基于改进元胞多目标遗传算法的机床主轴优化

为了进一步提高元胞遗传算法在求解多目标优化问题时的收敛性和分布性。在多目标元胞遗传算法的基础上,引入了三维空间元胞,提出了三维元胞多目标遗传算法。采用多目标基准测试函数对该算法进行了测试,并将其与目前比较流行的几种多目标遗传算法进行对比。结果表明,此种算法在收敛性和分布性上取得了更好的效果。采用以上这几种算法分别对机床主轴多目标优化问题进行了求解,相比其他几种算法,改进的多目标元胞遗传算法得到了更优的结果,说明了改进的算法在求解此问题时行之有效。     

一个多目标优化演化算法的收敛性分析框架*

由于演化算法求解多目标优化问题所得结果是一个优化解集——Pareto最优集,而现有的演化算法收敛性分析只适合针对单目标优化问题的单个。用有限马尔科夫链给出了演化算法求解多目标优化问题的收敛性分析框架,并给出了一个分析实例。     

遗传算法在多目标优化应用中的对比研究

多目标优化应用研究在过程工程领域越来越受重视。本文首先给出了多目标优化问题的一般形式，指出多目标问题求解任务：引导搜索向整个的Pareto优化范围；Pareto优化前沿上保持解集的多样性。在简要论述遗传算法求解多目标技术的基础上，对应用了遗传算法求解多目标的两种方法进行了对比研究，并给出了线性加权遗传算法和一种多目标遗传算法的计算框图。指出线性加权法求解Pareto最优解时不能不能很好地处理非凸区域、均匀分布的权重值不能生成均匀分布的Pareto前沿等局限性，以及多目标遗传算法生成种群多样性及Pareto最优解均匀分布的优点，并用实例进行了验证说明。     

基于分布估计算法的多目标优化

论述解决多目标优化问题的若干解法,为了提高多目标优化算法的收敛性和求解精度,提出了一种分布估计的多目标优化算法。给出了3个典型的测试函数的pateto解集。通过4个测试函数测试,并与非劣排序多目标遗传算法(NSGA-Ⅱ)和规则模型分布估计算法(RM-MEDA)两个算法进行了比较。测试结果表明,该算法具有良好的收敛性和分布性,并且效果稳定。     

一种改进的最优保存遗传算法

在已有的研究工作基础上，给出了一种改进的最优保存遗传算法，研究了算法的全局收敛性和收敛速度，并给出了收敛性证明．数值实验表明．该算法能够有效的求解全局优化问题．     

基于遗传算法求解多目标优化问题Pareto前沿

该文给出了传统的求解多目标优化方法存在的问题,引入了当前研究多目标优化的新方法———基于遗传算法求解问题的pareto解,讨论了该方法要解决的关键问题———多样性保持及解决策略,并给出了一个求解pareto解集的新算法,算法简单、高效、鲁棒性强。最后给出了实验结果。     

解非线性约束规划问题的新型多目标遗传算法

给出非线性约束规划问题的一种新解法。把带约束的非线性规划问题转化成为两个目标的多目标优化问题，并为转化后的多目标优化模型设计了一种新型多目标遗传算法，数据实验表明该算法对带约束的非线性规划问题求解是非常有效的。     

改进遗传算法全局收敛性分析

传统的遗传算法大多数没有给出收敛性准则。一类新的改进的遗传算法被提出，该算法即考虑了优化问题的全局性要求——每一步构造一个新函数，而这往往却比局部最优理论和方法困难得多；同时通过对选择算子的改进，对遗传算法后期进化缓慢问题得到了有效控制，最后给出了算法的收敛性证明以及收敛性准则。实例证明该算法是有效的。     

解非线性规划的多目标遗传算法及其收敛性

给出非线性约束规划问题的一种新解法。它既不需用传统的惩罚函数,又不需区分可行解和不可行解,新方法把带约束的非线性规划问题转化成为两个目标函数优化问题,其中一个是原约束问题的目标函数,另一个是违反约束的度函数,并利用多目标优化中的Pareto优劣关系设计了一种新的选择算子,通过对搜索操作和参数的合理设计给出了一种新型遗传算法,且给出了算法的收敛性证明,最后数据实验表明该算法对带约束的非线性规划问题求解是非常有效的。     

遗传算法求解复杂集装箱装载问题方法研究

现场集装箱装载问题多为多目标、多约束优化的复杂问题.遗传算法本身的鲁棒性、并行搜索性以及在NP完全问题求解中的广泛应用,表明遗传算法是解决复杂集装箱装载问题的有效途径.探讨了遗传算法在求解这一复杂问题过程中的应用,给出了有效的编码形式和解码运算.算例求解结果显示出很好的效果.     

The piecewise parametric optimal control of uncertain linear quadratic models

The optimal control of linear quadratic model is given in a feedback form and determined by the solution of a Riccati equation. However, the control-related Riccati equation usually cannot be solved analytically such that the form of optimal control will become more complex. In this paper, we consider a piecewise parametric optimal control problem of uncertain linear quadratic model for simplifying the form of optimal control. By introducing a piecewise control parameter, a piecewise parametric optimal control model is established. Then we present a parametric optimisation method for solving the optimal piecewise control parameter. Finally, an uncertain inventory-promotion optimal control problem is discussed and a comparison is made to show the effectiveness of proposed piecewise parametric optimal control model.     

Parametric optimal control for uncertain linear quadratic models

In recent few decades, linear quadratic optimal control problems have achieved great improvements in theoretical and practical perspectives. For a linear quadratic optimal control problem, it is well known that the optimal feedback control is characterized by the solution of a Riccati differential equation, which cannot be solved exactly in many cases, and sometimes the optimal feedback control will be a complex time-oriented function. In this paper, we introduce a parametric optimal control problem of uncertain linear quadratic model and propose an approximation method to solve it for simplifying the expression of optimal control. A theorem is given to ensure the solvability of optimal parameter. Besides, the analytical expressions of optimal control and optimal value are derived by using the proposed approximation method. Finally, an inventory-promotion problem is dealt with to illustrate the efficiency of the results and the practicability of the model.     

Dual hierarchical genetic-optimal control: A new global optimal path planning method for robots

A new two-stage analytical-evolutionary algorithm considering dynamic equations is presented to find global optimal path. The analytical method is based on the indirect open loop optimal control problem and the evolutionary method is based on genetic algorithm (GA). Initial solutions, as start points of optimal control problem, are generated by GA to be used by optimal control. Then, a new sub-optimal path is generated through optimal control. The cost function is calculated for every optimal solution and the best solutions are chosen for the next step. The obtained path is used by GA to produce new generation of start points. This process continues until the minimum cost value is achieved. In addition, a new GA operator is introduced to be compatible with optimal control. It is used to select the pair chromosomes for crossover. The proposed method eliminates the problem of optimal control (being trapped in locally optimal point) and problem of GA (lack of compatibility with analytical dynamic equations). Hence problem is formulated and verification is done by comparing the results with a recent work in this area. Furthermore effectiveness of the method is approved by a simulation study for spatial non-holonomic mobile manipulators through conventional optimal control and the new proposed algorithm.     

Lossless convexification of a class of optimal control problems with non-convex control constraints

We consider a class of finite time horizon optimal control problems for continuous time linear systems with a convex cost, convex state constraints and non-convex control constraints. We propose a convex relaxation of the non-convex control constraints, and prove that the optimal solution of the relaxed problem is also an optimal solution for the original problem, which is referred to as the lossless convexification of the optimal control problem. The lossless convexification enables the use of interior point methods of convex optimization to obtain globally optimal solutions of the original non-convex optimal control problem. The solution approach is demonstrated on a number of planetary soft landing optimal control problems.     

From human to humanoid locomotion—an inverse optimal control approach

The purpose of this paper is to present inverse optimal control as a promising approach to transfer biological motions to robots. Inverse optimal control helps (a) to understand and identify the underlying optimality criteria of biological motions based on measurements, and (b) to establish optimal control models that can be used to control robot motion. The aim of inverse optimal control problems is to determine—for a given dynamic process and an observed solution—the optimization criterion that has produced the solution. Inverse optimal control problems are difficult from a mathematical point of view, since they require to solve a parameter identification problem inside an optimal control problem. We propose a pragmatic new bilevel approach to solve inverse optimal control problems which rests on two pillars: an efficient direct multiple shooting technique to handle optimal control problems, and a state-of-the art derivative free trust region optimization technique to guarantee a match between optimal control problem solution and measurements. In this paper, we apply inverse optimal control to establish a model of human overall locomotion path generation to given target positions and orientations, based on newly collected motion capture data. It is shown how the optimal control model can be implemented on the humanoid robot HRP-2 and thus enable it to autonomously generate natural locomotion paths.     

基于马氏决策过程的概率离散事件系统最优控制

使用马氏决策过程研究了概率离散事件系统的最优控制问题.首先,通过引入费用函数、目标函数以及最优函数的定义,建立了可以确定最优监控器的最优方程.之后,又通过此最优方程获得了给定语言的极大可控、∈-包含闭语言.最后给出了获得最优费用与最优监控器的算法.     

“Optimal” Hopfield network for combinatorialoptimization with linear cost function

An "optimal" Hopfield network is presented for combinatorial optimization problems with linear cost function. It is proved that a vertex of the network state hypercube is asymptotically stable if and only if it is an optimal solution to the problem. That is, one can always obtain an optimal solution whenever the network converges to a vertex. In this sense, this network can be called the "optimal" Hopfield network. It is also shown through simulations of assignment problems that this network obtains optimal or nearly optimal solutions more frequently than other familiar Hopfield networks.     

最优预见伺服系统与最优预见FF补偿系统的统一处理

最优预见伺服系统一般与基本最优伺服系统共用同一个二次型性能指标函数设 计预见前馈补偿项,其设计的着眼点是进一步减小性能指标函数.当控制系统的基本反馈部 分不是采用最优控制方法设计时,历史上采用另一个性能指标函数设计预见前馈补偿,并把 所得系统称为预见FF(前馈)补偿系统.这里把两种设计方法统一起来处理后,不仅最优预见 伺服系统与最优预见FF补偿系统都仅仅是特例,而且给设计者扩大了选择的余地.最后给 出了数值仿真,把这种设计方法与最优伺服系统、最优预见伺服系统进行了比较.     

含状态和输入时滞的离散时间系统的近似最优跟踪控制

针对状 态和控制输入均含有时滞的离散时间系统, 提出最优跟踪控制的设计方法. 通 过引入一种新的状态向量, 将含有状态和控制输入时滞的离散时间系统转化为 含有虚拟扰动项的无时滞离散时间系统. 根据最优控制理论, 构造离散Riccati矩阵方 程和离散Stein矩阵方程的序列, 并证明该解序列一致收敛于变换后的离散时间系统的最优跟 踪控制策略. 利用最优控制的逐次逼近设计方法, 得到最优跟踪控制的近似 解, 并给出求解最优跟踪控制律的算法. 仿真算例表明了所提出最优跟踪控制 方法的有效性.     

具有正弦扰动的时滞系统前馈-反馈次优控制:灵敏度法

研究线性时滞系统在外部正弦扰动作用下的前馈-反馈最优减振问题,提出了一种最优控制律的灵敏度设计方法．通过引入灵敏度参数并围绕它展开幂级数,将系统的最优控制问题简化为不含超前项和时滞项的两点边值问题族．通过截取最优控制级数的有限和获得原系统的前馈-反馈次优控制律．仿真结果表明,与经典状态反馈最优控制相比,本文的算法更加鲁棒,能更加有效地抑制正弦扰动．