基于混沌粒子群算法的Tikhonov正则化参数选取

Tikhonov正则化方法是求解不适定问题最为有效的方法之一,而正则化参数的最优选取是其关键.本文将混沌粒子群优化算法与Tikhonov正则化方法相结合,基于Morozov偏差原理设计粒子群的适应度函数,利用混沌粒子群优化算法的优点,为正则化参数的选取提供了一条有效的途径.数值实验结果表明,本文方法能有效地处理不适定问题,是一种实用有效的方法.     

基于混沌优化和自适应反向学习的秃鹰搜索算法

针对秃鹰搜索算法求解精度低、收敛速度较慢、容易陷入局部最优的问题,提出一种基于混沌优化和自适应反向学习的秃鹰搜索算法.首先,在选择搜索空间阶段引入正弦混沌映射更新秃鹰群位置,增加随机性,优化全局搜索能力;其次,在俯冲捕获猎物阶段加入指数自适应,平衡了全局搜索和局部搜索,同时加快收敛速度;最后,对更新后的最优秃鹰位置使用反向学习策略,提高跳出局部最优的可能性.选取12个测试函数对算法的性能进行了测试,结果表明本文改进的秃鹰搜索算法具有更优的求解精度和收敛速度.     

混沌遗传算法对BP神经网络的改进研究

BP神经网络算法是目前应用最广泛的一种神经网络算法,但有收敛速度慢和易陷入局部极小值等缺陷.本文利用混沌遗传算法(CGA)具有混沌运动遍历性、遗传算法反演性的特性来改进BP神经网络算法.该算法的基本思想是用混沌遗传算法对BP神经网络算法的初始权值和初始阈值进行优化.把混沌变量加入遗传算法中,提高遗传算法的全局搜索能力和收敛速度;用混沌遗传算法优化后得到的最优解作为BP神经网络算法的初始权值和阈值.通过实验观察,改进后的结果与普通的BP神经网络算法的结果相比,具有更高的准确率.     

具有模糊行程的城市物流动态费用多车型车辆调度问题研究

针对城市物流配送中广泛存在的多车型问题,以及由于交通路况等因素导致的配送行程模糊化现象,给出了一种基于梯形模糊数的,以最小化行程费用为目标的具有模糊行程的动态费用多车型车辆调度问题模型.在问题求解方面,针对基本粒子群算法容易陷入局部最优的情况,引入混沌局部搜索策略,给出了一种基于混沌优化技术的混合粒子群算法.仿真实验表明,该算法具有可行性和有效性.     

基于圆形件排样问题的遗传算法研究

排样性问题是一类优化求解问题,在遗传算法求解过程中,若所用的算法是不收敛的,则无法得到最优解.给出了一种混合式遗传算法,并证明了算法是完全收敛的,能够得到全局最优解.     

基于混沌量子算法和MAGTD的多目标FJSP求解策略

针对多目标环境下柔性作业车间的调度问题,以最小化最大完工时间和惩罚值为目标,建立调度问题的数学模型,提出了基于混沌理论的量子粒子群算法。针对实际生产交货期不确定的特点,在量子粒子群算法基础上,提出引入混沌机制建立初始群的方法;利用混沌机制的遍历性,提出混沌局部优化策略;为获取最优调度方案提出了引入多指标加权灰靶选择策略。通过典型基准算例和对比测试,验证了所提出的算法获得最满意调度方案的可行性和求解多目标柔性作业车间调度问题的有效性。     

生化系统稳态优化的双层规划模型与求解方法

针对一类生化系统的稳态优化问题,建立了一种具有二层递阶结构的双层规划优化模型,其上层和下层问题的优化目标分别为最大化产物产率(或代谢物浓度)和最小化生化系统的代谢物浓度之和.模型的生物意义是在尽可能小的代谢成本条件下使产物的产率或浓度达到最大.为了有效求解所建立的NP-hard、非凸双层规划问题,在S-系统建模框架下应用等价变换策略提出了一种可求其最优解的优化算法.算法具有操作简便和计算成本低的优点.最后,将所提双层规划模型与求解方法应用于两个生化系统的稳态优化中.结果表明,方法可行且有效.     

基于Cubic混沌模型的自适应布谷鸟优化算法

针对基本布谷鸟算法(CS)求解精度有限、收敛速度慢,易陷入局部最优的不足,提出一种基于Cubic混沌模型的自适应布谷鸟优化算法.算法在迭代时,自动调整Lévy flights随机搜索的步长因子,提高算法的收敛速度;将Cubic混沌映射模型嵌入布谷鸟算法,产生混沌扰动信号,对鸟巢位置进行更新,扩大种群多样性,提高全局最优值的搜索能力.通过10个标准测试函数的实验及结果分析,表明算法在寻优精度和收敛速度两方面的改进是有效的.     

基于混沌粒子群优化算法的灰色GM(1,1)模型在地下水埋深预测中的应用

将混沌优化算法与粒子群优化算法相结合,形成新的混沌粒子群优化算法.利用混沌运动的遍历性,避免陷入局部最优.同时,粒子群算法能加快混沌优化算法的收敛速度,使搜索效率得到提高.用混沌粒子群优化算法优化灰色GM(1,1)模型中的参数,通过横向和纵向比较,优化效果良好,模型预测精度得到了提高.运用该模型对三江平原地下水埋深进行动态预测,预测结果可为有关决策部门提供参考.     

低阶精确罚函数的一种二阶光滑逼近

给出了求解约束优化问题的低阶精确罚函数的一种二阶光滑逼近方法,证明了光滑后的罚优化问题的最优解是原约束优化问题的ε-近似最优解,基于光滑后的罚优化问题,提出了求解约束优化问题的一种新的算法,并证明了该算法的收敛性,数值例子表明该算法对于求解约束优化问题是有效的.     

An Exact Solution Method for Reliability Optimization in Complex Systems

Systems reliability plays an important role in systems design, operation and management. Systems reliability can be improved by adding redundant components or increasing the reliability levels of subsystems. Determination of the optimal amount of redundancy and reliability levels among various subsystems under limited resource constraints leads to a mixed-integer nonlinear programming problem. The continuous relaxation of this problem in a complex system is a nonconvex nonseparable optimization problem with certain monotone properties. In this paper, we propose a convexification method to solve this class of continuous relaxation problems. Combined with a branch-and-bound method, our solution scheme provides an efficient way to find an exact optimal solution to integer reliability optimization in complex systems. This research was partially supported by the Research Grants Council of Hong Kong, grants CUHK4056/98E, CUHK4214/01E and 2050252, and the National Natural Science Foundation of China under Grants 79970107 and 10271073.     

Optimal Control for Multiscale Elliptic Equations with Rough Coefficients

This paper concerns the convex optimal control problem governed by multiscale elliptic equations with arbitrarily rough $L^\infty$ coefficients, which has not only complex coupling between nonseparable scales and nonlinearity, but also important applications in composite materials and geophysics. We use one of the recently developed numerical homogenization techniques, the so-called Rough Polyharmonic Splines (RPS) and its generalization (GRPS) for the efficient resolution of the elliptic operator on the coarse scale. Those methods have optimal convergence rate which do not rely on the regularity of the coefficients nor the concepts of scale-separation or periodicity. As the iterative solution of the nonlinearly coupled OCP-OPT formulation for the optimal control problem requires solving the corresponding (state and co-state) multiscale elliptic equations many times with different right hand sides, numerical homogenization approach only requires one-time pre-computation on the fine scale and the following iterations can be done with computational cost proportional to coarse degrees of freedom. Numerical experiments are presented to validate the theoretical analysis.     

Solving a system of the nonlinear equations by iterative dynamic programming

In this paper we use iterative dynamic programming in the discrete case to solve a wide range of the nonlinear equations systems. First, by defining an error function, we transform the problem to an optimal control problem in discrete case. In using iterative dynamic programming to solve optimal control problems up to now, we have broken up the problem into a number of stages and assumed that the performance index could always be expressed explicitly in terms of the state variables at the last stage. This provided a scheme where we could proceed backwards in a systematic way, carrying out optimization at each stage. Suppose that the performance index can not be expressed in terms of the variables at the last stage only. In other words, suppose the performance index is also a function of controls and variables at the other stages. Then we have a nonseparable optimal control problem. Furthermore, we obtain the path from the initial point up to the approximate solution.     

Sliding Mode Optimization in Dynamic LTI Systems

This paper deals with the problem of constrained optimization in dynamic linear time-invariant (LTI) systems characterized by a control vector dimension less than that of the system state vector. The problem consists in designing a control signal capable of generating a system state evolution confined to the feasible region delimited by a number of inequality constraints less than or equal to the number of control vector components, as well as of steering the state trajectory to an equilibrium point where a prespecified cost function depending on the system state is being minimized. The finite-time convergence to a vicinity of order of the optimal equilibrium point is proved.     

Optimization Implementation and Characterization of the Equal Allocation of Nonseparable Costs Value

This paper devotes to the study of the equal allocation of nonseparable costs value for cooperative games. On the one hand, we show that the equal allocation of nonseparable costs value is the unique optimal solution that minimizes the total complaints for individual players over the pre-imputation set. On the other hand, analogously to the way of determining the Nucleolus, we obtain the equal allocation of nonseparable costs value by applying the lexicographic order over the individual complaints. Moreover, we offer alternative characterizations of the equal allocation of nonseparable costs value by proposing several new properties such as dual nullifying player property, dual dummifying player property and grand marginal contribution monotonicity.     

Optimal control and synchronization of Lotka–Volterra model

In this paper we discuss the problem of optimal control for the steady state of Lotka–Volterra model. The conditions of the asymptotic stability of the steady state of this model are used to obtain the optimal control functions. In such study, the optimal Lyapunov function is used. The general solution of the equations of the perturbed state is obtained as a function of time. In addition, the optimal control is also applied to achieve the state synchronization of two identical Lotka–Volterra systems. Graphical and numerical simulation studies of the obtained results are presented.     

考虑订单合并和货物转运的多式联运路径优化研究

为了获得运输的规模经济效应,本文研究了一种考虑订单合并和货物转运的零担多式联运路径优化问题。首先,以总运输成本为目标函数,以网络中的运输工具容量、可以提供的运输工具最大数量、运输工具服务的关闭时间以及订单时间窗为约束,构建混合整数规划模型,在模型中允许多个订单进行合并运输并考虑运输过程中的转运成本。其次,由于多式联运路径优化问题是典型的NP-hard问题,为了快速求解该模型,开发了一种可以快速为该问题提供近似最优解和下界的列生成启发式算法。最后,生成并测试了大量算例,结果表明所开发的列生成启发式算法可以在较短的时间内提供高质量的近似最优解。文章所构建的模型和开发的列生成启发式算法可以为零担自营多式联运物流企业提供高效的决策支持。     

A New Iteration and Preconditioning Method for Elliptic PDE-Constrained Optimization Problems

Optimal control problems constrained by a partial differential equation (PDE) arise in various important applications, such as in engineering and natural sciences. Normally the problems are of very large scale, so iterative solution methods must be used. Thereby the choice of an iteration method in conjunction with an efficient preconditioner is essential. In this paper, we consider a new iteration method and a new preconditioning technique for an elliptic PDE-constrained optimal control problem with a distributed control function. Some earlier used iteration methods and preconditioners in the literature are compared, both analytically and numerically with the new iteration method and the preconditioner.     

Chaos control of chaotic dynamical systems using backstepping design

This work presents chaos control of chaotic dynamical systems by using backstepping design method. This technique is applied to achieve chaos control for each of the dynamical systems Lorenz, Chen and Lü systems. Based on Lyapunov stability theory, control laws are derived. We used the same technique to enable stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. Numerical simulations are shown to verify the results.