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.     

基于自适应子种群和动态反向学习的改进鸡群算法

针对鸡群算法(Chicken swarm optimization,CSO)求解复杂高维问题收敛精度低、容易陷入局部极值等问题,提出了一种基于自适应子种群和动态反向学习的改进鸡群(ICSO)算法.根据鸡群算法迭代进化进程,自适应确定公鸡种群规模大小,并据此将母鸡种群和小鸡分成若干个子种群;设计进化停滞判定机制,并引入动态反向学习因子以改进算法个体更新方式,有效保持鸡群样本多样性和算法全局深度搜索能力.典型测试函数仿真实验结果表明,与SFLA算法、PSO等智能优化算法相比,ICSO算法具有更高的收敛精度和更优的复杂函数优化能力.     

基于精英区域学习的多种群自适应的差分进化算法

为了进一步提高差分进化算法的收敛速度、算法精度和稳定性,采用多种群技术来增加算法收敛速度和降低复杂度;利用精英区域学习策略来对算法的全局搜索能力和算法精度进一步提升,引进自适应免疫搜索策略,以实现自适应修正差分算法的变异因子和交叉因子。通过五个测试函数,把本文算法与最新文献中的算法进行对比,表明算法在收敛速度、精度和高维问题寻优能力方面的优越性。     

一种多种群综合学习粒子群优化算法

针对综合学习算法(Comprehensive learning particle swarm optimization,CLPSO)在解决全局优化问题时精度不高且收敛速度慢的问题,提出一种多种群综合学习算法(MS_CLPSO).该算法将传统粒子群算法的社会部分引入CLPSO算法,有效提高了算法的收敛速度和局部开采能力;同时,为扩大粒子的空间搜索范围,算法引入多种群策略,提高了算法全局勘探能力;并针对可能陷入局部极值的粒子,采用全局学习策略更新学习样本,增加了种群中粒子多样性.实验结果表明,在处理单峰和多峰标准测试函数中,MSCLPSO算法有效提高了CLPSO算法的精度和收敛速度.     

非线性0-1规划问题的元胞灰狼优化算法

针对非线性0-1规划求解问题,基于元胞自动机原理和改进的灰狼算法,提出一种元胞灰狼优化算法.首先,为了避免基本灰狼算法种群分布的随机性问题,利用佳点集理论对灰狼种群进行初始化,增强算法种群的多样性,提高算法的全局收敛速度;其次,针对基本灰狼算法的开发和探索能力平衡能力差的问题,利用自适应精英学习策略分别对算法中的参数α、灰狼与猎物的距离进行修正,实现灰狼算法的全局搜索速度和开发探索能力的最优均衡性;最后,将元胞自动机的演化规则与次优解β灰狼位置以及第三优解δ灰狼位置进行更新,利用元胞及其邻居增强搜索过程的多样性和分布性,实现灰狼算法的全局优化能力;并选用14个典型的非线性0-1规划问题算例进行仿真解算,并将解算结果与其它算法进行比较,结果表明:该算法对大规模复杂问题求解的平均运行时间少10%左右,且具有较快的收敛速度、较多的最优解集和较好的全局寻优能力.     

改进种群多样性的双变异差分进化算法

差分进化算法(DE)是一种基于种群的启发式随机搜索技术,对于解决连续性优化问题具有较强的鲁棒性.然而传统差分进化算法存在种群多样性和收敛速度之间的矛盾,一种改进种群多样性的双变异差分进化算法(DADE),通过引入BFS-best机制(基于排序的可行解选取递减策略)改进变异算子"DE/current-to-best",将其与DE/rand/1构成双变异策略来改善DE算法中种群多样性减少的问题.同时,每个个体的控制参数基于排序自适应更新.最后,利用多个CEC2013标准测试函数对改进算法进行测试,实验结果表明,改进后的算法能有效改善种群多样性,较好地提高了算法的全局收敛能力和收敛速度.     

一种求解化工动态优化问题的改进磷虾觅食优化算法

智能算法原理简单、容易实现,且具有良好的全局收敛能力,近年来被广泛应用于化工过程的动态优化问题.提出一种改进的磷虾觅食优化算法求解化工动态优化问题.该算法通过跟踪磷虾种群的变化来更新速度因子,提高收敛速度;引入自适应柯西变异,增强了算法跳出局部最优值的能力.针对化工动态优化问题,首先通过控制向量参数化方法将其转化为非线性规划问题,并引入变时间区间分布法来优化区间划分,然后利用改进算法进行求解.最后,将改进算法应用于多个化工动态优化问题中,仿真结果表明,该算法具有良好的可行性.     

基于云自适应遗传算法的K-means聚类分析

现有的基于遗传算法的K-means聚类算法,利用遗传算法的全局优化性提高了K-means算法的寻优能力,收敛速度却过慢.为了解决上述问题,提出基于云自适应遗传算法的K-means聚类算法,利用云模型云滴的随机性和稳定趋向性设计遗传算法的交叉和变异概率,并在进化过程中引入K均值算子,以克服算法收敛速度过慢的问题.实验比较表明,算法具有较好的全局优化性,且收敛速度较快,提高了聚类算法解决物流管理中数据聚类工作的能力.     

采用复合规则约束的多种群自适应进化算法

针对种群固定的进化算法容易使个体集中分布在局部区域,不利于处理大尺度空间和多峰类型的优化问题,提出了一种多种群分布并且动态变化的种群自适应进化算法.采用Logistic模型模拟多个种群在有限资源下的竞争关系,设计了稳定性规则、熵规则和精英规则以确定不同种群的Logistic模型参数,从而控制种群数量的变化.同时,算法引入了算术内插和外插两种交叉算子,使得各个种群依据自身类型来缩小或扩展搜索空间.此外,算法还通过周期性的调整规则重新构建种群和分配资源.通过5组大尺度和多峰优化问题的测试结果表明,所提的种群自适应方法能够有效改善算法的寻优性能,在达到同等优化水平时所提算法消耗的函数调用次数为对比算法的61.08%～91.55%.     

免疫逃避型粒子群优化算法

针对基本粒子群优化算法容易陷入局部极值的缺陷,提出了一种免疫逃避型粒子群优化算法.其基本思想是将初始粒子群划分为寄生与宿主两个种群以模拟生物寄生行为,对寄生种群的粒子采用精英学习策略,对宿主群的粒子采用探索策略,再引入免疫系统的高频变异对寄生群采用相应的免疫逃避机制,以增强群体逃离局部极值、提高算法的全局寻优能力.采用标准测试函数的实验结果表明,该算法在收敛速度和求解精度方面均有显著改进.     

CFD-based optimization of fuel injection strategies in a diesel engine using an adaptive gradient method

A computationally efficient computational fluid dynamics (CFD)-based optimization method with the capability of finding optimal engine operating conditions with respect to emissions and fuel consumption has been developed. The approach taken uses a steepest descent method for an adaptive cost function, where the line search is performed with a backtracking algorithm. The backtracking algorithm utilizes quadratic and cubic polynomials to accelerate the convergence, and the initial backtracking step employs an adaptive step size mechanism which depends on the steepness of the search direction. The adaptive cost function is based on the penalty method such that the penalty term is stiffened after every line search. The engine simulations are performed with a KIVA-3-based CFD code which is equipped with well-established spray, combustion and emission models. The application of this optimization tool is demonstrated for a non-road, medium-speed DI diesel engine which, for these simulations, utilizes a multi-orifice, asynchronous injection system. It has been demonstrated that this new injection method has a large potential for reducing emissions while maintaining a low fuel consumption. In addition, this optimization approach is computationally very efficient when good enough initial values are available.     

AN ADAPTIVE NONMONOTONIC TRUST REGION METHOD WITH CURVILINEAR SEARCHES

In this paper,an algorithm for unconstrained optimization that employs both trustregion techniques and curvilinear searches is proposed.At every iteration,we solve thetrust region subproblem whose radius is generated adaptively only once.Nonmonotonicbacktracking curvilinear searches are performed when the solution of the subproblem isunacceptable.The global convergence and fast local convergence rate of the proposedalgorithms are established under some reasonable conditions.The results of numericalexperiments are reported to show the effectiveness of the proposed algorithms.     

非线性等式约束优化问题的仿射信赖域方法

提出非线性等式和有界约束优化问题的结合非单调技术的仿射信赖域方法. 结合信赖域方法和内点回代线搜索技术, 每一步迭代转到由一般信赖域子问题产生的回代步中且满足严格内点可行条件. 在合理的假设条件下, 证明了算法的整体收敛性和局部超线性收敛速率. 最后, 数值结果表明了所提供的算法具有有效性.     

Approximation of the distribution of convergence times for stochastic global optimisation

How long should we run a stochastic global optimisation algorithm such as simulated annealing? How should we tune such an algorithm? This paper proposes an approach to the study of these questions through successive approximation of a generic stochastic global optimisation algorithm with a sequence of stochastic processes, culminating in a backtracking adaptive search process. Our emerging understanding of backtracking adaptive search can thus be used to study the original algorithm. The first approximation, the averaged range process, has the same expected number of iterations to convergence as the original process.     

一簇非线性等式约束优化问题的过滤线搜索修正正割方法

本文提供了一簇新的过滤线搜索修正正割方法求解非线性等式约束优化问题.新算法簇的特点是:用修正正割算法簇中的一个算法获得搜索方向,回代线搜索技术得到步长,过滤准则用来决定是否接受步长,引入二阶校正技术减少不可行性并克服Maratos效应.在合理的假设条件下,分析了算法的总体收敛性.并证明了,通过附加二阶校正步,算法簇克服了Maratos效应,并二步Q-超线性收敛到满足二阶充分最优条件的局部解.数值结果表明了所提供的算法具有有效性.     

Adaptive nonmonotone line search method for unconstrained optimization

In this paper, an adaptive nonmonotone line search method for unconstrained minimization problems is proposed. At every iteration, the new algorithm selects only one of the two directions: a Newton-type direction and a negative curvature direction, to perform the line search. The nonmonotone technique is included in the backtracking line search when the Newton-type direction is the search direction. Furthermore, if the negative curvature direction is the search direction, we increase the steplength under certain conditions. The global convergence to a stationary point with second-order optimality conditions is established. Some numerical results which show the efficiency of the new algorithm are reported.      

A new trust region method with adaptive radius

In this paper we develop a new trust region method with adaptive radius for unconstrained optimization problems. The new method can adjust the trust region radius automatically at each iteration and possibly reduces the number of solving subproblems. We investigate the global convergence and convergence rate of this new method under some mild conditions. Theoretical analysis and numerical results show that the new adaptive trust region radius is available and reasonable and the resultant trust region method is efficient in solving practical optimization problems. The work was supported in part by NSF grant CNS-0521142, USA.     

基于正弦控制因子的Lateral变异鲨鱼优化算法

针对传统鲨鱼优化算法在求解高维目标函数时,易早熟收敛,陷入局部最优的缺陷.提出一种基于正弦控制因子的Lateral变异鲨鱼优化算法.通过正弦曲线的特性和自适应惯性权重,改善了传统鲨鱼优化算法中由于随机选取控制因子数值大小可能导致算法在迭代后期全局搜索能力降低的问题,提高了算法在迭代后期的全局收敛能力,并对最佳鲨鱼位置引入Lateral变异策略,加强了算法跳出局部最优的可能性.改进后的算法对多个shifted单峰,多峰以及固定维测试函数进行求解,实验结果表明,对比多种不同优化算法而言,本文所提LSSO算法具有更高的收敛精度和搜索速度.     

An affine scaling interior trust-region method combining with line search filter technique for optimization subject to bounds on variables

This paper proposes and analyzes an affine scaling trust-region method with line search filter technique for solving nonlinear optimization problems subject to bounds on variables. At the current iteration, the trial step is generated by the general trust-region subproblem which is defined by minimizing a quadratic function subject only to an affine scaling ellipsoidal constraint. Both trust-region strategy and line search filter technique will switch to trail backtracking step which is strictly feasible. Meanwhile, the proposed method does not depend on any external restoration procedure used in line search filter technique. A new backtracking relevance condition is given which is weaker than the switching condition to obtain the global convergence of the algorithm. The global convergence and fast local convergence rate of this algorithm are established under reasonable assumptions. Preliminary numerical results are reported indicating the practical viability and show the effectiveness of the proposed algorithm.     

On the final steps of Newton and higher order methods

The Newton method is one of the most used methods for solving nonlinear system of equations when the Jacobian matrix is nonsingular. The method converges to a solution with Q-order two for initial points sufficiently close to the solution. The method of Halley and the method of Chebyshev are among methods that have local and cubic rate of convergence. Combining these methods with a backtracking and curvilinear strategy for unconstrained optimization problems these methods have been shown to be globally convergent. The backtracking forces a strict decrease of the function of the unconstrained optimization problem. It is shown that no damping of the step in the backtracking routine is needed close to a strict local minimizer and the global method behaves as a local method. The local behavior for the unconstrained optimization problem is investigated by considering problems with two unknowns and it is shown that there are no significant differences in the region where the global method turn into a local method for second and third order methods. Further, the final steps to reach a predefined tolerance are investigated. It is shown that the region where the higher order methods terminate in one or two iteration is significantly larger than the corresponding region for Newton’s method.