Approximate subgradient projection algorithm for convex feasibility problem

An ε-subgradient projection algorithm for solving a convex feasibility problem is presented. Based on the iterative projection methods and the notion of ε-subgradient, a series of special projection hyperplanes is established. Moreover, compared with the existing projection hyperplanes methods with subgradient, the proposed hyperplanes are interactive with ε, and their ranges are more larger. The convergence of the proposed algorithm is given under some mild conditions, and the validity of the algorithm is proved by the numerical test.     

Multiobjective Imperialist Competitive Algorithm for Solving Nonlinear Constrained Optimization Problems

Nonlinear constrained optimization problem(NCOP) has been arisen in a diverse range of sciences such as portfolio, economic management, airspace engineering and intelligence system etc.In this paper, a new multiobjective imperialist competitive algorithm for solving NCOP is proposed.First, we review some existing excellent algorithms for solving NOCP; then, the nonlinear constrained optimization problem is transformed into a biobjective optimization problem. Second, in order to improve the diversity of evolution country swarm, and help the evolution country swarm to approach or land into the feasible region of the search space, three kinds of different methods of colony moving toward their relevant imperialist are given. Thirdly, the new operator for exchanging position of the imperialist and colony is given similar as a recombination operator in genetic algorithm to enrich the exploration and exploitation abilities of the proposed algorithm. Fourth, a local search method is also presented in order to accelerate the convergence speed. At last, the new approach is tested on thirteen well-known NP-hard nonlinear constrained optimization functions, and the experiment evidences suggest that the proposed method is robust, efficient, and generic when solving nonlinear constrained optimization problem. Compared with some other state-of-the-art algorithms, the proposed algorithm has remarkable advantages in terms of the best, mean, and worst objective function value and the standard deviations.     

Revisiting the ODE Method for Recursive Algorithms:Fast Convergence Using Quasi Stochastic Approximation

Several decades ago, Profs. Sean Meyn and Lei Guo were postdoctoral fellows at ANU,where they shared interest in recursive algorithms. It seems fitting to celebrate Lei Guo's 60 th birthday with a review of the ODE Method and its recent evolution, with focus on the following themes:The method has been regarded as a technique for algorithm analysis. It is argued that this viewpoint is backwards: The original stochastic approximation method was surely motivated by an ODE, and tools for analysis came much later(based on establishing robustness of Euler approximations). The paper presents a brief survey of recent research in machine learning that shows the power of algorithm design in continuous time, following by careful approximation to obtain a practical recursive algorithm.While these methods are usually presented in a stochastic setting, this is not a prerequisite. In fact,recent theory shows that rates of convergence can be dramatically accelerated by applying techniques inspired by quasi Monte-Carlo.Subject to conditions, the optimal rate of convergence can be obtained by applying the averaging technique of Polyak and Ruppert. The conditions are not universal, but theory suggests alternatives to achieve acceleration.The theory is illustrated with applications to gradient-free optimization, and policy gradient algorithms for reinforcement learning.     

基于LLE降维思想的自然计算方法

在自然计算方法中,高维问题的出现使现有一些优化算法虽然能够避免算法陷入局部最优,但是使得算法的性能变差、运行时间变长。在传统自然计算方法的基础上,提出基于LLE ( Local Linear Embedding)算法的自然计算方法,通过对算法中邻居粒子k和维数d的取值进行分析,降维后使算法得到较好的寻优效果。在此过程中,将降维后的数据增加一个小偏置s来增加种群的多样性。将该策略分别应用于粒子群算法和遗传算法中,采用经典测试函数以及主流针对维数进行优化的4个算法来验证其性能。实验结果表明,改进的算法在求解精度和收敛速度上均有明显的提升。     

A new <Emphasis Type="Italic">ɛ</Emphasis>-generalized projection method of strongly sub-feasible directions for inequality constrained optimization

In this paper, the nonlinear optimization problems with inequality constraints are discussed. Combining the ideas of the strongly sub-feasible directions method and the ɛ-generalized projection technique, a new algorithm starting with an arbitrary initial iteration point for the discussed problems is presented. At each iteration, the search direction is generated by a new ɛ-generalized projection explicit formula, and the step length is yielded by a new Armijo line search. Under some necessary assumptions, not only the algorithm possesses global and strong convergence, but also the iterative points always get into the feasible set after finite iterations. Finally, some preliminary numerical results are reported.     

基于投影滤波的突发事件危险源位置估计问题研究

针对确定突发事件中危险源的位置估计问题,提出一种基于hermit基函数的投影滤波方法.通过将其概率解投影到指定状态空间中,通过投影空间中的艾尔米特基函数构造出近似解,即状态的先验概率密度函数,最后由贝叶斯估计得到状态的后验概率密度函数,给出算法的收敛性和计算复杂度分析.仿真实验证明投影滤波方法有效减少滤波估计中所需的计算量,并提高了估计精度.     

基于个体差异移民的改进元胞遗传算法

针对灾变元胞遗传算法中的精英策略,在求解具有欺骗性的优化问题时易陷入次优解的情况,分析了几种移民策略。提出了一种基于个体差异的新移民策略,在灾变发生后,灾难区域以这种新的移民策略迁移个体。通过两个具有欺骗性典型函数的实验,表明在灾变机制元胞遗传算法中采用新的移民策略能提高数值优化函数的精度和收敛率,具有更好的全局搜索和局部搜索性。     

目标分配问题的蚁群算法研究

防空C3I系统的目标分配问题中如何使射击效率最佳,是非常重要又十分困难的问题。分析了目标分配问题各种解算方法的特点及存在的问题。结合蚁群算法思想,提出了一种新型的目标分配算法模型,并进行了算法实验。实验结果表明,基于蚁群算法思想的目标分配算法是有效的,特别是问题规模较大时更显示出其较快的收敛速度和较高的精度。     

基于等效控制的迭代学习控制

对一类含非参数不确定性的时变非线性系统,提出了一种新的迭代学习算法,应用类Lyapunov方法证明了其收敛性。为了提高其收敛速度,建立了该类非线性系统的等效系统,并应用线性扩张状态观测器直接给出了原非线性系统的等效控制,该等效控制是其期望控制的近似。为了消除线性扩张状态观测器应用中的初始时刻的峰值现象,提出了顺时针估计和逆时针估计相结合的等效控制求解方法,给出了基于等效控制的迭代学习控制算法的实现流程图。仿真表明所提的两种算法都是有效的,基于等效控制的迭代学习控制算法几乎一次学习后就可达到满意的效果。     

Transfer alignment of shipborne inertial-guided weapon systems

The transfer alignment problem of the shipborne weapon inertial navigation system (INS) is addressed. Specifically, two transfer alignment algorithms subjected to the ship motions induced by the waves are discussed. To consider the limited maneuver level performed by the ship, a new filter algorithm for transfer alignment methods using velocity and angular rate matching is first derived. And then an improved method using integrated velocity and integrated angular rate matching is introduced to reduce the effect of the ship body flexure. The simulation results show the feasibility and validity of the proposed transfer alignment algorithms.     

SGA(Simplex-Genetic Algorithm):一类求解Minimax问题的通用算法

在指出一般的迭代法不能保证收敛性之后,将注意力投向基于Stackelberg-NashEquilibrium的遗传算法(GA)的解决方法,并根据Minimax问题的特点指出该方法的不足之处.在此基础上,提出了SGA(Simplex-GeneticAlgorithm).仿真实例表明,这种方法速度和精度较之GA都有了很大提高,是求解最小最大问题的有效通用方法.     

三参数区间灰数信息下的决策方法

基于灰色系统理论的思想和方法,探讨了方案指标值为区间灰数且灰数取值可能性最大数已知的决策问题.首先定义了三参数区间灰数,利用这类灰数的特性及经典灰色关联决策的优势,提出了三参数灰色区间关联度方法;其次考虑到各方案的效果评价向量与理想最优方案及临界方案在空间位置及几何形状的接近度和相似性,构建了三参数灰色区间斜率关联系数公式,结合建立的三参数灰色区间关联系数公式,给出了灰色区间综合贴近度方法.最后借助三参数区间灰数评价值的期望值及一维投影寻踪法的分析技巧,引入了投影指标函数方法.并对上述三种决策方法建立了相应的算法,应用实例说明了文中提出的决策方法的合理性和有效性.为灰色决策理论与应用研究提供了新的思路.     

Hybrid anti-prematuration optimization algorithm

Heuristic optimization methods provide a robust and efficient approach to solving complex optimization problems. This paper presents a hybrid optimization technique combining two heuristic optimization methods, artificial immune system (AIS) and particle swarm optimization (PSO), together in searching for the global optima of nonlinear functions. The proposed algorithm, namely hybrid anti-prematuration optimization method, contains four significant operators, i.e. swarm operator, cloning operator, suppression operator, and receptor editing operator. The swarm operator is inspired by the particle swarm intelligence, and the clone operator, suppression operator, and receptor editing operator are gleaned by the artificial immune system. The simulation results of three representative nonlinear test functions demonstrate the superiority of the hybrid optimization algorithm over the conventional methods with regard to both the solution quality and convergence rate. It is also employed to cope with a real-world optimization problem.     

A Continuous Minimization Method for Solving Optimal Control Problem

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求解非线性双层规划问题的混合变邻域粒子群算法

针对非线性双层规划难以获得全局最优的问题,汲取粒子群算法的快速搜索能力及变邻域搜索算法的全局搜索优势,提出了求解非线性双层规划问题的混合变邻域粒子群算法.首先利用Kuhn-Tucker条件,将非线性双层规划转化为一个单层规划问题,然后由粒子群算法得到一个较优的群体,通过审敛因子判断陷入局部最优的粒子,并进一步利用变邻域搜索算法的全局搜索能力对陷入局部最优的粒子进行优化,从而得到全局最优.测试函数的仿真实验对比分析证明了该算法的有效性.     

自适应主动隔振中输出饱和抑制方法的仿真研究

针对自适应主动隔振中存在的控制器输出饱和,提出饱和抑制方法并进行算法仿真研究。该抑制方法基于跟踪滤波和归一化LMS算法,根据引起控制器饱和的直接原因提出约束优化函数,并在快速脱离饱和以及快速收敛的约束条件下确定权系数更新公式中的可变因子。新的自适应算法在理论上能够保证控制器尽快脱离输出饱和状态,使控制误差快速下降。以一个五自由度的振动系统进行算法数值仿真,并用Sigmoid函数描述饱和输出特性,显式表示可变因子,仿真结果表明所提方法能够有效地抑制输出饱和的不良影响,显著改善自适应主动隔振的控制效果。     

求解无容量设施选址问题的拉格朗日狼群算法及其应用

无容量设施选址问题(UFL)是应用于诸多领域的经典组合优化难题。首先，结合UFL问题的具体特征，重新定义了狼群算法中狼群协作捕食的智能行为，提出了求解该问题的狼群优化算法；其次，将狼群算法与拉格朗日松弛相结合，设计了一种求解UFL问题的拉格朗日狼群算法；最后，将本文提出的狼群智能优化算法及拉格朗日狼群算法用于UFL基准问题库中部分算例的求解，并将其求解结果与混合蚁群算法、半拉格朗日松弛方法以及优化软件CPLEX的求解结果进行比较。结果表明：拉格朗日狼群算法较狼群优化算法、混合蚁群算法及半拉格朗日松弛方法具有更好的求解效果，而且在一定程度上缓解了CPLEX求解时间长，消耗内存大的缺点，拥有良好的求解性能。     

利用多群体DNA遗传算法求解线性规划问题

针对经典遗传算法存在的问题 ,提出了多群体DNA遗传算法。该方法在经典遗传算法的基础上 ,通过借鉴生物学及社会学 ,引入了多群体及DNA片断等概念 ,并提出迁移与自适应变异算法 ,可以提高遗传算法的有效性与收敛性。为了验证算法的有效性 ,将该算法应用于线性规划问题的求解。在求解过程中 ,首先利用熵障碍对偶方法对原问题进行转换 ,然后使用多群体DNA遗传算法对转换后的目标函数进行求解。仿真结果表明 ,该方法具有良好的全局搜索能力和较快的收敛速度。以上工作为解决大规模线性规划问题的求解提供了全新的思路和方法 ,对遗传算法应用的发展具有重要意义     

ABMS中基于Q学习算法的空战目标分配方法

Q学习算法由于不需要先验知识即可学习,对于求解复杂的优化决策问题具有广泛的应用前景。本文针对当前空战目标分配算法的优缺点,提出了ABMS(agent based modeling and simulation)中基于Q学习算法的空战目标分配方法。首先介绍了空战Agent建模;然后给出了Q学习算法应用于空战目标分配的方法流程,并严格定义了“状态动作”对的选择规则,最后通过仿真实验证明了该方法的合理性和有效性。本文方法避免了对先验知识的依赖,并且脱离了局部最优陷阱。     

Using Genetic Algorithms to Improve the Search of the Weight Space in Cascade－Correlation Neural Network

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