遗传/粒子群混合算法在飞剪机结构优化中的应用

飞剪机结构参数设计需满足若干技术性能要求才能保证剪切质量。飞剪机结构参数优化设计问题要满足多个非线性约束要求,同时需优化多个目标函数,提出遗传算法/粒子群混合算法用于曲柄连杆式飞剪机结构参数优化设计,结合各自算法的优势,在算法运行初期利用遗传算法的全局搜索能力进行优化搜索,在算法运行后期利用粒子群较强的局部搜索能力进行搜索,综合考虑多个目标函数和约束条件,通过实例计算表明,该混合方法可以稳定、有效的获取到满意的优化设计结果。     

基于混合粒子群算法的烧结配料优化

在引入惩罚函数和对目标函数进行适当修改的前提下,充分利用粒子群优化算法的全局搜索能力和约束条件下共轭梯度法的局部搜索能力,设计了烧结配料优化算法．利用惩罚函数方法将约束条件优化问题转化为无约束条件优化问题,然后利用粒子群优化算法进行寻优．当群体最优信息陷入停滞时将目标函数进行适当变化,继续利用共轭梯度法进行寻优．计算结果表明,采用该方法能够在提高混合料中的有用成分、降低有害成分的前提下,更多地降低生产成本．     

约束优化模式搜索法研究进展

实际工程应用中的优化问题通常包含复杂的约束条件,其目标函数可能是非线性、非连续、不可微甚至随机函数;而约束函数可能是线性、非线性、离散变量集,甚至黑盒函数(例如,由程序代码生成的值集合);约束变量也可能是包含连续、离散或分类值的混合变量.这些复杂的情况,使得没有任何导数/梯度信息可供利用,因此无法利用现有的凸优化技术求解.文中研究如何利用模式搜索法对常见的混合变量约束优化模型进行求解.首先对直接搜索法的发展历史进行概述;特别地,给出模式搜索法统一的数学描述和收敛性分析.对约束条件从无约束(一般模式搜索)到线性约束(广义模式搜索GPS)、非线性约束(GPS过滤法)和混合约束(广义混合变量规划GMVP)的推广以及在边界约束条件下,算法搜索方向从有限集向紧致集的扩展(网格自适应直接搜索MADS),进行了全面分析;在此基础上对该领域尚存在的问题及进一步的研究方向进行了总结.     

非线性约束规划的极大熵多目标进化算法

解非线性约束规划的困难在于如何处理问题的约束,从问题的约束条件出发构造了一个新的极大熵函数,利用此函数将原非线性约束规划问题转化成了两个目标的多目标优化问题。通过对搜索操作和参数的合理设计给出了一种新的极大熵多目标进化算法。计算机仿真表明该算法对带约束的非线性优化问题求解是非常有效的。     

飞剪机结构参数优化设计

飞剪机是连续式轧钢机组中重要而复杂的辅助设备，其结构参数设计的好坏直接影响剪切质量。飞剪机结构参数优化设计问题属非线性的多目标优化问题，以模拟退火算法为代表的计算智能方法在求解此类优化问题中体现了一定了优势，本文利用改进的模拟退火算法（Improved Simulated Annealing，ISA）对曲柄连杆式飞剪机结构参数进行优化设计，将整个优化过程分成若干个阶段，根据各个子目标函数优化的状态，采用不同的退火系数和归一化系数，综合考虑多个目标函数和约束条件，通过实例计算表明，该方法可以稳定、有效的获取到满意的优化设计结果。     

基于元胞粒子群算法的数控切削参数优化

针对数控切削参数优化问题的非线性和多约束性质,采用一种元胞粒子群算法（CPSO）进行优化。在基本粒子群算法（PSO）思想的基础上,引入邻居的概念,以搜索解空间的局部信息,并将粒子的信息交流范围扩展到种群外部,从而能搜索到更有希望的解空间;在罚函数机制的基础上,引入标志变量记录粒子是否曾经满足过所有约束条件,根据标志变量进行粒子个体极值与种群全局极值的更新。通过比较CPSO算法与其他算法取得的结果,验证该算法解决数控切削参数优化问题的有效性和优越性。     

最大化个人偏好的多目标优化进化算法

针对多目标优化过程中如何将个人偏好信息融入寻优搜索过程的问题,本文提出一种最大化个人偏好 以确定搜索方向的多目标优化进化算法．该算法首先采用权重和法将多目标问题转换为单目标问题,再利用遗传算 法进行全局搜索,在满足个人偏好约束条件下,每一代进化结束后通过解约束优化问题获得能够使种群综合适应度 具有最大方差的权重组合,从而最大化个人偏好以选择综合最优的个体进行遗传操作．按照不同个人偏好应用于传 动系统进行控制器设计,仿真结果表明该算法能够获得满足个人偏好约束条件下的全局最优解．     

基于人工势场算法和RRT算法的多无人机路径规划

为了解决在城市和山区复杂环境中的多无人机任务分配及路径规划问题,提出了一种基于人工势场算法和RRT融合算法的多无人机协同路径规划方法。基于人工势场算法基础优化斥力函数,加入机间斥力因子,实现了协同避撞。引入RRT算法进行拓展搜索,解决了无人机陷入局部极值点时单一人工势场算法目标不可达的问题。通过三维路径规划仿真实验和算法对比实验验证该方法的可行性,结果表明,融合路径规划算法可以在约束条件下找到全局最优路径。     

多元插值全局优化算法及其应用

本文介绍一种多元插值逼近和动态搜索轨迹相结合的全局优化算法.该算法大大减少了目标函数计算次数,寻优收敛速度快,算法稳定,且可获得全局极小,有效地解决了大规模非线性复杂动态系统的参数优化问题.一个具有8个控制参数的电力系统优化控制问题,采用该算法仅访问目标函数78次,便可求得最优控制器参数。     

一类动态非线性约束优化问题的新解法

动态非线性约束优化是一类复杂的动态优化问题,其求解的困难主要在于如何处理问题的约束及时间（环境）变量。给出了一类定义在离散时间（环境）空间上的动态非线性约束优化问题的新解法,从问题的约束条件出发构造了一个新的动态熵函数,利用此函数将原优化问题转化成了两个目标的动态优化问题。进一步设计了新的杂交算子和带局部搜索的变异算子,提出了一种新的多目标优化求解进化算法。通过对两个动态非线性约束优化问题的计算仿真,表明该算法是有效的。     

桥式吊车系统的伪谱最优控制设计

对于桥式吊车系统的最优控制问题,根据实际的工况要求,性能指标有时不一定是标准的二次形式.同时,在实际的控制问题中,状态和控制输入往往会受到一些边界条件和路径过程中的约束.针对这一问题,本文应用Chebyshev伪谱优化算法来处理,它可以处理状态和控制约束的非线性最优化问题以及一个非标准的目标函数.首先对桥式吊车系统模型进行一系列的坐标变换,将其转变为上三角系统形式的误差模型.然后将桥式吊车最优控制问题转化成具有一系列代数约束的参数优化问题,即非线性规划问题.通过求解离散化后的参数优化问题,得到桥式吊车的最优控制律.本文还给出了Chebyshev伪谱最优解的可行性和一致性分析.最后,在仿真研究中验证该控制器的有效性.     

差分进化与有理谱方法求解奇异摄动问题

讨论一种数值求解奇异摄动问题的高精度有理谱配点法。用sinh变换的有理谱配点法使Chebyshev节点在边界层处加密,只需较少的节点即可达到较高的精度。为了获得sinh变换中边界层的宽度,设计了一个以误差最小为目标函数的无约束的非线性优化问题,并给出了求解该优化问题的差分进化算法。数值实验表明,与其他的智能算法和传统的优化算法相比,差分进化算法在sinh变换中的参数优化方面具有明显的优势。     

Sinc-Galerkin method for solving nonlinear weakly singular two point boundary value problems

A study of Sinc-Galerkin method based on double exponential transformation for solving a class of nonlinear weakly singular two point boundary value problems with non-homogeneous boundary conditions is given. The properties of the Sinc-Galerkin approach are utilized to reduce the computation of nonlinear problem to nonlinear system of equations with unknown coefficients. This method tested on several test examples. We compare our numerical results with several numerical results of existing methods. The demonstrated results confirm that proposed method is considerably efficient, accurate nature and rapidly converge.     

Nonlinear diffusions in topology optimization

Filtering has been a major technique used in homogenization-based methods for topology optimization of structures. It plays a key role in regularizing the basic problem into a well-behaved setting, but it has the drawback of a smoothing effect around the boundary of the material domain. In this paper, a diffusion technique is presented as a variational approach to the regularization of the topology optimization problem. A nonlinear or anisotropic diffusion process not only leads to a suitable problem regularization but also exhibits strong edge-preserving characteristics. Thus, we show that the use of nonlinear diffusions brings the desirable effects of boundary preservation and even enhancement of lower-dimensional features such as flow-like structures. The proposed diffusion techniques have a close relationship with the diffusion methods and the phase-field methods from the fields of materials and digital image processing. The proposed method is described and illustrated with 2D examples of minimum compliance that have been extensively studied in recent literature of topology optimization.     

Constrained mesh optimization on boundary

This paper presents a new mesh optimization approach aiming to improve the mesh quality on the boundary. The existing mesh untangling and smoothing algorithms (Vachal et al. in J Comput Phys 196: 627–644, 2004; Knupp in J Numer Methods Eng 48: 1165–1185, 2002), which have been proved to work well to interior mesh optimization, are enhanced by adding constrains of surface and curve shape functions that approximate the boundary geometry from the finite element mesh. The enhanced constrained optimization guarantees that the boundary nodes to be optimized always move on the approximated boundary. A dual-grid hexahedral meshing method is used to generate sample meshes for testing the proposed mesh optimization approach. As complementary treatments to the mesh optimization, appropriate mesh topology modifications, including buffering element insertion and local mesh refinement, are performed in order to eliminate concave and distorted elements on the boundary. Finally, the optimization results of some examples are given to demonstrate the effectivity of the proposed approach.     

Computational algorithm for solving problem of optimal boundary-control with nonseparated boundary conditions

The problem of optimal boundary-control with nonseparated boundary conditions is considered in the case where the motion of a plant is described by a system of nonlinear ordinary differential equations with a corresponding initial condition, which thereafter is taken as a control action. First, the system of corresponding nonlinear Euler–Lagrange equations is described and in order to solve it, the quasi-linearization method (the first method) is taken. After that, the quasi-linearization method is used with the aim to solve just the optimization problem with boundary control and the nonseparated boundary condition; as a result, the initial nonlinear problem is reduced to the solution of a corresponding linearly quadratic optimization problem (the second method). By the particular example (of oil production) we demonstrate that the second method converges considerably faster and its accuracy is five times higher than the accuracy of the first method. The numerical results reinforce the compliance of the constructed mathematical model with practice.     

Numerical experience with a derivative-free trust-funnel method for nonlinear optimization problems with general nonlinear constraints

A trust-funnel method is proposed for solving nonlinear optimization problems with general nonlinear constraints. It extends the one presented by Gould and Toint [Nonlinear programming without a penalty function or a filter. Math. Prog. 122(1):155–196, 2010], originally proposed for equality-constrained optimization problems only, to problems with both equality and inequality constraints and where simple bounds are also considered. As the original one, our method makes use of neither filter nor penalty functions and considers the objective function and the constraints as independently as possible. To handle the bounds, an active-set approach is employed. We then exploit techniques developed for derivative-free optimization (DFO) to obtain a method that can also be used to solve problems where the derivatives are unavailable or are available at a prohibitive cost. The resulting approach extends the DEFT-FUNNEL algorithm presented by Sampaio and Toint [A derivative-free trust-funnel method for equality-constrained nonlinear optimization. Comput. Optim. Appl. 61(1):25–49, 2015], which implements a derivative-free trust-funnel method for equality-constrained problems. Numerical experiments with the extended algorithm show that our approach compares favourably to other well-known model-based algorithms for DFO.     

Topological shape optimization of geometrically nonlinear structures using level set method

Using the level set method, a topological shape optimization method is developed for geometrically nonlinear structures in total Lagrangian formulation. The structural boundaries are implicitly represented by the level set function, obtainable from “Hamilton-Jacobi type” equation with “up-wind scheme,” embedded into a fixed initial domain. The method minimizes the compliance through the variations of implicit boundary, satisfying an allowable volume requirement. The required velocity field to solve the Hamilton-Jacobi equation is determined by the descent direction of Lagrangian derived from an optimality condition. Since the homogeneous material property and implicit boundary are utilized, the convergence difficulty is significantly relieved.     

Numerical solution of potential flow equations with a predictor-corrector finite difference method

We develop a numerical solution algorithm of the nonlinear potential flow equations with the nonlinear free surface boundary condition.A finite difference method with a predictor-corrector method is applied to solve the nonlinear potential flow equations in a two-dimensional (2D) tank.The irregular tank is mapped onto a fixed square domain with rectangular cells through a proper mapping function.A staggered mesh system is adopted in a 2D tank to capture the wave elevation of the transient fluid.The finite difference method with a predictor-corrector scheme is applied to discretize the nonlinear dynamic boundary condition and nonlinear kinematic boundary condition.We present the numerical results of wave elevations from small to large amplitude waves with free oscillation motion,and the numerical solutions of wave elevation with horizontal excited motion.The beating period and the nonlinear phenomenon are very clear.The numerical solutions agree well with the analytical solutions and previously published results.