基于Pareto最优的PID多目标优化设计

现有的PID优化方法往往难以同时兼顾系统对时域和频域性能的要求,针对这一缺陷,提出了一种PID多目标优化方法：将动态性能指标作为优化目标,频域性能指标作为约束条件,采用基于Pareto最优的多目标优化算法对其求解。该算法采用新的拥挤距离计算方法,引入双重精英机制,进化效率高,得到的Pareto最优解集多样性好,决策者可根据当前工作需求从中选择最终的满意解。仿真结果证明了本文方法的有效性。     

求解多目标流水车间调度Pareto最优解的遗传强化算法

针对多目标流水车间调度Pareto最优问题, 本文建立了以最大完工时间和最大拖延时间为优化目标的多目标流水车间调度问题模型, 并设计了一种基于Q-learning的遗传强化学习算法求解该问题的Pareto最优解. 该算法引入状态变量和动作变量, 通过Q-learning算法获得初始种群, 以提高初始解质量. 在算法进化过程中, 利用Q表指导变异操作, 扩大局部搜索范围. 采用Pareto快速非支配排序以及拥挤度计算提高解的质量以及多样性, 逐步获得Pareto最优解. 通过与遗传算法、NSGA-II算法和Q-learning算法进行对比实验, 验证了改进后的遗传强化算法在求解多目标流水车间调度问题Pareto最优解的有效性.     

改进PSO算法在软/硬件划分中的应用

针对嵌入式系统中的单MPU和单ASIC体系结构问题,提出一种改进粒子群算法,将该算法应用到数字音视频解码器的软/硬件划分中,一次运行可以获得较多Pareto最优解。讨论目标函数、系统约束、粒子比较准则、拥挤距离函数、变异算子和粒子适应度等问题的处理。实验结果表明,该算法改善了传统算法产生未成熟收敛、较少Pareto最优解和Pareto最优解前端分布不均匀的问题,增强算法的自适应性及结果的全局最优性。     

基于差分进化粒子群算法的多目标无功优化

针对电力系统有功网损最小、电压水平最好和电压稳定裕度最大的多目标无功优化问题,提出一种基于差分进化的改进多目标粒子群优化算法。该算法通过对Pareto最优解集的差分进化来增加Pareto最优解的多样性,通过拥挤距离来控制精英集中非支配解的分布,以提高对种群空间的均匀采集;采用擂台赛法则构造多目标Pareto最优解集,较大程度的提高了算法的运行效率;自适应惯性权重和加速度因子的动态变化可增强算法的全局搜索能力。将该算法在IEEE14、IEEE30节点标准测试系统上进行了无功优化仿真,结果表明,基于差分进化的改进多目标粒子群优化算法能够在保持Pareto最优解的多样性的同时具有较好的收敛性能,为多目标无功优化提供了一种新的方法。     

基于多目标粒子群算法的PID控制器设计

随着对控制系统的要求越来越高,进行比例积分微分(Proortion Integration Differentiation,PID)控制器的设计的时候应该同时考虑到系统时域指标和频域指标,常规的PID整定方法往往很难实现.为解决上述问题,采用多目标粒子群算法进行PID控制器参数的设计,算法将系统的超调量、上升时间和稳定时间作为目标函数,频域指标作为约束条件.算法的运算结果为一组Pareto最优解,运行者可以根据当前对系统的要求从中选取合适的解.通过与常规PID整定方法和采用单目标粒子群算法的方法进行比较,证明了改进方法的有效性.     

一种改进的多目标优化算法

为了提高非劣解向Pareto最优面收敛的速度以及解的多样性,设计了一种新的杂交算子并改进了NS-GA-Ⅱ算法。在此算法中,采用中心均值重组算子策略增强算法全局快速搜索能力,以获得最佳的Pareto近似解,同时,改进NSGA-Ⅱ快速非支配排序和拥挤机制将父代与子代的双种群进行截短,确保最优解不会丢失并保证解的多样性。数据实验表明,该算法能在解的收敛性、分布性以及自适应程度上均表现较好。     

基于多粒子群协同的动态多目标优化算法及应用

在现实生活中大多数多目标优化问题都随时间变化,这就要求优化算法在时间约束内快速找到动态变化Pareto最优解或Pareto边界.基于此,提出一种基于多种群协同的动态多目标粒子群改进算法,旨在利用多种群竞争和协作两种模式互相配合,从而达到快速高效求解动态多目标优化问题的目的,多种群竞争模式主要任务是对解空间进行“勘探”搜索,当竞争失效后,自适应切换到协作模式对解空间进行“开采”搜索.通过对多种群协同搜索概率分析,证明多种群相比单种群具有更高的搜索效率,通过对3类动态多目标测试函数仿真,验证了改进算法的有效性;最后将该方法应用于动态系统PID控制器的参数整定上,得到了较优的控制参数,取得满意的控制效果.     

支持向量机算法多目标模型选择

为适应支持向量机(Support Vector Machine,SVM)算法应用过程中的不同性能指标要求,将SVM算法的模型选择问题作为一个多目标优化(Multi-Object Optimization,MOO)问题进行处理。以改进的粒子群优化(Particle Swarm Optimization,PSO)算法对该多目标优化问题进行求解,得到其Pareto解集,在具体应用中根据实际需要从Pareto解集中选择适合的最优解作为支持向量机算法参数,实现支持向量机算法的模型选择。在几个数据集上的仿真实验表明,该方法能够较快地得到Pareto解集,解集中的参数组合能够满足对支持向量机算法速度和泛化能力的不同要求。     

基于黑洞多目标进化算法的永磁直线同步电机优化设计

应用一种改进的黑洞多目标进化算法(MOBH),实现对圆筒型无槽无铁芯直线永磁同步电机(LPMSM)的多目标优化设计.黑洞进化算法在不同Pareto区域的收敛速度、种群多样性、种群收敛性和亚种群获取等方面具有良好的性能.在分析无槽无铁芯圆筒直线电机的电磁解析模型和MOBH算法基础上,建立电机推力、推力体积比、铜损(效率)多目标优化模型,为3个目标对应的Pareto占优解空间提供更加全面和直观的最优解空间.可以根据应用需求和目标函数实际物理值分布范围来综合选取最终最优解,探讨单一目标函数情况下Pareto占优解分布与主要设计变量的关系.最后通过样机实验验证主要设计指标的计算准确性.     

基于群体距离的多目标粒子群优化算法

为实现偏好与群体决策的结合应用,提出基于群体距离的多目标粒子群优化算法。通过调整解与参考点的群体距离引导粒子靠近偏好区域,运用格栅方法和改进的剪枝策略实现解在Pareto边界的均匀分布,求出与群体成员偏好相关的部分Pareto最优集,从而减少计算成本、加快收敛速度。实验结果表明,该算法得到的解更靠近真实Pareto前沿,且对不同个体决策成员都有效。     

Optimal control for stochastic linear quadratic singular neuro Takagi–Sugeno fuzzy system with singular cost using genetic programming

In this paper, optimal control for stochastic linear quadratic singular neuro Takagi–Sugeno (T-S) fuzzy system with singular cost is obtained using genetic programming(GP). To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is computed by solving differential algebraic equation (DAE) using a novel and nontraditional GP approach. The obtained solution in this method is equivalent or very close to the exact solution of the problem. Accuracy of the solution computed by GP approach to the problem is qualitatively better. The solution of this novel method is compared with the traditional Runge–Kutta (RK) method. A numerical example is presented to illustrate the proposed method.     

Global Error Minimization method for solving strongly nonlinear oscillator differential equations

A modified variational approach called Global Error Minimization (GEM) method is developed for obtaining an approximate closed-form analytical solution for nonlinear oscillator differential equations. The proposed method converts the nonlinear differential equation to an equivalent minimization problem. A trial solution is selected with unknown parameters. Next, the GEM method is used to solve the minimization problem and to obtain the unknown parameters. This will yield the approximate analytical solution of the nonlinear ordinary differential equations (ODEs). This approach is simple, accurate and straightforward to use in identifying the solution. To illustrate the effectiveness and convenience of the suggested procedure, a cubic Duffing equation with strong nonlinearity is considered. Comparisons are made between results obtained by the proposed GEM method, the exact solution and results from five recently published methods for addressing Duffing oscillators. The maximal relative error for the frequency obtained by the GEM method compared with the exact solution is 0.0004%, which indicates the remarkable precision of the GEM method.     

Singular optimal control for stochastic linear quadratic singular system using ant colony programming

In this article, singular optimal control for stochastic linear singular system with quadratic performance is obtained using ant colony programming (ACP). To obtain the optimal control, the solution of matrix Riccati differential equation is computed by solving differential algebraic equation using a novel and nontraditional ACP approach. The obtained solution in this method is equivalent or very close to the exact solution of the problem. Accuracy of the solution computed by the ACP approach to the problem is qualitatively better. The solution of this novel method is compared with the traditional Runge Kutta method. An illustrative numerical example is presented for the proposed method.     

Application of the RKDG method for gas dynamics problems

The Runge-Kutta discontinuous Galerkin method (RKDG method) is widely used nowadays. The RKDG method is characterized by a high-order accurate solution. As is well known, for ensuring the monotonic solution by this method, it is necessary to use slope limiters. In particular, it is necessary when the solution contains strong discontinuities. However, the application of limiters can negatively affect the accuracy of the solution. In this paper a way of saving the order of accuracy of the solution and ensuring its monotony is investigated.     

Modified variational iteration method (nonlinear homogeneous initial value problem)

The modified variational iteration method is applied for analytical treatment of nonlinear homogeneous initial value problem. The modified variational iteration method accelerates the convergence of the power series solution and reduces the size of work. A comparison between modified variational iteration method (MVIM) and variational iteration method (VIM) was made. The comparison enhances the use of the modified variational iteration method if we wish to obtain an approximate power series solution that converges faster to the closed form solution. The method is very simple and easy.     

Optimal control for stochastic linear quadratic singular Takagi–Sugeno fuzzy delay system using genetic programming

In this paper, optimal control for stochastic linear singular Takagi–Sugeno (T–S) fuzzy delay system with quadratic performance is obtained using genetic programming (GP). To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is computed by solving differential algebraic equation (DAE) using a novel and nontraditional GP approach. The GP solution is equivalent or very close to the exact solution of the problem. Accuracy of the GP solution to the problem is qualitatively better. The solution of this novel method is compared with the traditional Runge Kutta (RK) method. An illustrative numerical example is presented for the proposed method.     

The application of homotopy perturbation method for MHD flows of UCM fluids above porous stretching sheets

In this study, by means of homotopy perturbation method (HPM) an approximate analytical solution of the magnetohydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid over a porous stretching sheet is obtained. The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve. HPM produces analytical expressions for the solution of nonlinear differential equations. The obtained analytic solution is in the form of an infinite power series. In this work, the analytical solution obtained by using only two terms from HPM solution. The results reveal that the proposed method is very effective and simple and can be applied to other nonlinear problems. Also it is shown that this method coincides with homotopy analysis method (HAM) for the studied problem.     

基于输入输出线性化的连续系统非线性模型预测控制

非线性约束预测控制关键是求得可行性优化解. 输入输出反馈线性化是非线性控制一种常用的方法, 其系统的初始线性输入约束转化成非线性基于状态的约束, 因而无法采用常规的二次规划(QP)求解优化问题. 针对连续状态空间模型系统, 本文提出迭代二次规划方法来寻求非线性优化解. 为了保证算法的收敛性, 系统加入另外一种迭代算法来保证其在整个预测时域上能得到可行解. 仿真控制结果表明了该方法的有效性.     

A combined genetic algorithms-shooting method approach to solving optimal control problems

In this paper, an alternative method for solving optimal control problems is presented. By applying calculus of variations, the optimal control problem can be reduced to solving a two-point boundary value problem. Here, the solution is generated with a combination of two methods genetic algorithms (GA) and the shooting method. An estimate of the optimal solution is first obtained using GA. This solution is in turn used as the initial guess for the shooting method. This combined method is applied to an optimal missile guidance problem. The performances of the combined method and GA are evaluated by simulation and compared. The results clearly show that the proposed combined method is able to locate the optimal solution more efficiently than GA. The results also show that the combined method never fails to correctly determine the optimal solution. Therefore, it proves to be more robust than the shooting method whose convergence is not always guaranteed.     

基于Radau伪谱法的非线性最优控制问题的收敛性

在过去的10年里,伪谱方法(如Legendre伪谱法、Gauss伪谱法、Radau伪谱法)逐步成为求解不同领域中非线性最优控制问题的一种高效、灵活的数值解法.本文从最优控制问题解的存在性、收敛性以及解的可行性3个方面对采用Radau伪谱法求解一般非线性最优控制问题解的收敛性进行研究.证明了原最优控制问题的离散解存在、存在收敛到原最优控制问题解上的离散解和离散形式的收敛解是原最优控制问题的最优解.在此基础上,证明了Radau伪谱法的收敛性.本文结论与现有文献相比,去掉了一些必要条件,更适合一般的非线性时不变系统.