A pegging algorithm for separable continuous nonlinear knapsack problems with box constraints

This article proposes an efficient pegging algorithm for solving separable continuous nonlinear knapsack problems with box constraints. A well-known pegging algorithm for solving this problem is the Bitran–Hax algorithm, a preferred choice for large-scale problems. However, at each iteration, it must calculate an optimal dual variable and update all free primal variables, which is time consuming. The proposed algorithm checks the box constraints implicitly using the bounds on the Lagrange multiplier without explicitly calculating primal variables at each iteration as well as updating the dual solution in a more efficient manner. Results of computational experiments have shown that the proposed algorithm consistently outperforms the Bitran–Hax in all baseline testing and two real-time application models. The proposed algorithm shows significant potential for many other mathematical models in real-world applications with straightforward extensions.     

基于线性互补原理的干摩擦振动系统非光滑数值算法

基于集值库仑定律的互补特性和Newmark速度求解格式,将干摩擦振动问题转化为线性互补问题,提出了Newmark-LCP非光滑数值算法.算法将干摩擦系统的不同运动模式统一进行LCP化处理,用互补条件代替等式条件来监测运动事件,解决了粘着区的数值不稳定问题,避免了当摩擦单元数目增加时的枚举计算量增加和算法逻辑结构复杂化问题.算例仿真表明,Newmark-LCP算法能够准确地描述干摩擦动力特性,与非光滑时间步进法相比,所给出的算法计算效率相对较高.     

Truss optimization on shape and sizing with frequency constraints based on genetic algorithm

Truss optimization on shape and sizing with frequency constraints are highly nonlinear dynamic optimization problems. Coupling of two different types of design variables, nodal coordinates and cross-sectional areas, often lead to divergence while multiple frequency constraints often cause difficult dynamic sensitivity analysis. So optimal criteria method and mathematical programming, which need complex dynamic sensitivity and are easily trapped into the local optima, are difficult to solve the problems. To solve the truss shape and sizing optimization simply and effectively, a Niche Hybrid Genetic Algorithm (NHGA) is proposed. The objective of NHGA is to enhance the exploitation capacities while preventing the premature convergence simultaneously based on the new hybrid architecture. Niche techniques and adaptive parameter adjustment are used to maintain population diversity for preventing the premature convergence while simplex search is used to enhance the local search capacities of GAs. The proposed algorithm effectively alleviates premature convergence and improves weak exploitation capacities of GAs. Several typical truss optimization examples are employed to demonstrate the validity, availability and reliability of NHGA for solving shape and sizing optimization of trusses with multiple frequency constraints.     

Mathematical programs with complementarity constraints in traffic and telecommunications networks

Given a suitably parametrized family of equilibrium models and a higher level criterion by which to measure an equilibrium state, mathematical programs with equilibrium constraints (MPECs) provide a framework for improving or optimizing the equilibrium state. An example is toll design in traffic networks, which attempts to reduce total travel time by choosing which arcs to toll and what toll levels to impose. Here, a Wardrop equilibrium describes the traffic response to each toll design. Communication networks also have a deep literature on equilibrium flows that suggest some MPECs. We focus on mathematical programs with complementarity constraints (MPCCs), a subclass of MPECs for which the lower level equilibrium system can be formulated as a complementarity problem and therefore, importantly, as a nonlinear program (NLP). Although MPECs and MPCCs are typically non-convex, which is a consequence of the upper level objective clashing with the users' objectives in the lower level equilibrium program, the last decade of research has paved the way for finding local solutions of MPCCs via standard NLP techniques.     

Wind farm layout design optimization through multi-scenario decomposition with complementarity constraints

This article presents a multi-scenario decomposition with complementarity constraints approach to wind farm layout design to maximize wind energy production under region boundary and inter-turbine distance constraints. A complementarity formulation technique is introduced such that the wind farm layout design can be described with a continuously differentiable optimization model, and a multi-scenario decomposition approach is proposed to ensure efficient solution with local optimality. To combine global exploration and local optimization, a hybrid solution algorithm is presented, which combines the multi-scenario approach with a bi-objective genetic algorithm that maximizes energy production and minimizes constraint violations simultaneously. A numerical case study demonstrates the effectiveness of the proposed approach.     

Solving and visualizing nonlinear parametric constraints in control based on quantifier elimination

We present a new method with a software tool for parametric robust control synthesis by symbolic-numeric computation. The method is a parameter space approach and it is especially effective for analysis and design of fixed-structure controllers of rational type, which encompass PI and PID controllers. The real quantifier elimination (QE), which is one of the recent progresses in the symbolic computation, plays a key role in our development. The QE-based approach can uniformly deal with a lot of important design specifications for robust control such as frequency restricted H _∞ norm constraints, stability (gain/phase) margin and stability radius specifications, and pole location requirement by reducing such specifications to a particular type of formulae called a “sign definite condition (SDC)”. This is also useful for improving the efficiency of QE computations since we can utilize an efficient QE algorithm specialized to the SDC using the Sturm-Habicht sequence. We have developed a MATLAB toolbox for robust parametric control based on a parameter space approach accomplished by QE. The QE-based parameter space approach and numerical simulation of performances for specific controller parameter values taken from a controller parameter space are integrated conveniently in our toolbox with the assistance of a graphical user interface (GUI). With our toolbox the feasible regions of controller parameters are visualized in a parameter space for the controllers with three or two parameters. This enables control engineers to achieve multi-objective robust controller synthesis smoothly. We also discuss how to merge the numerical computation and the symbolic operation to make our new design methods more efficient in practical control design.     

一种基于PSO算法的非线性模型预测控制方法

将微粒群优化(PSO)算法用于输入受限非线性系统,提出了一种基于PSO的非线性模型预测控制算法.该算法采用双模控制策略,将保证预测控制稳定性的终端等式约束转化为终端不等式约束,推导出使系统稳定的不变可行集.在不变集外,利用PSO算法优化求解预测控制律,使系统状态进入不变集;在不变集内,利用线性状态反馈使系统状态渐近稳定.同时对算法的稳定性进行了分析.仿真结果证明了该算法的可行性和有效性.     

基于关联监测点数据的非线性变形预测模型

基坑边坡变形具有非平稳性、非线性等特点,且现有的变形预测模型常用单个监测点或整体监测点的数据进行预测,忽略了不同监测点之间的关联性.以重庆某深基坑边坡为例,分别研究基于单个监测点数据和基于关联监测点数据的经验模态分解-粒子群优化算法-BP神经网络(EMD-PSO-BPNN)模型、PSO-BPNN模型、BP神经网络模型的...     

高斯型点扩展函数估计的最近邻算法

本文针对计算光学切片中的最近邻算法提出了一种改进算法.通过小波变换计算出高斯点扩展函数的方差值,再根据相邻图像成像及高斯函数特性,得出所需的高斯型层间点扩展函数.同时,文章还给出了两种高斯型层间点扩展函数方差的获得方式及获得过程,对最近邻算法中的加权因子的取值范围做出了讨论,对传统的最近邻算法做出了改进.实验表明,本算法能够更有效地复原符合最近邻要求的切片图像.在点扩展函数未知的情况下,复原效果要优于传统方法.     

An algorithm for multipoint constraints in finite element analysis

A method of introducing general constraint equations into finite element matrix equations is described. The characteristics of the method are that it requires no reordering or condensation of the equations, no large matrix operations, and no increase in the number of unknowns. The method is suitable for application in minicomputer implementations of finite element analysis unless a large number of constraints is to be applied.     

Improved genetic algorithm based on particle swarm optimization-inspired reference point placement

This article investigates the use of optimal reference point placement to improve performance of non-dominated sorting genetic algorithm (NSGA). Placement of reference points for many-objective optimization is inspired by wheel and Von Neumann topologies of Particle Swarm Optimization (PSO). Results obtained show that the pattern of reference point placement determines performance efficiency of NSGA. The better-performing wheel topology (called wheel reference point genetic algorithm (wRPGA), is compared to three other many-objective evolutionary algorithms: knee-driven evolutionary algorithm (KnEA), non-dominated sorting genetic algorithm III (NSGAIII) and multi-objective evolutionary algorithm based on dominance and decomposition (MOEAD/D). The selected many-objective benchmark problems are Walking Fish Group 2 (WFG2) and Deb-Thiele-Laumanns-Zitzler 2 (DTLZ2). It is also tested on a 3-objective cost function for a hypothetical model of a stand-alone microgrid. Through the simulations, the wheel configuration performed 88.9% better than the Von Neumann configuration. The wheel topology also achieved better performance with respect to inverted generational distance (IGD) compared to KnEA, NSGAIII and MOEAD/D for 7 out of 15 IEEE Congress on Evolutionary Computation (CEC) 2017 benchmark problems. wRPGA gave a good approximation of the Pareto front for the 3-objective model representing the hypothetical microgrid.     

BSCTC:传感网的基于切向约束的B样条等值线查询算法

针对目前传感网的等值线查询方法需要返回较多代表节点,代表节点选取的计算复杂度高且等值线还原结果不理想的情况,提出了一种基于切向约束(TC)的B条等值线(BSC)查询算法,简称BSCTC.该算法基于切向约束的2次B样条插值原理,首先选出等值线中的代表节点并传输代表节点信息给Sink,然后在Sink端对返回的代表节点进行分段还原,形成等值线.理论分析表明:BSCTC算法返回的代表节点期望数只是网络等值线节点数的39％,代表节点选取的计算复杂度为O(n)(n为等值线节点个数).实验结果表明:与目前最好的DABC算法相比,BSCTC算法返回的代表节点数减少了53％,而且可形成更精确的等值线.     

非线性动态WPLS航煤干点软测量

针对炼油工业过程存在的多变量、非线性和数据动态性问题,提出一种自回归移动平均模型与径向基函数-加权偏最小二乘相结合的非线性动态建模方法。首先建立基于径向基函数-加权偏最小二乘方法的软测量模型,然后利用自回归移动平均模型对数据进行时序分析校正,将动态误差信息加入到模型中去,实现模型的动态装换。将该方法应用到加氢裂化航煤干点的软测量建模中,从而获得比径向基函数-加权偏最小二乘算法更高的预测精度。     

An efficient algorithm for analysis of nonlinear heat transfer with phase changes

A new, simple and effective finite element procedure is presented for the practical solution of heat transfer conditions with phase changes. In this method, a fixed finite element mesh is employed, and a relatively coarse finite element mesh and large time step can be used in the incremental solution. The results of various numerical studies using the algorithm are presented that demonstrate the effectiveness of the procedure.     

A contact analysis approach based on linear complementarity formulation using smoothed finite element methods

Based on the subdomain parametric variational principle (SPVP), a contact analysis approach is formulated in the incremental form for 2D solid mechanics problems discretized using only triangular elements. The present approach is implemented for the newly developed node-based smoothed finite element method (NS-FEM), the edge-based smoothed finite element method (ES-FEM) as well as standard FEM models. In the approach, the contact interface equations are discretized by contact point-pairs using a modified Coulomb frictional contact model. For strictly imposing the contact constraints, the global discretized system equations are transformed into a standard linear complementarity problem (LCP), which can be readily solved using the Lemke method. This approach can simulate different contact behaviors including bonding/debonding, contacting/departing, and sticking/slipping. An intensive numerical study is conducted to investigate the effects of various parameters and validate the proposed method. The numerical results have demonstrated the validity and efficiency of the present contact analysis approach as well as the good performance of the ES-FEM method, which provides solutions of about 10 times better accuracy and higher convergence rate than the FEM and NS-FEM methods. The results also indicate that the NS-FEM provides upper-bound solutions in energy norm, relative to the fact that FEM provides lower-bound solutions.     

Interferometric data analysis based on Markov nonlinear filtering methodology

For data processing in conventional phase shifting interferometry, Fourier transform, and least-squares-fitting techniques, a whole interferometric data series is required. We propose a new interferometric data processing methodology based on a recurrent nonlinear procedure. The signal value is predicted from the previous step to the next step, and the prediction error is used for nonlinear correction of an a priori estimate of the parameters phase, visibility, or frequency of interference fringes. Such a recurrent procedure is correct on the condition that the noise component be a Markov stochastic process realization. The accuracy and stability of the recurrent Markov nonlinear filtering algorithm were verified by computer simulations. It was discovered that the main advantages of the proposed methodology are dynamic data processing, phase error minimization, and high noise immunity against the influence of non-Gaussian noise correlated with the signal and the automatic solution of the phase unwrapping problem.     

几何约束下曲面场景的立体匹配迭代算法

使用对极约束和同形映射两种几何约束,通过采用面积检测、一致性约束误差检测、概率筛选规则和对称优化等策略,成功地实现了曲面场景图像的特征点匹配.该方法未使用任何与灰度相关的信息和与场景相关的约束,极大地提高了方法的实用性和鲁棒性.整个匹配过程快速有效,并在不同的弱标定关系已知的真实图像数据上成功地得到实现.     

独立分量分析的图像融合算法

独立分量分析可实现图像的稀疏编码并具有能很好地捕捉图像重要边缘信息的特性.本文提出一种基于独立分量分析的图像融合算法,结合支持向量机对多聚焦图像的清晰域、模糊域进行判断以及在ICA域中进行图像分割以提取图像的主要边缘特征信息来实现特征级的多聚焦图像的融合.实验结果表明,本文提出的融合算法是有效的.     

An efficient algorithm for calculating the cutter location point based on projection method

Aiming at improving the efficiency of calculating the cutter location point with toroid cutter based on the projection method in NC machining for surface, a new algorithm is proposed to calculate the cutter location point directly by torus surface approximating the surface to be machined. According to the geometric information of the points on the surface, the geometrical conditions of the two tangential tori are figured out, and then the contact point is obtained by solving multivariate non-linear equations. Parameters of the tangent point on the surface to be machined are calculated in the next step. Finally, the cutter location point is calculated by a small adjustment. The proposed algorithm is applied to calculate the cutter location point with toroid cutter in surface machining and compared with the existing algorithm. The results show that the computing time of the proposed algorithm in this paper saved about 63–78%.     

Modelling and scheduling analysis of multi-cluster tools with residency constraints based on time constraint sets

This paper is dedicated to the scheduling problem of multi-cluster tools with process module residency constraints and multiple wafer product types. The problem is formulated as a non-linear programming model based on a set of time constraint sets. An effective algorithm called the time constraint sets based (TCSB) algorithm is presented as a new method to schedule the transport modules to minimise the makespan of a number of wafers. In approach, time constraint sets are maintained for all the resources and necessary operations to exploit the remaining production capacities during the scheduling process. To validate the proposed algorithm on a broader basis, a series of simulation experiments are designed to compare our TCSB algorithm with the benchmark with regard to cluster factor, configuration flexibilities and the variation of the processing times and residency constraint times. The results indicate that the proposed TCSB algorithm gives optimal or near optimal scheduling solutions in most cases.