自适应调整控制参数的差异演化算法

控制参数选取是包括差异演化在内的演化算法设计时所面临的一个重要问题,对算法的性能有着重大影响.针对差异演化算法参数选取问题,提出一种利用个体适应度作为参数调整决策依据,并结合一定的调整概率对F和CR进行自适应调整的方法,解决了手工设置控制参数的不便.同时利用交叉操作生成双子代个体与父代个体竞争形成新一代种群,加快了算法的收敛.对标准测试函数的仿真实验结果表明,该算法无论在最优解质量和收敛速度上都优于相关算法,尤其对于高维函数而言.     

差分进化算法参数控制与适应策略综述

差分进化算法逐渐成为进化计算领域最流行的随机搜索算法之一,已被成功用于求解各类应用问题.差分进化算法参数设置与其性能密切相关,因此算法参数控制与适应策略设计是目前该领域的研究热点之一,目前已涌现出大量参数控制方案,但尚缺乏系统性的综述与分析.首先简要介绍差分进化算法的基本原理与操作,然后将目前参数控制与适应策略分成基于经验的参数控制、参数随机化适应策略、基于统计学习的参数随机化适应策略和参数自适应策略4类进行系统性综述,重点介绍其中的参数适应与自适应策略.此外,为分析各种参数控制与适应策略的功效,以实值函数优化为问题背景设计了相关实验,进一步分析各种策略的效率与实用性,实验结果表明,参数自适应控制策略是目前该领域最有效的方法之一.     

差异演化算法及其改进形式的综述

差异演化算法是一种基于群体差异的演化算法,群体中每个向量代表问题的一个候选解,该算法利用向量之间的差异扰动整个种群,求解问题的最优解.综述了差异演化算法的基本原理、常用测试函数和算法优缺点,讨论了多种改进手段,如:三角变异、混沌理论、逆向计算、均匀设计表等,并给出了未来可能的研究方向.     

Improved differential evolution approach based on cultural algorithm and diversity measure applied to solve economic load dispatch problems

Evolutionary algorithms (EAs) are general-purpose stochastic search methods that use the metaphor of evolution as the key element in the design and implementation of computer-based problems solving systems. During the past two decades, EAs have attracted much attention and wide applications in a variety of fields, especially for optimization and design. EAs offer a number of advantages: robust and reliable performance, global search capability, little or no information requirement, and others. Among various EAs, differential evolution (DE), which characterized by the different mutation operator and competition strategy from the other EAs, has shown great promise in many numerical benchmark problems and real-world optimization applications. The potentialities of DE are its simple structure, easy use, convergence speed and robustness. To improve the global optimization property of DE, in this paper, a DE approach based on measure of population's diversity and cultural algorithm technique using normative and situational knowledge sources is proposed as alternative method to solving the economic load dispatch problems of thermal generators. The traditional and cultural DE approaches are validated for two test systems consisting of 13 and 40 thermal generators whose nonsmooth fuel cost function takes into account the valve-point loading effects. Simulation results indicate that performance of the cultural DE present best results when compared with previous optimization approaches in solving economic load dispatch problems.     

CMOS analogue amplifier circuits optimisation using hybrid backtracking search algorithm with differential evolution

This paper proposes a novel hybrid optimisation algorithm which combines the recently proposed evolutionary algorithm Backtracking Search Algorithm (BSA) with another widely accepted evolutionary algorithm, namely, Differential Evolution (DE). The proposed algorithm called BSA-DE is employed for the optimal designs of two commonly used analogue circuits, namely Complementary Metal Oxide Semiconductor (CMOS) differential amplifier circuit with current mirror load and CMOS two-stage operational amplifier (op-amp) circuit. BSA has a simple structure that is effective, fast and capable of solving multimodal problems. DE is a stochastic, population-based heuristic approach, having the capability to solve global optimisation problems. In this paper, the transistors’ sizes are optimised using the proposed BSA-DE to minimise the areas occupied by the circuits and to improve the performances of the circuits. The simulation results justify the superiority of BSA-DE in global convergence properties and fine tuning ability, and prove it to be a promising candidate for the optimal design of the analogue CMOS amplifier circuits. The simulation results obtained for both the amplifier circuits prove the effectiveness of the proposed BSA-DE-based approach over DE, harmony search (HS), artificial bee colony (ABC) and PSO in terms of convergence speed, design specifications and design parameters of the optimal design of the analogue CMOS amplifier circuits. It is shown that BSA-DE-based design technique for each amplifier circuit yields the least MOS transistor area, and each designed circuit is shown to have the best performance parameters such as gain, power dissipation, etc., as compared with those of other recently reported literature.     

An improved differential evolution algorithm with fitness-based adaptation of the control parameters

Differential Evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. DE operates through the similar computational steps as employed by a standard Evolutionary Algorithm (EA). However, unlike the traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used, which makes the scheme self-organizing in this respect. Scale Factor (F) and Crossover Rate (Cr) are two very important control parameters of DE since the former regulates the step-size taken while mutating a population member in DE and the latter controls the number of search variables inherited by an offspring from its parent during recombination. This article describes a very simple yet very much effective adaptation technique for tuning both F and Cr, on the run, without any user intervention. The adaptation strategy is based on the objective function value of individuals in the DE population. Comparison with the best-known and expensive variants of DE over fourteen well-known numerical benchmarks and one real-life engineering problem reflects the superiority of proposed parameter tuning scheme in terms of accuracy, convergence speed, and robustness.     

基于模拟退火的混合差分演化算法研究

介绍了一种求解函数优化问题的新策略--差分演化算法,与其它算法相比,该算法具有稳健性强,收敛速度快的优点;同时,把模拟退火策略融入到差分演化的过程中,提出了一个混合演化算法--基于模拟退火的混合差分演化算法,实验表明混合后的算法比单一的差分演化算法更稳健,收敛速度也略有提高.     

A differential evolution algorithm with self-adapting strategy and control parameters

This paper presents a Differential Evolution algorithm with self-adaptive trial vector generation strategy and control parameters (SspDE) for global numerical optimization over continuous space. In the SspDE algorithm, each target individual has an associated strategy list (SL), a mutation scaling factor F list (FL), and a crossover rate CR list (CRL). During the evolution, a trial individual is generated by using a strategy, F, and CR taken from the lists associated with the target vector. If the obtained trial individual is better than the target vector, the used strategy, F, and CR will enter a winning strategy list (wSL), a winning F list (wFL), and a winning CR list (wCRL), respectively. After a given number of iterations, the FL, CRL or SL will be refilled at a high probability by selecting elements from wFL, wCRL and wSL or randomly generated values. In this way, both the trial vector generation strategy and its associated parameters can be gradually self-adapted to match different phases of evolution by learning from their previous successful experience. Extensive computational simulations and comparisons are carried out by employing a set of 19 benchmark problems from the literature. The computational results show that overall the SspDE algorithm performs better than the state-of-the-art differential evolution variants.     

基于粗糙集理论与差分进化的混合多目标优化算法

针对传统算法求解约束多目标优化所得近似解精度不高、分布性能不好的问题,提出一种基于粗糙集理论与差分进化的混合算法.首先利用多目标差分进化生成一个初始的近似 Pareto 前沿;然后利用粗糙集理论提高Pareto 前沿的分布质量.选取一组标准的多目标约束测试问题,采用混合算法与 NSGA-II 算法进行仿真求解,对比结果表明,所提出的算法在求解约束多目标优化问题时具有更好的近似解分布和更优越的近似解性能.     

一类求解方程全部根的改进差分进化算法

求解高次实复系数代数方程的根,提出了一种改进的差分进化算法,计算种群中每个个体的适应度并排序,利用二分之一规则选取个体,并引入自适应差分变异算子和进化策略重组算子.对5个高次代数方程求根问题进行了数值计算,结果表明,该算法能求解任意次数的实复系数代数方程的全部根,而且求解精度高,收敛速度快,是求解代数方程根的一种有效算法.     

基于优进策略的新差分进化算法动力学模型参数的估计

为准确估计反应动力学参数,针对标准差分进化算法(DEA)全局寻优效率偏低的弱点,提出一种优进策略的差分进化算法(EDEA).它将确定性寻优的单纯形(SM)算子引入随机的DEA中.DEA将依概率调用SM寻优操作,测试结果表明,EDEA克服了DEA的缺点,比其它方法全局寻优性能好.该法成功的用于重油热解三集总动力学复杂数学模型的非线性参数估计,效果良好,结果有改进,显出EDEA的优越性.     

Gene sorting in differential evolution with cross-generation mutation

Gene sorting is proposed in this paper as a method of ordering trial vector’s component in dif- ferential evolution (DE). This method tends to significantly increase the convergence speed of DE with just a little modification on the original algorithm. In the meantime, a new concept of cross-generation mutation is introduced in order to perform the evolution process serially rather than parallelly. When combined with gene sorting, this method will further increase the convergence speed. A benchmar...     

基于GPU的并行协同差分进化算法研究

针对大规模高维数复杂非线性函数优化的问题,提出一种新的基于GPU的协同差分进化算法。该方法将协同进化的思想引入启发式差分进化算法,随机分解大规模计算问题,利用GPU处理数据的并行性,同步计算分解后的子问题,加快算法的精度和收敛速度。实验对比结果表明,所提出的基于GPU的协同差分进化算法对大规模非线性函数优化具有更高的精度和效率。     

Exploring dynamic self-adaptive populations in differential evolution

Although the Differential Evolution (DE) algorithm has been shown to be a simple yet powerful evolutionary algorithm for optimizing continuous functions, users are still faced with the problem of preliminary testing and hand-tuning of the evolutionary parameters prior to commencing the actual optimization process. As a solution, self-adaptation has been found to be highly beneficial in automatically and dynamically adjusting evolutionary parameters such as crossover rates and mutation rates. In this paper, we present a first attempt at self-adapting the population size parameter in addition to self-adapting crossover and mutation rates. Firstly, our main objective is to demonstrate the feasibility of self-adapting the population size parameter in DE. Using De Jong's F1–F5 benchmark test problems, we showed that DE with self-adaptive populations produced highly competitive results compared to a conventional DE algorithm with static populations. In addition to reducing the number of parameters used in DE, the proposed algorithm actually outperformed the conventional DE algorithm for one of the test problems. It was also found that that an absolute encoding methodology for self-adapting population size in DE produced results with greater optimization reliability compared to a relative encoding methodology.     

Parallel differential evolution with self-adapting control parameters and generalized opposition-based learning for solving high-dimensional optimization problems

Solving high-dimensional global optimization problems is a time-consuming task because of the high complexity of the problems. To reduce the computational time for high-dimensional problems, this paper presents a parallel differential evolution (DE) based on Graphics Processing Units (GPUs). The proposed approach is called GOjDE, which employs self-adapting control parameters and generalized opposition-based learning (GOBL). The adapting parameters strategy is helpful to avoid manually adjusting the control parameters, and GOBL is beneficial for improving the quality of candidate solutions. Simulation experiments are conducted on a set of recently proposed high-dimensional benchmark problems with dimensions of 100, 200, 500 and 1,000. Simulation results demonstrate that GjODE is better than, or at least comparable to, six other algorithms, and employing GPU can effectively reduce computational time. The obtained maximum speedup is up to 75.     

基于分布估计的离散差分演化算法

差分演化(DE)是解决优化问题的非常有效的新兴智能算法,但它主要用于连续优化领域,至今尚不能象解决连续优化问题那样有效的处理组合优化问题.首先提出了离散DE用于组合优化问题,然后在离散DE中引入分布估计算法(EDA)来提高性能,把EDA抽样得到的全局统计信息和离散DE获得的局部演化信息相结合来产生新解,形成基于EDA的离散DE算法.为了保持种群多样性,在提出的算法中引入了位翻转变异操作.实验结果表明,EDA能大大提高离散DE的性能.     

Self-adapting control parameters modified differential evolution for trajectory planning of manipulators

Control parameters of original differential evolution （DE） are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE for different optiinization problems. According to the relative position of two different individual vectors selected to generate a difference vector in the searching place, a self-adapting strategy for the scale factor F of the difference vector is proposed. In terms of the convergence status of the target vector in the current population, a self-adapting crossover probability constant CR strategy is proposed. Therefore, good target vectors have a lower CFI while worse target vectors have a large CFI. At the same time, the mutation operator is modified to improve the convergence speed. The performance of these proposed approaches are studied with the use of some benchmark problems and applied to the trajectory planning of a three-joint redundant manipulator. Finally, the experiment results show that the proposed approaches can greatly improve robustness and convergence speed.     

差分进化法在风电并网系统中的应用

为解决多机风电并网系统的稳定性问题,提出在风电并网系统的同步发电机(SG)中安装电力系统稳定器(PSS),利用差分进化算法解决SG中自动电压调节器(AVR)和PSS参数的最优调节问题。在有、无PSS以及是否使用差分进化法的各种情况下对风电并网系统稳定性进行了研究分析,研究表明通过差分进化法的协同调节使含AVR和PSS的风电并网系统有良好的阻尼作用,能减少发电机转子角差振荡,提高电压稳定性,通过仿真结果对比可知差分进化法可使并网系统稳定性明显提高。     

Kernel-induced fuzzy clustering of image pixels with an improved differential evolution algorithm

A modified differential evolution (DE) algorithm is presented for clustering the pixels of an image in the gray-scale intensity space. The algorithm requires no prior information about the number of naturally occurring clusters in the image. It uses a kernel induced similarity measure instead of the conventional sum-of-squares distance. Use of the kernel function makes it possible to partition data that is linearly non-separable and non hyper-spherical in the original input space, into homogeneous groups in a transformed high-dimensional feature space. A novel search-variable representation scheme is adopted for selecting the optimal number of clusters from several possible choices. Extensive performance comparison over a test-suite of 10 gray-scale images and objective comparison with manually segmented ground truth indicates that the proposed algorithm has an edge over a few state-of-the-art algorithms for automatic multi-class image segmentation.     

差分进化算法的性能分析及其动力学模型参数估计

差分进化算法以遗传算法为基础,在算法中引入扰动矢量,利用个体间的距离和方向等信息进行搜索,克服遗传算法容易“早熟”的缺陷。此外,差分进化算法收敛性及鲁棒性好,控制变量需要得不多,简单易用。分析差分进化算法的寻优性能,并将它应用于铯一铷一钒系低温硫酸催化剂中,SO2氧化反应的参数估计,证明利用差分进化算法得到的模型更加精确。