一种优化高维复杂函数的PSO算法

对于高维复杂函数,一般粒子群优化算法收敛速度慢,易早熟收敛。本文重构一个适合高维复杂函数惯性权重函数,使粒子群算法寻优过程中的全局收搜能力和局部收搜能力良好平衡,以达到快速收敛,高效避免早熟问题,获得最优解。对典型高维复杂函数的仿真表明：算法在求解质量和求解速度两方面都得到了好的结果。     

求解随机机会约束规划的混合智能算法

随机机会约束规划是一类有着广泛应用背景的随机规划问题,采用随机仿真产生样本训练BP网络以逼近随机函数,然后在微粒群算法中利用神经网络计算适应值和实现检验解的可行性,从而提出了一种求解随机机会约束规划的混合智能算法。最后通过两个实例的仿真结果说明了算法的正确性和有效性。     

一种基于引导策略的自适应粒子群算法

为解决粒子群算法前期搜索“盲目”,后期搜索速度慢且易陷入局部极值的问题,对算法中粒子更新方式和惯性权重进行了改进,提出了一种基于引导策略的自适应粒子群算法。该算法在种群中引入4种粒子,即主体粒子、双中心粒子、协同粒子和混沌粒子对粒子位置更新进行引导,克服算法的随机性,从而提高搜索效率;为进一步克服粒子群优化算法进化后期易陷入早熟收敛的缺点,引入聚焦距离变化率的概念,通过聚焦距离变化率的大小动态调整惯性权重,以提高算法的收敛速度和精度,两者结合极大地提高了搜索到全局最优解的有效性。对4个标准测试函数进行仿真,实验结果表明IPSO算法在收敛速度、收敛精度以及成功率上都明显优于LDWPSO和WPSO算法。     

基于分层多子群的混沌粒子群优化算法

在分层多子群结构模型的基础上,提出一种混沌粒子群优化算法(HCPSO).该算法对非线性递减的惯性权重进行混沌变异,并采用了混沌搜索方法.在更新全局历史最优位置每一维分量时,选取不同的若干个体作为学习对象,并计算它们的平均位置.混沌搜索区域半径可根据粒子个体最优位置与上述平均位置间的距离自适应地调整.通过对几种典型函数的测试结果表明,该算法具有较好的全局搜索和局部搜索能力,可有效避免早熟收敛问题.     

改进混沌PSO算法的BP网络优化

提出了一种改进混沌粒子群算法(MCPSO)与BP算法的混合算法(MCPSO—BP),该算法综合了改进粒子群算法全局寻优的高效性,混沌算法局部搜索的遍历性和BP算法快速的局部搜索能力。仿真结果表明,MCPSO—BP算法网络结构简单,收敛速度快,并具有良好的逼近能力和泛化能力。     

一种动态改变惯性权重的自适应粒子群算法

针对标准粒子群算法在进化过程中种群多样性降低而早熟的问题,提出一种动态改变惯性权重的自适应粒子群算法.采用种群中平均粒子相似程度作为种群多样性的测度,并用于平衡算法的全局探索和局部开发.基于对惯性权重随种群多样性测度变化的动态分析,建立了惯性权重随种群多样性测度的变化关系,并将其引入该算法中.最后对6个经典测试函数进行仿真,结果表明该算法在平均最优值和成功率上都有所提高,特别是对多峰函数效果更明显.     

一种基于种群速度的自适应粒子群算法

分析了粒子群算法的收敛性,指出早熟是由于粒子速度降低而失去继续搜索可行解的能力.进而提出一种基于种群速度动态改变惯性权重的粒子群算法,该算法以种群粒子平均速度为信息动态改变惯性权重,避免了粒子速度过早接近0.通过5个标准测试函数的仿真实验并与其他算法相比,结果表明该算法在进化中期能很好地保持种群多样性,有效地改善算法的平均最优值和成功率.     

An improved GA and a novel PSO-GA-based hybrid algorithm

Inspired by the natural features of the variable size of the population, we present a variable population-size genetic algorithm (VPGA) by introducing the “dying probability” for the individuals and the “war/disease process” for the population. Based on the VPGA and the particle swarm optimization (PSO) algorithms, a novel PSO-GA-based hybrid algorithm (PGHA) is also proposed in this paper. Simulation results show that both VPGA and PGHA are effective for the optimization problems.     

Minimizing control variation in nonlinear optimal control

In any real system, changing the control signal from one value to another will usually cause wear and tear on the system’s actuators. Thus, when designing a control law, it is important to consider not just predicted system performance, but also the cost associated with changing the control action. This latter cost is almost always ignored in the optimal control literature. In this paper, we consider a class of optimal control problems in which the variation of the control signal is explicitly penalized in the cost function. We develop an effective computational method, based on the control parameterization approach and a novel transformation procedure, for solving this class of optimal control problems. We then apply our method to three example problems in fisheries, train control, and chemical engineering.     

A unified framework for the numerical solution of optimal control problems using pseudospectral methods

A unified framework is presented for the numerical solution of optimal control problems using collocation at Legendre-Gauss (LG), Legendre-Gauss-Radau (LGR), and Legendre-Gauss-Lobatto (LGL) points. It is shown that the LG and LGR differentiation matrices are rectangular and full rank whereas the LGL differentiation matrix is square and singular. Consequently, the LG and LGR schemes can be expressed equivalently in either differential or integral form, while the LGL differential and integral forms are not equivalent. Transformations are developed that relate the Lagrange multipliers of the discrete nonlinear programming problem to the costates of the continuous optimal control problem. The LG and LGR discrete costate systems are full rank while the LGL discrete costate system is rank-deficient. The LGL costate approximation is found to have an error that oscillates about the true solution and this error is shown by example to be due to the null space in the LGL discrete costate system. An example is considered to assess the accuracy and features of each collocation scheme.     

Particle swarm optimization with an aging leader and challengers algorithm for the solution of optimal power flow problem

Solution of optimal power flow (OPF) problem aims to optimize a selected objective function such as fuel cost, active power loss, total voltage deviation (TVD) etc. via optimal adjustment of the power system control variables while at the same time satisfying various equality and inequality constraints. In the present work, a particle swarm optimization with an aging leader and challengers (ALC-PSO) is applied for the solution of the OPF problem of power systems. The proposed approach is examined and tested on modified IEEE 30-bus and IEEE 118-bus test power system with different objectives that reflect minimization of fuel cost or active power loss or TVD. The simulation results demonstrate the effectiveness of the proposed approach compared with other evolutionary optimization techniques surfaced in recent state-of-the-art literature. Statistical analysis, presented in this paper, indicates the robustness of the proposed ALC-PSO algorithm.     

State waypoint approach to continuous‐time nonlinear optimal control problems

In this paper, we propose an optimal control technique for a class of continuous‐time nonlinear systems. The key idea of the proposed approach is to parametrize continuous state trajectories by sequences of a finite number of intermediate target states; namely, waypoint sequences. It is shown that the optimal control problem for transferring the state from one waypoint to the next is given an explicit‐form suboptimal solution, by means of linear approximation. Thus the original continuous‐time nonlinear control problem reduces to a finite‐dimensional optimization problem of waypoint sequences. Any efficient numerical optimization method, such as the interior‐reflection Newton method, can be applied to solve this optimization problem. Finally, we solve the optimal control problem for a simple nonlinear system example to illustrate the effectiveness of this approach. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Pseudospectral methods for solving infinite-horizon optimal control problems

An important aspect of numerically approximating the solution of an infinite-horizon optimal control problem is the manner in which the horizon is treated. Generally, an infinite-horizon optimal control problem is approximated with a finite-horizon problem. In such cases, regardless of the finite duration of the approximation, the final time lies an infinite duration from the actual horizon at t=+∞. In this paper we describe two new direct pseudospectral methods using Legendre–Gauss (LG) and Legendre–Gauss–Radau (LGR) collocation for solving infinite-horizon optimal control problems numerically. A smooth, strictly monotonic transformation is used to map the infinite time domain t∈[0,∞) onto a half-open interval τ∈[−1,1). The resulting problem on the finite interval is transcribed to a nonlinear programming problem using collocation. The proposed methods yield approximations to the state and the costate on the entire horizon, including approximations at t=+∞. These pseudospectral methods can be written equivalently in either a differential or an implicit integral form. In numerical experiments, the discrete solution exhibits exponential convergence as a function of the number of collocation points. It is shown that the map ?:[−1,+1)→[0,+∞) can be tuned to improve the quality of the discrete approximation.     

微粒群算法中惯性权重的调整策略

惯性权重是微粒群算法中的关键参数,可以平衡算法全局搜索能力和局部搜索能力的关系,提高算法的收敛性能。该文分析了惯性权重对微粒群算法收敛性能的影响,为了进一步提高算法的全局最优性,提出了几种对惯性权重的调整策略。通过对4个测试函数的仿真实验,验证了这些策略的可行性,表明这些策略能够简便高效地提高算法的全局收敛性和收敛速度。     

Consistent approximation of a nonlinear optimal control problem with uncertain parameters

This paper focuses on a non-standard constrained nonlinear optimal control problem in which the objective functional involves an integration over a space of stochastic parameters as well as an integration over the time domain. The research is inspired by the problem of optimizing the trajectories of multiple searchers attempting to detect non-evading moving targets. In this paper, we propose a framework based on the approximation of the integral in the parameter space for the considered uncertain optimal control problem. The framework is proved to produce a zeroth-order consistent approximation in the sense that accumulation points of a sequence of optimal solutions to the approximate problem are optimal solutions of the original problem. In addition, we demonstrate the convergence of the corresponding adjoint variables. The accumulation points of a sequence of optimal state-adjoint pairs for the approximate problem satisfy a necessary condition of Pontryagin Minimum Principle type, which facilitates assessment of the optimality of numerical solutions.     

A hybrid algorithm based on particle swarm and chemical reaction optimization for multi-object problems

Over the past decade, the particle swarm optimization (PSO) has been an effective algorithm for solving single and multi-object optimization problems. Recently, the chemical reaction optimization (CRO) algorithm is emerging as a new algorithm used to efficiently solve single-object optimization.In this paper, we present HP-CRO (hybrid of PSO and CRO) a new hybrid algorithm for multi-object optimization. This algorithm has features of CRO and PSO, HP-CRO creates new molecules (particles) not only used by CRO operations as found in CRO algorithm but also by mechanisms of PSO. The balancing of CRO and PSO operators shows that the method can be used to avoid premature convergence and explore more in the search space.This paper proposes a model with modified CRO operators and also adding new saving molecules into the external population to increase the diversity. The experimental results of the HP-CRO algorithm compared to some meta-heuristics algorithms such as FMOPSO, MOPSO, NSGAII and SPEA2 show that there is improved efficiency of the HP-CRO algorithm for solving multi-object optimization problems.     

A hybrid particle swarm optimization algorithm for high-dimensional problems

In recent years, particle swarm optimization (PSO) emerges as a new optimization scheme that has attracted substantial research interest due to its simplicity and efficiency. However, when applied to high-dimensional problems, PSO suffers from premature convergence problem which results in a low optimization precision or even failure. To remedy this fault, this paper proposes a novel memetic PSO (CGPSO) algorithm which combines the canonical PSO with a Chaotic and Gaussian local search procedure. In the initial evolution phase, CGPSO explores a wide search space that helps avoid premature convergence through Chaotic local search. Then in the following run phase, CGPSO refines the solutions through Gaussian optimization. To evaluate the effectiveness and efficiency of the CGPSO algorithm, thirteen high dimensional non-linear scalable benchmark functions were examined. Results show that, compared to the standard PSO, CGPSO is more effective, faster to converge, and less sensitive to the function dimensions. The CGPSO was also compared with two PSO variants, CPSO-H, DMS-L-PSO, and two memetic optimizers, DEachSPX and MA-S2. CGPSO is able to generate a better, or at least comparable, performance in terms of optimization accuracy. So it can be safely concluded that the proposed CGPSO is an efficient optimization scheme for solving high-dimensional problems.     

A multivariate adaptive regression B-spline algorithm (BMARS) for solving a class of nonlinear optimal feedback control problems

In this paper we present a novel method for solving a class of nonlinear optimal feedback control problems with moderately high dimensional state spaces, based on an adapted version of the BMARS algorithm. Numerical experiments were performed using problems with up to six state variables. The numerical results clearly demonstrate the efficiency and potential of the method for solving high dimensional problems.