Duality of regularizations and hullfunctions for mathematical programming problems

For the study of mathematical programming problems and solution methods the duality theory forms a powerful tool. There are also some concepts ofregularization andstabilization of a given problem for a better behavior in practical solution procedures. The aim of this paper is the investigation of duality aspects of such regularizations and the forming ofhullfunctions on the other hand. Applications for handling of so-calledill-posed problems (Eremin) using some parametrizations of the original problem will emphasize the importance for practical numerical methods, especially. This results will inspire some applications to solution methods for parametric and multicriteria optimization.     

A Class of Mathematical Programs with Equilibrium Constraints: A Smooth Algorithm and Applications to Contact Problems

We discuss a special mathematical programming problem with equilibrium constraints (MPEC), that arises in material and shape optimization problems involving the contact of a rod or a plate with a rigid obstacle. This MPEC can be reduced to a nonlinear programming problem with independent variables and some dependent variables implicity defined by the solution of a mixed linear complementarity problem (MLCP). A projected-gradient algorithm including a complementarity method is proposed to solve this optimization problem. Several numerical examples are reported to illustrate the efficiency of this methodology in practice.     

一类非凸集值优化问题的对偶定理

对偶理论是数学规划研究领域的重点问题之一,通对偶模型可以实现一个最小化问题与一个最大化问题之间的相互转化.本文的目的是建立一类非凸约束集值优化问题的对偶理论,在逼近多值函数定义的不变凸性假设下,研究了原集值优化问题的Mond-Weir型和Wolfe型对偶问题.利用分析的方法,本文得到了两种对偶模型下关于弱极小元的弱对偶定理,强对偶定理和逆对偶定理.这些对偶定理揭示了原问题与所讨论的Mond-Weir型和Wolfe型对偶问题之间存在着明确的对偶关系.本文所得结果丰富和深化了集值优化理论及其应用的研究内容.     

在线连续测量轮轨接触点的神经网络方法

尽管轮轨力测量的测力轮对技术已相对成熟,轮轨作用点位置的测量却一直很困难。作用点位置的在线连续测量对脱轨机理的研究、机车车辆性能的研究有十分重要的意义。在常规测力轮对的基础上,增加一个电桥感应作用点位置的变化。采用神经网络拟合轮轨作用力位置变化与电桥输出间复杂的非线性映射关系,用不同作用点位置下各种横、垂向力的组合来训练神经网络,从而达到由电桥输出值得到作用点位置的目的。实验结果表明,网络不仅训练精度好,而且预测能力也令人满意。     

Lagrangian Coordination and Analytical Target Cascading: Solving ATC-Decomposed Problems with Lagrangian Duality

Lagrangian duality is a powerful tool for dealing with large mathematical programs which require decomposition. We consider a large-scale convex nonlinear program that is decomposed according to the scheme of analytical target cascading and propose a Lagrangian duality-based coordination in which solutions of resulting subproblems converge to a solution of the original problem. We present a subgradient algorithm to achieve said solution, demonstrate with an example, and conclude with an extension to multiple level problems with multiple subsystems on each level.     

Optimal Aeroacoustic Shape Design Using the Surrogate Management Framework

Shape optimization is applied to time-dependent trailing-edge flow in order to minimize aerodynamic noise. Optimization is performed using the surrogate management framework (SMF), a non-gradient based pattern search method chosen for its efficiency and rigorous convergence properties. Using SMF, design space exploration is performed not with the expensive actual function but with an inexpensive surrogate function. The use of a polling step in the SMF guarantees that the algorithm generates a convergent subsequence of mesh points in the parameter space. Each term of this subsequence is a weak local minimizer of the cost function on the mesh in a sense to be made precise later. We will discuss necessary optimality conditions for the design problem that are satisfied by the limit of this subsequence. Results are presented for an unsteady laminar flow past an acoustically compact airfoil. Constraints on lift and drag are handled within SMF by applying the filter pattern search method of Audet and Dennis, within which a penalty function is used to form and optimize a surrogate function. Optimal shapes that minimize noise have been identified for the trailing-edge problem in constrained and unconstrained cases. Results show a significant reduction (as much as 80%) in acoustic power with reasonable computational cost using several shape parameters. Physical mechanisms for noise reduction are discussed.     

A multiple surrogate assisted evolutionary algorithm for optimization involving iterative solvers

In many real-world optimization problems, the underlying objective and constraint function(s) are evaluated using computationally expensive iterative simulations such as the solvers for computational electro-magnetics, computational fluid dynamics, the finite element method, etc. The default practice is to run such simulations until convergence using termination criteria, such as maximum number of iterations, residual error thresholds or limits on computational time, to estimate the performance of a given design. This information is used to build computationally cheap approximations/surrogates which are subsequently used during the course of optimization in lieu of the actual simulations. However, it is possible to exploit information on pre-converged solutions if one has the control to abort simulations at various stages of convergence. This would mean access to various performance estimates in lower fidelities. Surrogate assisted optimization methods have rarely been used to deal with such classes of problem, where estimates at various levels of fidelity are available. In this article, a multiple surrogate assisted optimization approach is presented, where solutions are evaluated at various levels of fidelity during the course of the search. For any solution under consideration, the choice to evaluate it at an appropriate fidelity level is derived from neighbourhood information, i.e. rank correlations between performance at different fidelity levels and the highest fidelity level of the neighbouring solutions. Moreover, multiple types of surrogates are used to gain a competitive edge. The performance of the approach is illustrated using a simple 1D unconstrained analytical test function. Thereafter, the performance is further assessed using three 10D and three 20D test problems, and finally a practical design problem involving drag minimization of an unmanned underwater vehicle. The numerical experiments clearly demonstrate the benefits of the proposed approach for such classes of problem.     

Surrogate modelling and optimization using shape-preserving response prediction: A review

Computer simulation models are ubiquitous in modern engineering design. In many cases, they are the only way to evaluate a given design with sufficient fidelity. Unfortunately, an added computational expense is associated with higher fidelity models. Moreover, the systems being considered are often highly nonlinear and may feature a large number of designable parameters. Therefore, it may be impractical to solve the design problem with conventional optimization algorithms. A promising approach to alleviate these difficulties is surrogate-based optimization (SBO). Among proven SBO techniques, the methods utilizing surrogates constructed from corrected physics-based low-fidelity models are, in many cases, the most efficient. This article reviews a particular technique of this type, namely, shape-preserving response prediction (SPRP), which works on the level of the model responses to correct the underlying low-fidelity models. The formulation and limitations of SPRP are discussed. Applications to several engineering design problems are provided.     

基于拐点和区域划分的高维多目标进化算法

针对高维多目标优化问题中收敛性和分布性难以同时保持的问题,提出一种基于拐点和区域划分的高维多目标进化算法KnSP.算法选取拐点作为第1次区域划分的中心点,自适应生成邻域;然后采用角度分层法进行二次区域划分,将点到超平面的距离作为个体选择的准则;最后通过候选解与其余个体的角度来增加或删除个体以保证种群规模.实验结果表明,...     

基于TRIZ和类比设计的服务接触点优化应用研究

目的通过改善服务接触点构成要素之间的作用关系来优化服务接触点,提升用户体验。方法在分析服务接触内涵和服务要素的基础上,对服务接触点构成要素及其作用关系进行研究;基于类比设计,将服务接触点构成要素与TRIZ中物质—场模型进行类比分析,构建服务接触点模型;运用TRIZ中标准解求解方法对服务接触点模型进行优化。结果由服务接触点三要素(服务提供者、媒介和顾客)构建服务接触点模型,并通过标准解的应用改善了此模型,实现了对服务接触点的优化。结论通过构建服务接触点模型,结合TRIZ中物质—场分析工具和标准解的应用,为服务接触点的优化设计提供一种新的方法。以丰巢智能快递柜服务系统中的服务接触点优化设计为例,验证该方法的可行性及有效性。     

Contact Analysis for Solids Based on Linearly Conforming Radial Point Interpolation Method

To simulate the contact nonlinearity in 2D solid problems, a contact analysis approach is formulated using incremental form of the subdomain parametric variational principle (SPVP). The formulation is based on a linearly conforming radial point interpolation method (LC-RPIM) using nodal integration technique. Contact interface equations are also presented using a modified Coulomb frictional contact model and discretized by contact point-pairs. In the present approach, the global discretized system equations are transformed into a standard linear complementarity problem (LCP) that can be solved readily using the Lemke method. The present approach can simulate various contact behaviors including bonding/debonding, contacting/departing, and sticking/slipping. An intensive numerical study is performed to validate the proposed method via comparison with the ABAQUS^® and to investigate the effects of the various parameters used in computations. These parameters include normal and tangential adhesions, frictional coefficient, nodal density, the dimension of local nodal support domain, nodal irregularity, shape parameters used in the radial basis function and the external load. The numerical results have demonstrated that the present approach is accurate and stable for contact analysis of 2D solids.     

线性特征值问题的高精度矩阵摄动法

线性特征值问题摄动重分析的基本理论已趋于成熟。本文进一步探讨了提高摄动计算精度的策略,提出了一种分步摄动一摄动迭代算法。通过实例计算表明,该算法可在结构具有大修改量的情况下有效地实现广义特征值问题的高精度重分析。     

An interior‐point algorithm for elastoplasticity

The problem of small‐deformation, rate‐independent elastoplasticity is treated using convex programming theory and algorithms. A finite‐step variational formulation is first derived after which the relevant potential is discretized in space and subsequently viewed as the Lagrangian associated with a convex mathematical program. Next, an algorithm, based on the classical primal–dual interior point method, is developed. Several key modifications to the conventional implementation of this algorithm are made to fully exploit the nature of the common elastoplastic boundary value problem. The resulting method is compared to state‐of‐the‐art elastoplastic procedures for which both similarities and differences are found. Finally, a number of examples are solved, demonstrating the capabilities of the algorithm when applied to standard perfect plasticity, hardening multisurface plasticity, and problems involving softening. Copyright © 2006 John Wiley & Sons, Ltd.     

基于平衡原理的液滴接触角估计方法

基于液滴表面力的平衡原理推导了一种新的液滴表面曲线方程,通过提取图像上的样本点,以牛顿-拉夫逊法拟合曲线方程为基础来获取接触角的估计值,从而得到了一种基于平衡原理的液滴接触角估计方法。通过JGW-360A接触角测定仪采集实测图像,针对水滴与不同材料的接触场景进行了实验,采用Canny法获取液滴边缘曲线并提取采样点,计算出液滴表面接触角。将该算法与传统的影像分析法进行了比较,在大角度下与传统影像类方法相比估计值差别约为0.2°~0.3°,实验结果验证了算法的有效性。     

Non-smooth Nonlinear Equations Methods for Solving 3D Elastoplastic Frictional Contact Problems

Based on the non-smooth nonlinear equations method for modeling three-dimensional elastic frictional contact problems (hereafter called NNEM), the extension to elastoplastic case in which the material nonlinearity is also involved is presented in this paper. Two approaches which combine two methods for solving elastoplastic problem with NNEM are proposed. A Numerical example is given to demonstrate the validation of the approaches.     

Electro-Thermal Transport in Quantum Point Contact Nanodevice

The Peltier effect was discovered several decades ago. The Peltier effect has been combined with modern low-dimensional quantum system materials, e.g., the quantum point contact (QPC), to open up a new research field. The Peltier coefficient and thermal transport in a QPC, under the influence of photon-assisted and different temperatures are investigated. Numerical calculations of the Peltier coefficient have been performed at different applied voltages, amplitudes, and temperatures. The obtained results are consistent with experimental results in the literature.     

基于遗传算法和梯度算法的桁架结构动力学形状优化

本文提出了一种基于遗传算法和梯度算法的桁架动力学形状优化方法 ,该方法综合了梯度算法的快速收敛与遗传算法的全局搜索能力。算例表明了本文方法的有效性和工程适应性。     

An Evolutionary Lagrange Method For Mixed-Integer Constrained Optimization Problems

This study proposes a method for solving mixed-integer constrained optimization problems using an evolutionary Lagrange method. In this approach, an augmented Lagrange function is used to transform the mixed-integer constrained optimization problem into an unconstrained min—max problem with decision-variable minimization and Lagrange-multiplier maximization. The mixed-integer hybrid differential evolution (MIHDE) is introduced into the evolutionary min—max algorithm to accomplish the implementation of the evolutionary Lagrange method. MIHDE provides a mixed coding to denote genetic representations of teal and integer variables, and a rounding operation is used to guide the genetic evolution of integer variables. To fulfill global convergence, self-adaptation for penalty parameters is involved in the evolutionary min—max algorithm so that small penalty parameters can be used, not affecting the final search results. Some numerical experiments are tested to evacuate the performance of the proposed method. Numerical experiments demonstrate that the proposed method converges to better solutions than the conventional penalty function method     

AMBO: All Members-Based Optimizer for Solving Optimization Problems

There are many optimization problems in different branches of science that should be solved using an appropriate methodology. Population-based optimization algorithms are one of the most efficient approaches to solve this type of problems. In this paper, a new optimization algorithm called All Members-Based Optimizer (AMBO) is introduced to solve various optimization problems. The main idea in designing the proposed AMBO algorithm is to use more information from the population members of the algorithm instead of just a few specific members (such as best member and worst member) to update the population matrix. Therefore, in AMBO, any member of the population can play a role in updating the population matrix. The theory of AMBO is described and then mathematically modeled for implementation on optimization problems. The performance of the proposed algorithm is evaluated on a set of twenty-three standard objective functions, which belong to three different categories: unimodal, high-dimensional multimodal, and fixed-dimensional multimodal functions. In order to analyze and compare the optimization results for the mentioned objective functions obtained by AMBO, eight other well-known algorithms have been also implemented. The optimization results demonstrate the ability of AMBO to solve various optimization problems. Also, comparison and analysis of the results show that AMBO is superior and more competitive than the other mentioned algorithms in providing suitable solution.     

基于毫米波雷达获取料堆DEM的插值方法研究

针对现有的全自动堆取料机技术的发展过程中存在料堆高程模型获取困难、测量装置环境适应性差、成本高和模型精度低的问题,提出利用77GHz毫米波雷达、差分北斗和角度编码器的集成技术获取大型料堆表面的离散点云数据。推导出多传感数据融合获取离散点云数据的公式,并提出采用量子化鸽群优化Kriging插值算法获取料堆的数字高程模型(DEM),采用交叉验证的方式对比分析了优选参数后改进的普通Kriging、普通Kriging、反距离加权、基于三角剖分的线性和自然邻域插值算法,改进后的Kriging插值算法均方根误差低于0.37m,均方误差低于0.14m,均方根误差相比普通Kriging插值算法降低了39.9%。在现场的测试过程中,该方法可不受天气和粉尘的影响得到料堆的DEM,能够满足堆取料机全自动项目对精度的需求。