点射线算法的基本原理，提出扇片零件顶点射线算法，解决了任意包角以及任意半径的扇片零件在硅钢板材上的优化排样问题。同时，以该算法为基础，利用VC++6.0开发了一套激光切割排样系统，进行了大量实际排样优化计算。实验结果表明，该算法既满足了实际生产中激光切割的工艺要求，又能够有效地提高硅钢板材的利用率。     

Active control of time-delay in cutting vibration

The system dynamics of turning processes can be described by a delay differential equation. How to improve the stability and suppress the vibration of cutting is of an interesting topic. In this paper, a multiple time-delay controller is developed based on discrete optimal control method for the turning vibrations control. Numerical simulations are carried out to verify the efficiency of the controller. Results indicate the designed controller can suppress the cutting vibration efficiently and improve the stability of the cutting processes. The influence of designed time-delay and sampling time on the control performance is also discussed.     

Parallel bucket sorting on graphics processing units based on convex optimization

We found an interesting relation between convex optimization and sorting problem. We present a parallel algorithm to compute multiple order statistics of the data by minimizing a number of related convex functions. The computed order statistics serve as splitters that group the data into buckets suitable for parallel bitonic sorting. This led us to a parallel bucket sort algorithm, which we implemented for many-core architecture of graphics processing units (GPUs). The proposed sorting method is competitive to the state-of-the-art GPU sorting algorithms and is superior to most of them for long sorting keys.