面向工程全局优化的混沌优化算法研究进展Research advances of chaos optimization algorithms for engineering global optimization

近年来,基于混沌的初值敏感性、伪随机性、遍历性以及自相似分形等非线性动力学特性所发展的混沌优化方法,是一种有潜力的工程全局优化新工具,已广泛应用于科学与工程技术的各学科领域。根据混沌优化方法的发展历程,以算法基本思想和工程应用研究状况为重点,评述了混沌神经网络优化方法、第一类混合混沌优化算法（基于混沌搜索）、第二类混合混沌优化算法（混沌序列代替随机序列）以及混沌分形优化四种主要混沌优化算法。混沌映射最早被引入神经网络,发展了混沌神经网络优化方法,可解决复杂的组合优化等全局优化问题。遗传算法及粒子群等启发式随机算法虽具全局搜索能力,但易出现早熟并陷入局部最优。然后,出现了混沌搜索的概念,研究者将其嵌入启发式算法建立了第一类混合混沌优化算法,可有效克服原启发式算法早熟收敛的缺点。随后,利用混沌映射产生的混沌序列代替启发式算法中的随机参数形成了第二类混合混沌优化算法。混合混沌优化算法有益于实现快速全局收敛和提高计算精度。最后,利用混沌分形特性,从分形理论出发提出一类新颖的混沌分形优化算法,可搜索到优化问题的所有全局最优解。此外,对混沌优化算法研究的几个发展方向进行了展望,诸如加强混沌优化算法的参数设计、处理大规模优化、多目标优化问题以及使用代理模型等。     

基于填充函数与DCD的全局优化算法及其反演

岩土工程中以监测位移为已知信息的反演问题可通过带未知变量约束空间的优化模型去求解。该模型中的优化函数常具有非线性、非凸性等特点,使得反演结果容易陷入局部最优的困境。为了应对在运用优化算法反演此类问题时存在的困境,并提高其算法效率,依据填充函数优化思想与DCD(Dynamic Canonical Descent)思想在反演时的优良全局搜索能力及其算法优化特点,提出了基于填充函数和DCD思想的联合反演全局优化算法,并给出了其反演迭代形式。数值计算和工程应用结果均表明:对于随机给定的任何一组初始反演值,本算法都能稳定且快速地收敛到反演真值。该联合算法具有数值计算稳定性好、全局优化能力强、收敛速度快等优点,将其应用于岩土工程中的非线性反演求解中具有较好的前景。     

计算具有区间参数结构特征值范围的一种新方法

基于区间效学的包含单调性和区间函效所表述的实际物理意义，把广义区间特征值问题转化为两个以非确定参效为优化变量，以关心的特征值为目标函效的全局优化问题，并采用遗传算法对优化问题求解，计算得到结构特征值的区间范围。通过效值算例对本文方法的有效性进行了验证，并和区间摄动法的计算结果进行了比较。     

粒子群算法优化的捷联罗经初始对准方法

初始对准是惯导系统的关键技术,罗经法对准是实现捷联惯导系统初始对准的重要手段。罗经对准回路的参数选择直接影响对准结果的好坏。对于不同的捷联惯导系统,罗经回路的最优参数也是不同的。传统的方法是根据经验以及大量的反复试验确定罗经对准参数,不能保证对准参数为最优。针对此问题,提出以水平罗经对准回路阻尼振荡周期T_(d1)和航向罗经对准回路阻尼振荡周期T_(d2)为寻优目标,用粒子群算法对参数(T_(d1),T_(d2))进行寻优的方法,以确定出满足条件的最优对准参数,从而提高捷联罗经初始对准的性能。实验结果表明:粒子群算法能够快速、准确地搜索出罗经对准回路的最优参数,提高捷联罗经对准的性能。将粒子群算法应用到捷联罗经初始对准中是有效的。     

The application of the gradient-based adjoint multi-point optimization of single and double shock control bumps for transonic airfoils

A shock control bump (SCB) is a flow control method that uses local small deformations in a flexible wing surface to considerably reduce the strength of shock waves and the resulting wave drag in transonic flows. Most of the reported research is devoted to optimization in a single flow condition. Here, we have used a multi-point adjoint optimization scheme to optimize shape and location of the SCB. Practically, this introduces transonic airfoils equipped with the SCB that are simultaneously optimized for different off-design transonic flight conditions. Here, we use this optimization algorithm to enhance and optimize the performance of SCBs in two benchmark airfoils, i.e., RAE-2822 and NACA-64-A010, over a wide range of off-design Mach numbers. All results are compared with the usual single-point optimization. We use numerical simulation of the turbulent viscous flow and a gradient-based adjoint algorithm to find the optimum location and shape of the SCB. We show that the application of SCBs may increase the aerodynamic performance of an RAE-2822 airfoil by 21.9 and by 22.8 % for a NACA-64-A010 airfoil compared to the no-bump design in a particular flight condition. We have also investigated the simultaneous usage of two bumps for the upper and the lower surfaces of the airfoil. This has resulted in a 26.1 % improvement for the RAE-2822 compared to the clean airfoil in one flight condition.     

基于非概率可靠性的结构优化设计研究

基于不确定参量的凸集合描述,研究了考虑非概率可靠性约束时,结构优化设计模型的求解问题。由于非概率可靠性指标是用一个极小极大模型来定义的,故以该指标作为设计约束,将得到一个嵌套的二级优化模型。为了求解该模型,提出了一种序列线性化的计算方法。利用非概率可靠性分析的拉格朗日乘子,逐步构造可靠性指标的一阶近似,通过序列线性规划法求解二级优化问题。该算法可用于区间变量和超椭球凸集模型并存的情形,具有较好的适用性。论文给出了主要的敏度计算公式,并通过简单算例对所提算法进行了验证。     

基于拟满应力设计和遗传算法的网架截面优化方法

通过在遗传算法中嵌入拟满应力算子,提出了一种以网架结构杆件截面作为离散变量的优化设计方法,即基于拟满应力设计和遗传算法的网架截面优化方法.分析结果表明,该法能够提高遗传算法的搜索效率和获得全局最优解的可靠性,对于同时有应力和位移约束的网架等空间结构截面优化问题,这种混合算法有较高的效率.     

基于多目标优化策略的结构可靠性稳健设计

应用可靠性稳健优化设计理论和多目标决策方法,将结构可靠性稳健优化设计转化为多目标优化问题。运用灰色理论中的关联分析法,选取粒子群算法中的全局极值和个体极值,提出了灰色粒子群算法求解可靠性稳健优化设计问题。与传统方法相比,该方法简便易行并能迅速准确地得到结构可靠性稳健优化设计信息。     

Studies on optimal topology design of structures with discrete variables

Some problems in the optimal topology design of structures with discrete variables are studied in this paper. The problem of a model of discrete optimization is discussed and a neglected fact that discrete optimum design may be controlled by the discreteness of sizing variables and global constraints is pointed out. A heuristic algorithm for solving discrete topology optimization problems of trusses and frames is proposed.     

Nonlinear model predictive control based on Nelder Mead optimization method

In this paper, a model predictive control (MPC) scheme based on Hammerstein model is carried on. The use of such nonlinear models complicates the implementation of the MPC in terms of computational time and burden since a nonlinear and so a nonconvex optimization problem will result. The Nelder Mead (NM) algorithm, as a free derivative method, is used to solve the resulting optimization problem. NM algorithm proves its efficiency in terms of computation time and global optimum seeking that can be successfully exploited especially with fast dynamic systems. A comparative study between the NM algorithm and the gradient-based method (GBM) based on computation time is established. The efficiency of the NM algorithm is illustrated with SISO and MIMO examples compared to GBM algorithm.     

Model-free chaos control based on AHGSA for a vibro-impact system

For a vibro-impact system with clearance, the model-free chaos control method based on adaptive hybrid gravitational search algorithm (or AHGSA algorithm for short) is proposed. Nonparametric time-varying dynamic linear model based on pseudo-partial-derivative is established using input/output data of the controlled system, and on this basis, the optimal controller is designed according to the quadratic performance index, and the controller parameters is optimized using AHGSA algorithm. By combining the artificial bee colony search operator and chaos optimization strategy, gravitational search algorithm (or GSA algorithm for short) is improved from three aspects (i.e., population initialization, velocity and position update, gravity coefficient adjustment) to achieve a balance between the global detection ability and the local development ability. AHGSA algorithm has good optimization accuracy and efficiency: The arbitrariness is avoided in controller parameters selection, and the quality of the chaos control is ensured as well. In simulation experiment, the model-free controller optimized is used to control the chaotic motion of a single-degree-of-freedom vibro-impact system with clearance to verify the validity and feasibility of the proposed chaos control method. The simulation results show that the control effect is good, and the proposed chaos control method has the following advantages: the proposed chaos control method does not depend on the precise model of the controlled system, and the controller is easy to be designed and implemented.     

Parameter determination and response analysis of viscoelastic material

The parameter determination of viscoelastic material is a multi-variable, multi-aim nonlinear optimization problem, which made the optimization process very complicated. In this paper a hybrid optimal algorithm was proposed to determine the viscoelastic parameters in the constitutive relation according to the experimentally obtained mechanical properties. This algorithm merges the Broydon–Fletcher–Goldfarb–Shanno search into a genetic algorithm framework as a basic operator in order to enhance the local search capability. The proposed hybrid algorithm not only can reduce the iterative times greatly but can abolish the limitation of initial parameter values. Nonlinear material characteristic curve-fitting was carried out using the proposed algorithm and other existing approaches. And the comparison results show this algorithm is accurate and effective. The numerical simulation and experimental study of viscoelastic cantilever beam also indicates that the finite element formulation and the calculative viscoelastic model parameters are reliable. The proposed optimization method can be extended to further complex parameter estimation researches.     

非线性函数的混沌优化方法比较研究

已有的混沌优化方法几乎都是利用Logistic映射作为混沌序列发生器，而Logistic映射产生的混沌序列的概率密度函数服从两头多、中间少的切比雪夫型分布，不利于搜索的效率和能力。为此，首先根据Logistie映射混沌轨道点密度函数的特点，建立改进的混沌-BFGS混合优化算法。之后，考虑到Kent映射混沌轨道点密度为均匀分布，建立了基于Kent映射的混沌-BFGS混合优化算法。然后对五种混合优化方法——不加改进的和改进的基于Logistic映射的混沌-BFGS法，基于Kent映射的混沌-BFGS法，Monte Carlo试验-BFGS法，网格-BFGS法进行了研究，分别对3个低维和2个高维非线性复杂测试函数进行优化计算，对它们的全局优化计算效率和寻优能力做了比较，并探讨了混合优化方法全局优化性能差异的原因。结果表明，混沌优化方法是与Monte Carlo方法类似的一种随机性试验优化方法。而且，这类优化方法的计算性能至少与以下因素有关：混沌／随机序列的统计性质，优化问题全局最优点位置。     

A combinatorial algorithm for the discrete optimization of structures

The definition of local optimum solution of the discrete optimization is first given, and then a comprehensive combinatorial algorithm is proposed in this paper. Two-level optimum method is used in the algorithm. In the first level optimization, an approximate local optimum solution is found by using the heuristic algorithm, relative difference quotient algorithm, with high computational efficiency and high performance demonstrated by the performance test of random samples. In the second level, a mathematical model of (-1, 0, 1) programming is established first, and then it is changed into (0, 1) programming model. The local optimum solution X^* will be from the (0, 1) programming by using the delimitative and combinatorial algorithm or the relative difference quotient algorithm. By this algorithm, the local optimum solution can be obtained certainly, and a method is provided to judge whether or not the approximate optimum solution obtained by heuristic algorithm is an optimum solution. The above comprehensive combinatorial algorithm has higher computational efficiency.Project supported by Natural Science Foundation of Shandong Province     

A COMBINAT0RIAL ALGORITHM FOR THE DISCRETE OPTIMIZATION OF STRUCTURES

I.Intr0ducti0nAmajorithofthestructuraloptimumproblemsarediscreteonesinengineeringpractice.Becauseofthebasicreason,namelythediscontinuityofdesignvariables,thediscreteoptimizationhastwoprominentdifficulties:(l)Themodelsofdiscreteoptimizationsarenonconvexpro…     

工程结构优化的进化策略-高斯过程协同优化方法

针对采用仿生全局优化方法进行复杂工程结构优化时数值计算量浩大导致的计算代价过高的公开问题,将自适应协方差矩阵进化策略(CMAES)全局优化算法、高斯过程(GP)机器学习技术与有限元方法相结合,提出了基于自适应协方差矩阵进化策略-高斯过程协同优化算法(CMAES-GP)的结构优化方法。该方法利用全局寻优性好且寻优效率高的CMAES算法进行全局最优搜索,当搜索进入局部寻优阶段时,采用回归性能优秀的GP模型对适应度函数进行动态拟合,进而利用GP模型替代有限元分析进行个体适应度评价,以减小局部寻优阶段的有限元重分析次数,从而实现有效降低工程结构优化计算代价的目的。算例研究表明,与传统结构优化方法相比较,本文方法具有全局性好、计算效率高的优点。     

Fruit fly optimization algorithm based fractional order fuzzy-PID controller for electronic throttle

By adding an electronic throttle and a torque sensor to an engine, it is potentially possible to improve emissions and fuel economy while preserving the torque response of a conventional engine. To do so effectively, however, requires the use of proper control strategy for electronic throttle. In this paper, a kind of fractional order fuzzy PID controller is proposed and it is applied to an electronic throttle. An efficient way to tune fractional order fuzzy PID controller parameters is proposed using a fruit fly optimization algorithm (FOA), which treats the controller parameters tuning as an optimization problem with a proper fitness function. The obtained simulation results show the effective performance of the proposed method.     

基于差分进化和RBF响应面的混合优化算法

针对气动优化等昂贵优化问题,提出了一种基于差分进化和RBF响应面的混合优化算法HSADE,该方法结合了差分进化算法的强全局寻优能力和RBF响应面方法的快速局部搜索能力,能够同时有效地提高算法的局部搜索效率和全局寻优能力.对各子算法中的策略和逻辑进行了多项改进,提出和应用了基于双败淘汰赛的竞赛赛制和参数自适应等改进策略.对HSADE使用多个典型算例进行了测试,并横向对比了NSGA-II,MOPSO和多目标差分进化算法.测试结果表明,在大多数问题中HSADE在以世代距离表征的局部搜索效率和以超体积比表征的全局寻优能力两项指标上都优于其他算法,证实了以上混合策略及算法改进的有效性.将该算法应用于一个翼型优化问题和一个二维超声速喷管膨胀面优化问题,并横向对比未经改良的差分进化算法DE和另一种混合算法NARSGA,结果表明在接近1 000次的函数评估下,HSADE能相对其他算法进一步对翼型减阻0.5 count,在喷管优化中HSADE得到的结果也好于其他两种算法,表明该方法具有较强工程应用价值.     

Low-thrust trajectory optimization for multiple target bodies tour mission

Spacecraft science missions to planets or asteroids have historically visited only one or several celestial bodies per mission. The research goal of this paper is to create a trajectory design algorithm that generates trajectory allowing a spacecraft to visit a significant number of asteroids during a single mission. For the problem of global trajectory optimization, even with recent advances in low-thrust trajectory optimization, a full enumeration of this problem is not possible. This work presents an algorithm to traverse the searching space in a practical fashion and generate solutions. The flight sequence is determined in ballistic scenario, and a differential evolution method is used with constructing a three-impulse transfer problem, then the local optimization is implemented with low-thrust propulsion on the basis of the solutions of impulsive trajectories. The proposed method enables trajectory design for multiple asteroids tour by using available low thrust propulsion technology within fuel and time duration constraints.     

A new design method for adaptive IIR system identification using hybrid particle swarm optimization and gravitational search algorithm

Design of adaptive infinite impulse response (IIR) filter is the process of utilizing adaptive algorithm to iteratively determine the filter parameters to obtain an optimal model for the unknown plant based on minimizing the error cost function. However, the error cost surface of IIR filter is generally nonlinear, non-differentiable and multimodal. Hence, an efficient global optimization technique is required to minimize the error cost objective. A novel hybrid particle swarm optimization and gravitational search algorithm (HPSO–GSA) is proposed in this paper for IIR filter design. The proposed HPSO–GSA updates particle positions through obeying the influence of gravity acceleration in GSA and receiving direction of cognitive memory and social sharing information from PSO by means of coevolutionary strategy. The effect of key parameters on the performance of the proposed algorithm is firstly studied, and the proper parameters in HPSO–GSA are established using five benchmark plants along with the same-order model. The simulation studies have been performed for the performance comparison of eight algorithms such as PSO, GSA, QPSO, DPSO, FO-DPSO, GAPSO, PSOGSA and the proposed HPSO–GSA for unknown IIR system identification with the same-order and reduced-order filters. Simulation results show that the proposed algorithm has advantages over PSO, GSA and other PSO-based variants in terms of the convergence speed and the MSE levels.