遗传算法和小波分析在函数优化中的运用

对于一些非线性、多模型、多目标的函数优化问题,用传统优化方法较难求解,而遗传算法却可以方便地得到较好的结果。本文分别用传统寻优算法和遗传算法对Rosenbrock函数作了测试比较,证明了遗传算法优于其他优化算法的全局寻优能力。对遗传算法寻优的标准偏差数据作小波分析,得到一些新颖的结果。     

求解非线性规划问题的改进直觉模糊遗传算法

提出一种改进的直觉模糊遗传算法用于求解带有多维约束的非线性规划问题。以遗传算法在迭代寻优中的个体适应度大小构造相应可行解的隶属度和非隶属度函数,将非线性规划问题直觉模糊化转化为直觉模糊非线性规划问题,通过建立直觉模糊推理系统,自适应地调节遗传算法的交叉率和变异率;并采用一种改进的选择策略,将个体按适应度值大小排序、等量分组,对适应度低的个体组随机选择复制,保留不可行解中可能隐含的有利寻优信息,增强种群个体的多样性和竞争性。仿真实验结果表明,该算法求解非线性规划问题时是可行和有效的。     

基于量子遗传算法的移动机器人的一种路径规划方法

以人工势场法和栅格法为基础,考虑到遗传算法的“收敛速度慢”和“早熟收敛”问题,提出了一种基于量子遗传算法的机器人路径规划方法。该方法采用栅格法进行路径规划,利用人工势场法控制移动机器人,利用量子遗传算法选择最优或次优个体,并且引入双适应度评价函数评价进化个体,为最优或次优个体进入下一代提供了保障。仿真实验表明,该方法的寻优能力及稳定性均优于遗传算法和量子遗传算法,且具有更好的收敛性以及更强的连续空间搜索能力,适于求解复杂优化问题。     

离散非线性规划问题的改进遗传算法

针对实际离散非线性规划问题,分析了离散与连续变量优化问题和求解方法的不同及特性．根据离散变量与遗传算法的特点,将单纯形搜索与算术交叉思想相结合,提出离散单纯形交叉算子以提高遗传算法的局部寻优能力,将种群逐步向离散极值点进行引导,实现算法的快速离散寻优．同时,设计了离散变异算子,使遗传算子真正在离散空同中进行搜索．基于梯度下降思想提出离散修复算子,提高算法对非线性约束的处理能力．实际离散非线性规划问题的应用研究验证了方法的有效性．     

改进的遗传算法求解旅行商问题

提出一种解决旅行商问题的改进遗传算法.在传统遗传算法的基础上,引入贪婪算法进行种群初始化;从遗传进化代数和个体适应函数值两个方面实现遗传参数自适应调节,在加快寻优速度的同时防止寻优陷入局部最优;采用基于贪婪方法的启发式交叉算子优化交叉结果;对交叉前后的种群分别实施精英个体保留策略,保证最优基因结构得以延续.实验结果分析表明,改进的遗传算法可以在种群规模较小的情况下具有更可靠的寻优能力.     

进化蚁群优化理论实现障碍距离分析

借鉴了机器人路径规划问题的解决思路,将遗传算法中交叉算子引入到蚁群优化算法的路径寻优过程,提出了一种基于进化蚁群优化算法的障碍距离分析算法。实验结果表明,该方法不仅能处理复杂形状的障碍,与基于遗传算法的障碍距离计算方法相比,具有较好的路径寻优能力,并且能够很好地降低搜索陷入局部最优的可能性。     

基于遗传算法的半导体制冷器非线性PID设计

针对常规线性PID对具有非线性特征的半导体制冷器温度控制系统存在快速性和超调量难以兼得、抗干扰能力差的问题,提出将非线性PID控制用于半导体制冷器温度控制的策略.通过对线性PID存在问题以及PID各增益参数与偏差信号之间非线性关系的分析,构建了增益参数的非线性函数,针对非线性函数中参数较多问题提出了自适应遗传寻优的求解方法.仿真和实验结果表明,基于此遗传算法寻优的非线性PID控制器相比线性PID控制器,调节时间缩短,超调量减小,抗干扰能力更强.     

一种基于改进遗传算法的单神经元控制方法

为实现在实际的炉群多变量燃烧系统中,对各个燃烧的子系统的控制参数进行优化,提出了一种基于改进适应度函数的遗传单神经元控制算法,该算法克服了采用神经网络方法收敛速度慢、在求解过程中陷入局部极小点等缺点,利用遗传算法的全局寻优特性和神经网络对非线性函数较强的逼近能力,将改进的遗传算法和单神经元控制相结合,实现对一类非线性系统的参数进行优化。模拟实验和真实结果验证了这种方法是可行的。     

应用遗传算法估算溶液热力学模型参数

应用遗传算法估算溶液热力学模型参数,并对标准遗传算法中的变异策略和竞争方式作了适当的改进,得到改进的遗传算法。举DMF(二甲基甲酰胺)+water体系的溶液热力学模型参数的估算为例,并与POWELL法比较。计算结果表明,遗传算法比POWELL法具有更强的寻优能力,而本文所提出的改进的遗传算法比标准遗传算法的寻优速度明显较快,对解决溶液热力学模型这类复杂的非线性函数的参数估算问题,本文所提出的改进的遗传算法是一种较好的寻优算法。     

基于小生境遗传算法的足球机器人路径规划

将基于共享机制的小生境遗传算法应用到足球机器人路径规划中,对比其他算法说明其在求解多峰值函数优化计算问题时具有时间最优性,并能保持解的多样性,具有很高的全局寻优能力和收敛速度。通过仿真试验证明了小生境遗传算法在路径寻优过程中的有效性和正确性。     

机械臂最优运动规划问题的混合求解

提出一种基于GA和SQP求解机械臂最优运动规划问题的混合算法．首先采用B样条函数逼近关节运动轨迹，将最优控制问题转化为有约束的非线性规划问题，然后引入基于种群的GA算法，给出全局最优解的初始估计；最后利用序列二次规划(SQP)得到高精度全局最优解．仿真结果表明该方法优于单纯的GA或SQP方法。     

求解二层规划的混合微粒群算法

对于二层规划问题有许多经典的求解方法,如极点搜索法、分支定界法和罚函数法等。文中给出了基于微粒群算法的二层规划的一种新的求解方法。提出了分别先用单纯形法和内部映射牛顿法的子空间置信域法求解下层规划,然后用微粒群算法求解上层规划的求解方法,这两种混合微粒群算法分别用于求解线性二层规划和非线性二层规划。并结合实例的对比分析,说明了这两种混合微粒群算法求解二层规划的可行性和有效性。     

基于伪谱法的滑翔轨迹多级迭代优化策略

伪谱法可实时求解具有高度非线性动态特性的飞行器最优轨迹;以X-51A相似飞行器模型为研究对象,采用增量法与查表插值建立纵向气动力模型,伪谱法与序列二次规划算法求解滑翔轨迹最优控制问题;提出使用多级迭代优化策略,为序列二次规划算法求解伪谱法参数化得到的大规模非线性规划问题提供初值,弥补序列二次规划算法在求解大规模非线性规划问题过程中,出现的初值敏感、收敛速度减慢等问题。通过与传统方法求解出的状态量与控制量仿真飞行状态进行对比,证明了多级迭代优化策略的有效性和高效性,该策略在实际工程应用中取得了良好效果。     

一种无约束凸规划多平面修正TWSVM

对支持向量机（Twin Support Vector Machine,TWSVM）的优化思想源于基于广义特征值近似支持向量机（Proximal SVM based on Generalized Eigenvalues,GEPSVM）。该算法将传统SVM问题分解为两个凸规划问题,使得训练速度缩减到原来的1/4。对TWSVM做了修正,基于新的优化准则设计了一种特殊TWSVM（GTWSVM）,在此基础上,提出了快速GTWSVM（FGTWSVM）,其将GTWSVM转换为无约束凸规划问题求解。该算法在保证得到与TWSVM相当的分类性能以及较快的计算速度的同时,还减少了输入空间的特征数以及内存占用。对于非线性问题,FGTWSVM可以减少核函数数目。     

Robust portfolio optimization via solution to the Hamilton–Jacobi–Bellman equation

We consider a problem of dynamic stochastic portfolio optimization modelled by a fully non-linear Hamilton–Jacobi–Bellman (HJB) equation. Using the Riccati transformation, the HJB equation is transformed to a simpler quasi-linear partial differential equation. An auxiliary quadratic programming problem is obtained, which involves a vector of expected asset returns and a covariance matrix of the returns as input parameters. Since this problem can be sensitive to the input data, we modify the problem from fixed input parameters to worst-case optimization over convex or discrete uncertainty sets both for asset mean returns and their covariance matrix. Qualitative as well as quantitative properties of the value function are analysed along with providing illustrative numerical examples. We show application to robust portfolio optimization for the German DAX30 Index.     

Optimum dynamic design for beam shapes subjected to a moving concentrated load

We are concerned with an optimum dynamic design of beams subjected to a moving concentrated load with constant speed. The influence of the dynamic behaviour of the beams is considered in a proposed optimum design problem. The optimum shapes of beams are determined by the minimization of two kinds of performance indices. The optimization procedure is performed by non-linear programming on the basis of the exterior penalty function and BFGS methods. Optimization is calculated by the modal coordinates transformation and the numerical integration method     

Kinematic Control of Omni-directional Robots for Time-optimal Movement between Two Configurations

The main goal of this study is to investigate the time-optimal control problem of an omni-directional mobile robot between two configurations. In the proposed method, this problem is formulated and solved as a constrained nonlinear programming (NLP) one. During the optimization process, the count of control steps is fixed initially and the sampling period is treated as a variable to be determined. The goal is to minimize the sampling period such that it is below a specific minimum value, which is set in advance considering the accuracy of discretization. To generate initial feasible solutions of the NLP problem, a systematic approach is also proposed. Since different initial feasible solutions can be generated, the optimization process of the NLP problem can be started from many different points to find the optimal solution. To show the feasibility of the proposed method, simulation and experimental results are included for illustration.     

Probabilistic dual heuristic programming-based adaptive critic

Adaptive critic (AC) methods have common roots as generalisations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, non-linear and non-stationary environments. In this study, a novel probabilistic dual heuristic programming (DHP)-based AC controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) AC method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterised by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the probabilistic critic network is then calculated and shown to be equal to the analytically derived correct value. Full derivation of the Riccati solution for this non-standard stochastic linear quadratic control problem is also provided. Moreover, the performance of the proposed probabilistic controller is demonstrated on linear and non-linear control examples.     

Shape design of elastostatic structures based on local perturbation analysis

This paper describes a non-gradient formulation for solving shape optimal design problems involving structures in plane stress or having an axially symmetric geometry. The minimization of the maximum von Mises stress value at a traction free boundary poses a non-linear optimization problem in which the design variables do not appear explicitly in the formulation. The most commonly used approach is to apply a standard non-linear programming technique. There exists in this field no universally accepted solution method. The major difficulty of shape optimization in connection with FEM is to perform an accurate and efficient sensitivity analysis. The perturbation analysis introduced here takes advantage of the character of the problem. It is based on methods from the theory of notches. The results are applied to an FE-model of the structural component. The iterative method with such a direction of search works efficiently even for a large number of design variables as shown by Schnack (1977b, 1978, 1979, 1980, 1983 and 1985). Using a dynamic programming formulation (see also Schnack and Spörl 1986), the existence of a solution for the shape optimal problem will be discussed. Examples of applications to structural components from mechanical engineering are presented to demonstrate the power of this approach.     

Quasi-static path optimization for industrial robots with dress packs

Problems with robot dress packs are a major reason for on-line adjustments of robot programs and down-time in robot stations. It is therefore of high value if the physical behaviour of the dress packs can be considered with simulation methods already during the off-line programming process for a robot station.This paper presents a method for quasi-static path optimization for an industrial robot with respect to its deformable dress pack. Given an initial collision-free path generated by an automatic path planner, the via point configurations of the path are optimized with respect to the performance aspects of the dress pack. The method is derived from a general framework for parameter optimization of a mechanical system subject to quasi-static motions and deformations. The optimal parameter values are obtained from numerical solutions to a non-linear programming problem in which the static equilibrium equations of the system hold at discrete times. Due to the large-scale nature of this problem, a dress pack is modelled as a discrete Cosserat rod, which is the preferred choice for modeling large spatial deformations of a slender flexible structure with coarse discretization.The method is applied to an industrial robot moving in-between stud welding operations in a stud welding station. The optimized path reduces the stress in the dress pack and keeps the dressed robot from the surrounding geometry with a prescribed safety clearance during the entire robot motion.