基于Lévy分布的柔软自适应演化采样算法

已经有相关工作将演化思想引入采样算法中,并结合 Lévy 分布提出了自适应的采样算法。针对 Lévy 分布的参数设 置和“厚尾”特性的关系进行了研究,改进了基于 Lévy 分布的演化采样算法,通过设置该分布的参数 ? 值为 1.0,1.3,1.7, 2.0,分别对应四种转移概率分布,从而增加了生成的候选样本的多样性。理论分析和实验表明,改进算法在收敛速率和精度 上优于基于高斯分布,柯西分布,对称指数分布的演化采样算法和其他自适应的演化采样算法。     

A space search optimization algorithm with accelerated convergence strategies

Evolutionary algorithms (EAs), which have been widely used to solve various scientific and engineering optimization problems, are essentially stochastic search algorithms operating in the overall solution space. However, such random search mechanism may lead to some disadvantages such as a long computing time and premature convergence. In this study, we propose a space search optimization algorithm (SSOA) with accelerated convergence strategies to alleviate the drawbacks of the purely random search mechanism. The overall framework of the SSOA involves three main search mechanisms: local space search, global space search, and opposition-based search. The local space search that aims to form new solutions approaching the local optimum is realized based on the concept of augmented simplex method, which exhibits significant search abilities realized in some local space. The global space search is completed by Cauchy searching, where the approach itself is based on the Cauchy mutation. This operation can help the method avoid of being trapped in local optima and in this way alleviate premature convergence. An opposition-based search is exploited to accelerate the convergence of space search. This operator can effectively reduce a substantial computational overhead encountered in evolutionary algorithms (EAs). With the use of them SSOA realizes an effective search process. To evaluate the performance of the method, the proposed SSOA is contrasted with a method of differential evolution (DE), which is a well-known space concept-based evolutionary algorithm. When tested against benchmark functions, the SSOA exhibits a competitive performance vis-a-vis performance of some other competitive schemes of differential evolution in terms of accuracy and speed of convergence, especially in case of high-dimensional continuous optimization problems.     

Multidimensional mutations in evolutionary algorithms based on real-valued representation

This work is focused on the fact that the most probable distance of mutated points in multi-dimensional Gaussian and Cauchy mutations is not in a close neighborhood of the origin, but at a certain distance from it. In the case of the Gaussian mutation, this distance is proportional to the norm of the standard deviation vector and increases with the landscape dimension. This may cause a decrease in the sensitivity of the evolutionary algorithm to narrow peaks when the landscape dimension increases, but, simultaneously, it strengthens the exploration property of the algorithm. Moreover, the influence of the reference frame orientation on the effectiveness of the non-spherical multi-dimensional Cauchy mutation is analyzed using simulation experiments. Four multi-dimensional mutations (Gaussian, modified Gaussian, non-spherical and spherical Cauchy mutations) are applied to two classes of evolutionary algorithms based on real-valued representation, i.e. Galar's evolutionary search with soft selection and evolutionary programming. A comparative analysis is provided for convergence to the local optimum, sensitivity to narrow peaks, saddle crossing and symmetry problems.     

自适应混合变异的蛙跳算法

蛙跳算法是一种受自然界生物现象启发产生的群体进化算法,计算速度快,寻优能力强,但局部搜索能力较弱,容易陷入早熟收敛。针对其缺点,结合高斯变异和柯西变异的优点,提出了一种改进的混合蛙跳算法。改进后的算法收敛速度加快,在一定程度上避免陷入局部最优,提高了蛙跳算法解决复杂函数问题的能力。实验验证了其有效性。     

具有组合变异策略的回溯搜索优化算法

针对回溯搜索优化算法收敛速度慢和易陷入局部最优的缺陷,提出了一种基于组合变异策略的改进回溯搜索优化算法。为了提高历史种群的多样性并扩大算法的搜索空间,在算法迭代过程中采用柯西种群生成策略,利用柯西分布尺度系数生成历史种群;引入基于混沌映射和伽玛分布的组合变异策略,在一定概率下对较差个体进行变异生成质量较好的个体;对新种群中越界个体采用越界处理策略,确保算法在预定的搜索空间内搜索。选取了11个标准测试函数,在低维和高维状态下进行数值仿真,并与3种表现良好的算法进行比较,结果表明该改进算法在收敛速度和收敛精度上有很大优势。     

Harris Hawk Optimization Algorithm Based on Cauchy Distribution Inverse Cumulative Function and Tangent Flight Operator

Harris Hawk Optimization (HHO) algorithm is a new population-based and nature-inspired optimization paradigm, which has strong global search ability, but its diversified local search strategies easily make it fall into local optimum. In order to enhance its search mechanism and speed of convergence, an new improved HHO algorithm based on the inverse cumulative function operator of Cauchy distribution and tangent flight operator was proposed. The proposed two operators are used as scale factors to control the step size. The walk path of Cauchy inverse cumulative integral function shows that its trajectory step length is relative to the average, which can further enhance the search stability of the algorithm. The Tangent flight has the function of balanced exploitation and exploration, and enhances the convergence ability of the algorithm. In order to verify the performance of the proposed algorithm, the 30 benchmark functions of the 2017 Institute of Electrical and Electronic Engineers (IEEE) Conference on Evolutionary Computation (CEC2017) and two practical engineering design problems are adopted to carry out the simulation experiments. On the other hand, the covariance matrix adaptation evolutionary strategies (CMA-ES), arithmetic optimization algorithm (AOA), butterfly optimization algorithm (BOA), bat algorithm (BA), whale optimization algorithm (WOA), sine cosine algorithm (SCA), and the proposed HHO algorithms were used for comparison experiments. Simulation results show that the proposed the Cauchy-distribution and Tangent-Flight Harris Hawk Optimization (CTHHO) Algorithm has strong optimization capability.

     

混合柯西变异和均匀分布的蝗虫优化算法

由于位置更新公式存在局部开发能力较强而全局探索能力较弱的缺陷,导致蝗虫优化算法(GOA)易陷入局部最优以及早熟收敛,对此,提出一种混合柯西变异和均匀分布的蝗虫优化算法(HCUGOA).受柯西算子和粒子群算法的启发,提出具有分段思想的位置更新方式以增加种群多样性,增强全局探索能力;将柯西变异算子与反向学习策略相融合,对最...     

一种新的求解函数优化问题的快速演化算法

提出一种新的求解函数优化的快速演化算法;新算法的特征是引入一种基于高斯变异和Cauchy变异的混合自适应变异算子,并作为算法的唯一遗传算子;提出多父体变异的群体爬山搜索策略;采用随机排序选择策略,克服了经典算法易于陷入局部最优解的常见弊病;新算法具有保持群体的多样性、全概率收敛、淘汰压力小、子空间搜索、快速收敛、评价次数少等特性;通过7个标准测试函数测试结果表明,新算法在所有的测试函数中体现出很好的性能,具有稳定、高效和快速等特点.     

柯西种群分布的自适应范围粒子群优化算法

为了提高粒子群优化算法的求解性能,提出了一种具有柯西种群分布的自适应范围搜索的粒子群优化算法(ARPSO/C)。该算法在种群服从柯西分布的假设下,在每一次迭代中利用个体分布的中位数和尺度参数来自适应地调整种群的搜索范围,从而在局部搜索和全局搜索之间达到了一个很好的平衡。最后的数值实验结果表明：与ARPSO和PSO算法相比,该算法收敛速度得到了显著提高,并且能够有效地克服早熟现象。     

基于改进粒子群优化算法的IIR数字滤波器设计

针对粒子群优化(PSO)算法存在早熟收敛问题,提出了一种改进算法——带有柯西扰动的重分布粒子群优化(RPSO)算法,并应用于IIR数字滤波器的优化设计。RPSO在检测到粒子群早熟收敛时,自动触发粒子重分布机制,帮助粒子逃离局部收敛区域,同时在迭代过程中对种群的全局最优位置施加柯西扰动以保持种群的多样性。仿真实验结果表明,在对IIR数字滤波器设计时,RPSO算法的性能优于粒子群、量子粒子群以及基于混沌变异的粒子群优化等算法。     

柯西变异和自适应权重优化的蝴蝶算法

针对基本蝴蝶优化算法（Butterfly Optimization Algorithm,BOA）存在的收敛精度较低、容易陷入局部最优解的问题,提出柯西变异和自适应权重优化的蝴蝶算法（Cauchy variation and adaptive Weight Butterfly Optimization Algorithm,CWBOA）。通过在全局位置更新处引入柯西分布函数进行变异,在局部位置更新处引入自适应权重因子,改进了蝴蝶算法的局部搜索能力;并且引入动态切换概率[p]来权衡全局探索与局部开发过程的比重。改进的算法通过对多个单峰、多峰和固定测试维度的函数进行求解,结果表明,CWBOA对大多数测试函数有更好的求解精度、速度和稳定性。     

结合质心思想和柯西变异策略的粒子群优化算法

针对基本粒子群优化（PSO）算法收敛精度低、容易陷入局部最优的问题,提出了一个结合质心思想和柯西变异策略的粒子群优化算法。首先,在粒子的初始化阶段采用混沌初始化策略,以提高初始粒子的均匀分布能力;其次,为了提高粒子群的收敛速度和寻优能力,引入了质心的概念,通过计算获得种群中所有粒子所构成的全局质心和所有个体极值构成的个体质心,使得粒子群内部可以实现充分的信息共享;为避免粒子陷入局部最优解,在粒子群算法中引入了柯西变异运算对当前最优粒子进行扰动,并依据柯西变异运算的规律,适应性地调整扰动步长,该算法以群体多样性为依据,动态调整惯性权重;最后,使用7个经典的测试函数对算法进行验证,通过函数运行结果的均值、方差和最小值能够表明,新算法在收敛精度上有较好的优越性。     

Extending standard evolutionary programming with self-adaptive stable distributions

Applications in evolutionary programming have suggested the use of further stable probability distributions, such as Cauchy and Lévy, in the random process associated with the mutations, as an alternative to the traditional, also stable, normal distribution. This work goes further along the encouraging results of the latter, by extending them in a self-adaptive way, with algorithms that are in tune with the standard lineage of evolutionary programming. Evaluations that rely upon standard analytical benchmarking functions and comparative performance tests between them were carried out in respect to the baseline defined by the standard evolutionary programming algorithm that relies on normal distribution. Additional comparative studies were made in respect to various self-adaptive approaches, also proposed herein, and a method drawn from the literature. The results lead to numerical and statistical superiority of the more general stable distribution based approach, when compared with the baseline, and is unclear in regard to the method drawn from the literature, possibly due to distinct implementation details.     

自适应柯西蜂群及其收敛性分析

针对人工蜂群算法容易陷入局部最优的缺陷,提出一种自适应柯西变异人工蜂群算法.该算法引入自适应因子来扩大蜂群的搜索范围,并利用柯西分布的特点对全局进行搜索,提高了蜂群搜索的普遍性.然后利用随机过程理论,对自适应柯西变异人工蜂群算法进行了理论分析,论证了该算法的收敛性.最后将改进的人工蜂群算法应用到风电功率短期预测模型参数的优化中,与单一支持向量机模型比较,表明该方法拟合精度更高.     

基于动态全局搜索和柯西变异的花授粉算法

针对基本花授粉算法（FPA）收敛速度慢、寻优精度低以及容易陷入局部最优的缺点,提出了一种基于动态全局搜索和柯西变异的花授粉算法DCFPA。利用混沌映射增强花粉种群初始分布的随机性和均匀性,在全局授粉过程中,引入全局平均最优花粉位置和动态权重递减因子共同实现花粉个体位置的更新,牵引算法朝着正确的搜索方向进行,避免算法早熟收敛,最后利用Cauchy变异,增加种群多样性,帮助算法跳出局部最优。对6个测试函数进行仿真实验表明,DCFPA算法比FPA具有更好的全局优化能力,提升了算法的收敛速度与求解精度;与相关的改进算法比较结果也表明,DCFPA整体上也具有更好的优化性能。     

基于混合策略改进的鲸鱼优化算法

针对标准WOA算法初始种群分布不均、收敛速度较慢、全局搜索能力弱且易陷入局部最优等问题,提出一种混合策略改进的鲸鱼优化算法。采用Sobol序列初始化种群以使初始解在解空间分布更均匀;通过非线性时变因子和惯性权重平衡并提高全局搜索及局部开发能力,并结合随机性学习策略增加迭代过程中种群的多样性;引入柯西变异提升算法跳出局部最优的能力。通过对12个基准函数和一个水资源需求预测模型的参数估计进行优化实验,结果表明,基于混合策略改进的鲸鱼优化算法在寻优精度及收敛速度上均有明显提升。     

基于混合凸迁移和趋优柯西变异的对偶生物地理学优化算法

通过分析生物地理学优化算法(BBO)性能的不足,提出了一种基于混合凸迁移和趋优柯西变异的对偶生物地理学优化算法(DuBBO).在迁移算子中,采用动态的混合凸迁移算子,使算法能够快速地向最优解方向收敛;在变异机制中,采用趋优变异策略,并加入了柯西分布随机数帮助算法跳出局部最优解;最后将对偶学习策略集成到算法中,加快了算法收敛速度并提升了搜索能力.在23个benchmark函数上的实验结果证明了提出的三种改进策略的有效性和必要性.最后将DuBBO与BBO以及另外六种优秀的改进算法进行对比.实验结果表明,DuBBO在整体性能上最好、收敛速度更快、收敛精度更高.     

基于柯西-高斯动态消减变异的果蝇优化算法研究

针对果蝇优化算法易陷入局部极值收敛速度减慢的不足,结合柯西变异和高斯变异的各自优点,提出了变异效能系数和柯西-高斯动态消减变异因子等概念,进而提出了一种柯西-高斯动态消减变异方法,将该方法应用于改进果蝇优化算法,提出了一种基于柯西-高斯动态消减变异的果蝇优化算法。该算法兼顾了全局探索和局部开发两个特性,丰富了种群的多样性,有效地消除了易陷入局部极值的弊端,提高了算法的收敛速度。仿真实验采用经典函数用例和实际工程用例进行验证,结果表明该算法的求解速度和精度更高,稳定性更好。     

一种更简化而高效的粒子群优化算法

针对基本粒子群优化(basic particle swarm optimization,简称bPSO)算法容易陷入局部极值、进化后期的收敛速度慢和精度低等缺点,采用简化粒子群优化方程和添加极值扰动算子两种策略加以改进,提出了简化粒子群优化(simple particle swarm optimization,简称sPSO)算法、带极值扰动粒子群优化(extremum disturbed particle swarm optimization,简称tPSO)算法和基于二者的带极值扰动的简化粒子群优化(ext     

一种自适应多策略行为粒子群优化算法

针对粒子群优化算法收敛速度慢、局部搜索能力差等缺点,提出一种自适应多策略行为粒子群优化算法.算法中每个粒子拥有4种行为进化策略,在迭代过程中通过计算每种进化策略的立即价值、未来价值和综合奖励来决定粒子的进化行为,并通过策略行为概率变异算法提升个体寻优速度或避免陷入局部最优解.在经典的基准测试函数上,对新算法与其他7个群智能进化算法的测试结果进行比较分析,结果表明所提出算法具有很好的求解精度和收敛速度,尤其适合应用于一些高维优化问题.