多策略协方差矩阵学习差分进化算法

针对差分进化算法（DE）存在的早熟收敛和搜索停滞的问题,提出了多策略协方差矩阵学习的差分进化算法。通过协方差矩阵建立特征坐标系,通过在特征坐标系中执行变异和交叉操作,来充分利用当前种群的分布信息以及各变量之间的关系,保证种群能朝着全局最优解的方向进化;根据历史进化信息来选择变异策略的方式使得个体能选择当前最合适的变异策略,提高找到最优解的概率;交叉概率的自适应也一定程度上平衡算法的全局探索能力和局部探索能力。对算法的收敛性进行了证明,同时将算法在CEC2017测试集上进行了仿真实验,并将实验结果跟其他优秀的差分进化算法进行了对比,对比结果表明了该算法的有效性。     

基于多代种群进化信息改进的差分进化算法研究

差分进化算法是进化算法中一种性能较为优良的全局数值优化算法,已在人工智能、信号处理等方面取得广泛应用,但当前研究往往仅考虑进化过程中某一代种群的分布信息,而忽略进化过程中多代种群累积的分布信息,造成信息利用不充分。借助自适应协方差矩阵进化策略的思想,充分利用进化过程中累积的种群分布信息,同时,由于自适应协方差矩阵存在收敛早熟、易陷入局部最优的缺点,先后对变异和交叉操作进行相应改进,以平衡算法的全局搜索能力和局部搜索能力。首先,根据种群中个体适应度值进行排序,由余弦函数改进的概率模型计算个体参与变异操作的概率,基向量和差分向量中末端向量根据概率值降序选择,差分向量中起始向量升序选择,从而提高种群的搜索范围;然后,对协方差矩阵进行特征分解,并在由特征向量构建的坐标系中执行交叉操作,该种方式生成的实验向量更接近全局最优解。针对上述改进操作,采用IEEE CEC2014作为评估函数,实验结果表明,相比现有的差分进化改进算法,本改进算法的实验性能提升更为明显。     

融合多种策略的改进粒子群算法

为有效解决粒子群优化算法(Particle Swarm Optimization, PSO)容易陷入局部极值及进化后期收敛速度慢、精度低等缺点, 提出了一种融合多种策略的改进粒子群算法(Improved Particle Swarm Optimization, IPSO). 该算法包括以下4点改进:(1)采取分组控制策略, 按适应度值将种群分为优解组和劣解组, 优解组进行遗传交叉操作, 劣解组进行变异操作; (2)精英策略用来更新种群, 根据适应度值从经过交叉和变异操作后的种群及初始种群中选出前一半粒子作为新种群; (3)改进粒子学习模式, 充分利用种群信息, 以优良种群的均值代替个体最优位置;(4)引入概率控制来控制算法进入交叉和变异操作的概率. 测试函数的仿真结果表明, 与标准PSO及其改进算法相比, IPSO算法能有效兼顾全局探索和局部挖掘能力, 具有收敛速度快、求解精度高、避开局部最优解的优点.     

广义逆向学习方法的自适应差分算法

针对差分算法(differential evolution,DE)在解决高维优化问题时参数设置复杂、选择变异策略困难的现象,提出了广义逆向学习方法的自适应差分进化算法(self-adaptive DE algorithm via generalized opposition-based learning,SDE-GOBL)。利用广义的逆向学习方法(generalized opposition-based learning,GOBL)来进行多策略自适应差分算法(Self-adaptive DE,Sa DE)的初始化策略调整,求出各个候选解的相应逆向点,并在候选解和其逆向点中选择所需要的最优初始种群,然后再进行自适应变异、杂交、选择操作,最后通过CEC2005国际竞赛所提供的9个标准测试函数对SDE-GOBL算法进行验证,结果证明该算法具有较快的收敛速度和较高的求解精度。     

集成协方差矩阵自适应进化策略与差分进化的优化算法

不同智能优化算法在求解优化问题时通常表现出显著的性能差异.差分进化(DE)算法具备较好的全局搜索能力,但存在收敛慢、效率低的不足,协方差矩阵自适应进化策略(CMA–ES)局部搜索能力强,具备旋转不变性,但容易陷入局部最优,因此, DE和CMA–ES之间具有潜在的协同互补能力.针对上述问题,提出了一种集成协方差矩阵自适应进化策略与差分进化的优化算法(CMADE).在CMADE框架中, DE算法负责全局搜索, CMA–ES算法进行局部搜索.通过周期性解交换机制实现CMA–ES和DE两个算法间协同交互和反馈控制.在解交换时,从DE种群中选择优秀个体,利用CMA–ES算法在优秀个体周围进行局部搜索.同时在DE和CMA–ES的混合种群中,综合考虑解的多样性和最优性,选取一定比例的解作为DE算法的新种群进行全局搜索,实现全局搜索与局部搜索的动态平衡.将CMADE算法与CMA–ES, DE, SaDE, jDE, EPSDE, ACODE和SHADE算法在CEC2014标准测试集上进行比较实验.结果表明, CMADE整体性能显著优于其它比较算法.     

一种改进搜索策略的人工蜂群算法

为克服人工蜂群算法原有搜索策略存在探索能力强而开采能力弱的缺点,受差分进化算法的启发,提出了一种新的搜索策略,在种群最优解的附近产生新的候选位置,有助于提高人工蜂群算法的开采能力.同时,为了平衡算法的探索和开采能力,将种群中的个体随机分成两组,每组采用不同的搜索策略同时寻优.对6个基准测试函数进行仿真的结果表明,改进的搜索算法相比基本人工蜂群算法能有效地改善寻优性能,增强算法摆脱局部最优的能力.     

混合蚁群算法及其用于有机物毒性的QSAR研究

设计一种新的混合蚁群算法.该算法以一种新的二进制蚁群算法为基础,混合PBIL(population based incremental learning)算法及遗传算法的交叉操作和变异操作,从而大大提高了种群的多样性及收敛速度,改善全局最优解的搜索能力.通过函数优化测试,表明该算法具有良好的收敛速度和稳定性,最后用于有机物毒性的QSAR研究中,取得较好效果.     

受粒子群和差分进化启发的人工蜂群算法

针对基本人工蜂群算法搜索策略探索能力强而开发能力弱的特点,受粒子群和差分进化思想的启发,提出了两种新的搜索策略：PSO-DE-PABC和PSO-DE-GABC。前者在随机个体附近产生新的候选位置以提高算法的多样性;后者在最优解附近产生新的候选位置以提高算法的收敛速度,并加入差分进化中的差异向量来增加种群的多样性。在此基础上,引入维度因子来控制算法的收敛速度,并且使用一种利用当前种群信息的侦查策略来增强算法的局部搜索能力。通过对10组标准测试函数的实验仿真并与基本ABC、GABC和ABC/best算法相比,结果表明PSO-DE-GABC和PSO-DE-PABC对数值优化具有更高的收敛速度和收敛精度。     

演化信息协助的动态协同随机漂移粒子群优化算法

为了改善随机漂移粒子群算法的群体多样性,通过演化信息的协助,提出动态协同随机漂移粒子群优化（CRDPSO）算法。利用上下文粒子的向量信息,粒子之间的动态协作增加了种群多样性,这有助于提高群体的搜索能力,并使整个群体协同搜索全局最优值。同时在演化过程中的每次迭代,利用二维空间分割树结构来存储算法中的估计解的位置和适应度值,从而实现快速适应度函数逼近。由于适应度函数逼近增强了变异策略,因此变异是自适应且无参数的。通过典型测试函数将CRDPSO算法和差分进化算法（DE）、协方差矩阵适应进化策略算法（CMA-ES）、非重复访问遗传算法（cNrGA）以及三种改进的量子行为粒子群算法（QPSO）进行比较。实验结果表明,不管是对于单峰还是多峰测试函数,CRDPSO的性能均是最优的,证明了该算法的有效性。     

基于混合变异策略的改进差分进化算法及函数优化

针对差分进化算法DE 传统变异策略不能有效平衡全局搜索和局部搜索,并且算 子固定,导致算法早收敛、搜索效率较低。基于DE 变异策略性能,提出一种混合变异策略, 力图平衡算法探索和开发能力,使得前期增强全局搜索,保持种群多样性; 后期偏重局部搜 索,尽快收敛到全局最优值。同时操作算子采用随机正态缩放因子F 和时变交叉概率因子CＲ, 进一步改善算法性能。几个典型Benchmarks 测试函数实验表明: 该改进型差分进化算法能有 效避免早收敛,较好地提高算法的全局收敛能力和搜索效率。     

An improved teaching-learning-based optimization algorithm for numerical and engineering optimization problems

The teaching-learning-based optimization (TLBO) algorithm, one of the recently proposed population-based algorithms, simulates the teaching-learning process in the classroom. This study proposes an improved TLBO (ITLBO), in which a feedback phase, mutation crossover operation of differential evolution (DE) algorithms, and chaotic perturbation mechanism are incorporated to significantly improve the performance of the algorithm. The feedback phase is used to enhance the learning style of the students and to promote the exploration capacity of the TLBO. The mutation crossover operation of DE is introduced to increase population diversity and to prevent premature convergence. The chaotic perturbation mechanism is used to ensure that the algorithm can escape the local optimal. Simulation results based on ten unconstrained benchmark problems and five constrained engineering design problems show that the ITLBO algorithm is better than, or at least comparable to, other state-of-the-art algorithms.     

Differential evolution based on covariance matrix learning and bimodal distribution parameter setting

Differential evolution (DE) is an efficient and robust evolutionary algorithm, which has been widely applied to solve global optimization problems. As we know, crossover operator plays a very important role on the performance of DE. However, the commonly used crossover operators of DE are dependent mainly on the coordinate system and are not rotation-invariant processes. In this paper, covariance matrix learning is presented to establish an appropriate coordinate system for the crossover operator. By doing this, the dependence of DE on the coordinate system has been relieved to a certain extent, and the capability of DE to solve problems with high variable correlation has been enhanced. Moreover, bimodal distribution parameter setting is proposed for the control parameters of the mutation and crossover operators in this paper, with the aim of balancing the exploration and exploitation abilities of DE. By incorporating the covariance matrix learning and the bimodal distribution parameter setting into DE, this paper presents a novel DE variant, called CoBiDE. CoBiDE has been tested on 25 benchmark test functions, as well as a variety of real-world optimization problems taken from diverse fields including radar system, power systems, hydrothermal scheduling, spacecraft trajectory optimization, etc. The experimental results demonstrate the effectiveness of CoBiDE for global numerical and engineering optimization. Compared with other DE variants and other state-of-the-art evolutionary algorithms, CoBiDE shows overall better performance.     

A differential evolution algorithm with intersect mutation operator

This paper proposes a novel differential evolution (DE) algorithm with intersect mutation operation called intersect mutation differential evolution (IMDE) algorithm. Instead of focusing on setting proper parameters, in IMDE algorithm, all individuals are divided into the better part and the worse part according to their fitness. And then, the novel mutation and crossover operations have been developed to generate the new individuals. Finally, a set of famous benchmark functions have been used to test and evaluate the performance of the proposed IMDE. The experimental results show that the proposed algorithm is better than, or at least comparable to the self-adaptive DE (JDE), which is proven to be better than the standard DE algorithm. In further study, the IMDE algorithm has also been compared with several improved Particle Swarm Optimization (PSO) algorithms, Artificial Bee Colony (ABC) algorithm and Bee Swarm Optimization (BSO) algorithm. And the IMDE algorithm outperforms these algorithms.     

求解函数优化的新型差异演化算法*

针对差异演化算法存在早熟收敛和后期求解效率低的缺点,提出一种新型差异演化算法。该算法基于单种群,在演化过程中直接对当前种群进行变异、交叉和选择操作,无须差异演化算法中的中间过渡种群。此外,新型差异演化算法的变异与交叉概率是时变的,其中变异概率随着迭代次数的增加而减小;交叉概率随着迭代次数的增加而增加。对几个典型的测试函数进行仿真实验表明,该算法能够有效避免早熟收敛,改善了差异演化算法的优化性能。     

An evolving surrogate model-based differential evolution algorithm

Differential evolution (DE) is a simple and effective approach for solving numerical optimization problems. However, the performance of DE is sensitive to the choice of mutation and crossover strategies and their associated control parameters. Therefore, to achieve optimal performance, a time-consuming parameter tuning process is required. In DE, the use of different mutation and crossover strategies with different parameter settings can be appropriate during different stages of the evolution. Therefore, to achieve optimal performance using DE, various adaptation, self-adaptation, and ensemble techniques have been proposed. Recently, a classification-assisted DE algorithm was proposed to overcome trial and error parameter tuning and efficiently solve computationally expensive problems. In this paper, we present an evolving surrogate model-based differential evolution (ESMDE) method, wherein a surrogate model constructed based on the population members of the current generation is used to assist the DE algorithm in order to generate competitive offspring using the appropriate parameter setting during different stages of the evolution. As the population evolves over generations, the surrogate model also evolves over the iterations and better represents the basin of search by the DE algorithm. The proposed method employs a simple Kriging model to construct the surrogate. The performance of ESMDE is evaluated on a set of 17 bound-constrained problems. The performance of the proposed algorithm is compared to state-of-the-art self-adaptive DE algorithms: the classification-assisted DE algorithm, regression-assisted DE algorithm, and ranking-assisted DE algorithm.     

混合差分进化算法

为了克服差分进化算法容易出现早熟和收敛速度慢的问题,提出了一种混合差分进化算法.该算法在趋药性差分进化算法(CDE)的基础上,通过对较优个体进行变异操作,维护了种群多样性、避免早熟;通过将较差的个体与较优个体进行杂交,提高了开采能力、加快了收敛速度.基于这两种策略,算法的开采能力与探索能力达到了平衡.用该算法解决标准函数优化问题,并将仿真结果与其他算法进行比较,数值结果表明该文算法具有较快的收敛速度和很强的跳出局部最优的能力.     

A Differential Covariance Matrix Adaptation Evolutionary Algorithm for real parameter optimization

Hybridization in context to Evolutionary Computation (EC) aims at combining the operators and methodologies from different EC paradigms to form a single algorithm that may enjoy a statistically superior performance on a wide variety of optimization problems. In this article we propose an efficient hybrid evolutionary algorithm that embeds the difference vector-based mutation scheme, the crossover and the selection strategy of Differential Evolution (DE) into another recently developed global optimization algorithm known as Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES). CMA-ES is a stochastic method for real parameter (continuous domain) optimization of non-linear, non-convex functions. The algorithm includes adaptation of covariance matrix which is basically an alternative method of traditional Quasi-Newton method for optimization based on gradient method. The hybrid algorithm, referred by us as Differential Covariance Matrix Adaptation Evolutionary Algorithm (DCMA-EA), turns out to possess a better blending of the explorative and exploitative behaviors as compared to the original DE and original CMA-ES, through empirical simulations. Though CMA-ES has emerged itself as a very efficient global optimizer, its performance deteriorates when it comes to dealing with complicated fitness landscapes, especially landscapes associated with noisy, hybrid composition functions and many real world optimization problems. In order to improve the overall performance of CMA-ES, the mutation, crossover and selection operators of DE have been incorporated into CMA-ES to synthesize the hybrid algorithm DCMA-EA. We compare DCMA-EA with original DE and CMA-EA, two best known DE-variants: SaDE and JADE, and two state-of-the-art real optimizers: IPOP-CMA-ES (Restart Covariance Matrix Adaptation Evolution Strategy with increasing population size) and DMS-PSO (Dynamic Multi Swarm Particle Swarm Optimization) over a test-suite of 20 shifted, rotated, and compositional benchmark functions and also two engineering optimization problems. Our comparative study indicates that although the hybridization scheme does not impose any serious burden on DCMA-EA in terms of number of Function Evaluations (FEs), DCMA-EA still enjoys a statistically superior performance over most of the tested benchmarks and especially over the multi-modal, rotated, and compositional ones in comparison to the other algorithms considered here.     

改进的PSO混合算法

为了提高粒子群算法的寻优速度和寻优精度,提出一种改进的PSO混合算法。在差分进化(DE)算法中引入了动态比例因子,在PSO算法中引入DE算法的变异、交叉操作,重新构造PSO算法的粒子位置更新公式。选取了4个基准函数进行测试,并与其他PSO混合算法作了比较。仿真结果表明该方法是有效的。