Three modified versions of differential evolution algorithm for continuous optimization

Differential evolution (DE) is one simple and effective evolutionary algorithm (EA) for global optimization. In this paper, three modified versions of the DE to improve its performance, to repair its defect in accurate converging to individual optimal point and to compensate the limited amount of search moves of original DE are proposed. In the first modified version called bidirectional differential evolution (BDE), to generate a new trial point, is used from the bidirectional optimization concept, and in the second modified version called shuffled differential evolution (SDE), population such as shuffled frog leaping (SFL) algorithm is divided in to several memeplexes and each memeplex is improved by the DE algorithm. Finally, in the third modified version of DE called shuffled bidirectional differential evolution (SBDE) to improve each memeplex is used from the proposed BDE algorithm. Three proposed modified versions are applied on two types of DE and six obtained algorithms are compared with original DE and SFL algorithms. Experiments on continuous benchmark functions and non-parametric analysis of obtained results demonstrate that applying bidirectional concept only improves one type of the DE. But the SDE and the SBDE have a better success rate and higher solution precision than original DE and SFL, whereas those are more time consuming on some functions. In a later part of the comparative experiments, a comparison of the proposed algorithms with some modern DE and the other EAs reported in the literature confirms a better or at least comparable performance of our proposed algorithms.     

Opposition-Based Differential Evolution

Evolutionary algorithms (EAs) are well-known optimization approaches to deal with nonlinear and complex problems. However, these population-based algorithms are computationally expensive due to the slow nature of the evolutionary process. This paper presents a novel algorithm to accelerate the differential evolution (DE). The proposed opposition-based DE (ODE) employs opposition-based learning (OBL) for population initialization and also for generation jumping. In this work, opposite numbers have been utilized to improve the convergence rate of DE. A comprehensive set of 58 complex benchmark functions including a wide range of dimensions is employed for experimental verification. The influence of dimensionality, population size, jumping rate, and various mutation strategies are also investigated. Additionally, the contribution of opposite numbers is empirically verified. We also provide a comparison of ODE to fuzzy adaptive DE (FADE). Experimental results confirm that the ODE outperforms the original DE and FADE in terms of convergence speed and solution accuracy.     

基于反向学习的自适应差分进化算法

为解决差分进化（DE）算法过早收敛与搜索能力低的问题,讨论对控制参数的动态调整,提出一种基于反向学习的自适应差分进化算法。该算法通过反向精英学习机制来增强种群的局部搜索能力,获取精确度更高的最优个体;同时,采用高斯分布随机性提高单个个体的开发能力,通过扩充种群的多样性,避免算法过早收敛,整体上平衡全局搜索与局部寻优的能力。采用CEC 2014中的6个测试函数进行仿真实验,并与其他差分进化算法进行对比,实验结果表明所提算法在收敛速度、收敛精度及可靠性上表现更优。     

基于反向学习的跨种群差分进化算法

针对差分进化（DE）算法存在的寻优精度低、收敛速度慢等问题,借鉴混沌分散策略、反向学习策略（OBL）以及跨种群并行机制,提出一种基于反向学习的跨种群差分进化算法（OLCPDE）。采用混沌分散策略进行种群初始化,将种群划分为精英种群和普通种群,对两个子种群分别采用标准的差分进化策略和基于反向学习的差分进化策略;同时,为进一步提高算法对单峰函数的求解精度和稳定性,采用了一种跨种群的差分进化策略,运用三种策略对子种群进行操作,达到共同进化的目的。实验独立运行30次,OLCPDE在12个标准的测试函数中,有11个函数都能稳定地收敛到全局最优解,优于对比算法。实验结果表明,OLCPDE收敛精度高,能有效避免陷入局部最优点。     

应用反向学习和差分进化的群搜索优化算法

针对标准群搜索优化算法在解决一些复杂优化问题时容易陷入局部最优且收敛速度较慢的问题,提出一种应用反向学习和差分进化的群搜索优化算法(Group Search Optimization with Opposition-based Learning and Diffe-rential Evolution,OBDGSO)。该算法利用一般动态反向学习机制产生反向种群,扩大算法的全局勘探范围;对种群中较优解个体实施差分进化的变异操作,实现在较优解附近的局部开采,以改善算法的求解精度和收敛速度。这两种策略在GSO算法中相互协同,以更好地平衡算法的全局搜索能力和局部开采能力。将OBDGSO算法和另外4种群智能算法在12个基准测试函数上进行实验,结果表明OBDGSO算法在求解精度和收敛速度上具有较显著的性能优势。     

基于反向学习与Levy飞行的改进蜂群算法

为了优化蜂群算法(BCA),平衡局部搜索与全局搜索,避免算法陷入局部最优,并提高蜂群算法的收敛速度,提出了一种多策略改进的方法优化蜂群算法(MSO-BCA).算法在种群初始化阶段采用了反向学习(OBL)初始化的方法;在种群更新与邻域搜索中采用了具有Levy飞行特征的改进搜索策略.经过对经典Benchmark函数的反复实验并与其他算法的比较,表明了所提出的算法具有良好的加速和收敛效果,提高了全局搜索能力与效率.     

具有人工蜂群搜索策略的差分进化算法

针对差分进化算法易出现早熟现象和收敛速度慢等问题,提出一种具有人工蜂群搜索策略的差分进化算法.利用人工蜂群搜索策略很强的探索能力,对种群进行引导以帮助算法快速跳出局部最优点.此外,为了提高算法的全局收敛速度,采用一种基于反学习的初始化方法.通过对12个标准测试函数进行仿真实验并与其他算法相比较,表明了所提出的算法具有较快的收敛速度和很强的跳出局部最优的能力.     

保存基因的2-Opt一般反向差分演化算法

为了进一步提高差分演化算法的性能,提出一种采用保存基因的2-Opt一般反向差分演化算法,并把它应用于函数优化问题中.新算法具有以下特征:(1)采用保存被选择个体基因的方式组成参加演化的新个体.保存基因的方法可以很好的保持种群多样性;(2)采用一般反向学习(GOBL)机制进行初始化,提高了初始化效率;(3)采用2-Opt算法加速差分演化算法的收敛速度,提高搜索效率.通过测试函数的实验,并与其他差分演化算法进行比较.实验结果证实了新算法的高效性,通用性和稳健性.     

基于随机邻域变异和趋优反向学习的差分进化算法

传统差分进化（DE）算法在迭代过程中不能充分平衡全局勘探与局部开发,存在易陷入局部最优、求解精度低、收敛速度慢等缺点。为提升算法性能,提出一种基于随机邻域变异和趋优反向学习的差分进化（RNODE）算法并对其进行复杂度分析。首先,为种群中每个个体生成随机邻域,用全局最佳个体引导邻域最佳个体生成复合基向量,结合控制参数自适应更新机制构成随机邻域变异策略,使算法在引导种群向最优方向趋近的同时保持一定的勘探能力;其次,为了进一步帮助算法跳出局部最优,对种群中较差个体执行趋优反向学习操作,扩大搜索区域;最后,将RNODE与九种算法进行对比以验证RNODE的有效性和先进性。在23个Benchmark函数和两个实际工程优化问题上的实验结果表明,RNODE算法收敛精度更高、速度更快、稳定性更优。     

A charging-scheme decision model for electric vehicle battery swapping station using varied population evolutionary algorithms

This paper proposes a new battery swapping station (BSS) model to determine the optimized charging scheme for each incoming Electric Vehicle (EV) battery. The objective is to maximize the BSS’s battery stock level and minimize the average charging damage with the use of different types of chargers. An integrated objective function is defined for the multi-objective optimization problem. The genetic algorithm (GA), differential evolution (DE) algorithm and three versions of particle swarm optimization (PSO) algorithms have been implemented to solve the problem, and the results show that GA and DE perform better than the PSO algorithms, but the computational time of GA and DE are longer than using PSO. Hence, the varied population genetic algorithm (VPGA) and varied population differential evolution (VPDE) algorithm are proposed to determine the optimal solution and reduce the computational time of typical evolutionary algorithms. The simulation results show that the performances of the proposed algorithms are comparable with the typical GA and DE, but the computational times of the VPGA and VPDE are significantly shorter. A 24-h simulation study is carried out to examine the feasibility of the model.     

Enhanced artificial bee colony algorithm through differential evolution

Artificial bee colony algorithm (ABC) is a relatively new optimization algorithm. However, ABC does well in exploration but badly in exploitation. One possible way to improve the exploitation ability of the algorithm is to combine ABC with other operations. Differential evolution (DE) can be considered as a good choice for this purpose. Based on this consideration, we propose a new algorithm, i.e. DGABC, which combines DE with gbest-guided ABC (GABC) by an evaluation strategy with an attempt to utilize more prior information of the previous search experience to speed up the convergence. In addition, to improve the global convergence, when producing the initial population, a chaotic opposition-based population initialization method is employed. The comparison results on a set of 27 benchmark functions demonstrate that the proposed method has better performance than the other algorithms.     

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.     

混合模式搜索的分布式memetic差分进化算法

针对差分进化（DE）算法存在的早熟收敛与搜索停滞的问题,提出memetic分布式差分进化（DDE）算法。将memetic算法的思想融入到差分进化算法中,采用分布式的种群结构以及memetic算法中的混合策略,前者将初始种群分为多个子种群,子种群间根据冯·诺依曼拓扑结构周期性地实现信息交流,后者将差分进化算法作为进化的主要框架,模式搜索作为辅助手段,从而平衡算法的探索与开发能力。所提算法充分利用了模式搜索和差分进化算法的优势,建立了有效的搜索机制,增强了算法摆脱局部最优的能力,能够满足搜索过程对种群多样性及收敛速度的需求。将所提算法与几种先进的差分进化算法相比较,对标准测试函数进行优化的实验结果显示：所提算法在解的质量和收敛性能方面,均优于其他几种相比较的先进的差分进化算法。     

A modified artificial bee colony algorithm

Artificial bee colony algorithm (ABC) is a relatively new optimization technique which has been shown to be competitive to other population-based algorithms. However, there is still an insufficiency in ABC regarding its solution search equation, which is good at exploration but poor at exploitation. Inspired by differential evolution (DE), we propose an improved solution search equation, which is based on that the bee searches only around the best solution of the previous iteration to improve the exploitation. Then, in order to make full use of and balance the exploration of the solution search equation of ABC and the exploitation of the proposed solution search equation, we introduce a selective probability P and get the new search mechanism. In addition, to enhance the global convergence, when producing the initial population, both chaotic systems and opposition-based learning methods are employed. The new search mechanism together with the proposed initialization makes up the modified ABC (MABC for short), which excludes the probabilistic selection scheme and scout bee phase. Experiments are conducted on a set of 28 benchmark functions. The results demonstrate good performance of MABC in solving complex numerical optimization problems when compared with two ABC-based algorithms.     

一种求解多模态复杂问题的混合和声差分算法

针对多模态复杂优化问题,提出了一种基于和声搜索和差分进化的混合优化算法:HHSDE算法。在不同的进化阶段,HHSDE算法依据累积加权更新成功率来自适应地选择和声算法或差分算法作为更新下一代种群的方式,并改进了差分算法的变异策略来平衡差分算法的全局与局部搜索能力。通过对10个多模态Benchmark函数进行测试,利用Wilcoxon秩和检验对不同算法的计算结果进行比较,结果表明HHSDE算法具有收敛速度快,求解精度高,稳定性好等优势。     

双种群差分进化规划算法

标准差分进化算法（SDE）具有算法简单,控制参数少,易于实现等优点。但在难优化问题中,算法存在收敛速度较慢和容易早熟等缺陷。为克服此缺点,提出一种改进算法--双种群差分进化规划算法（BGDEP）。该算法将种群划分为两个子群独立进化,分别采用DE/rand/1/bin和DE/best/2/bin版本生成变异个体。每隔δt（取5~10）代,将两个子群合并为一个种群,再应用混沌重组算子将之划分为两个子群,以实现子群间的信息交流。在双种群协同差分进化的同时,应用非均匀变异算子对其最优个体执行进化规划操作,使得算法具有较快的收敛速度和较强的全局寻优能力。为测试BGDEP的性能,给出了4个30维benchmark函数优化问题的对比数值实验。结果表明,BGDEP的求解精度、收敛速度、鲁棒性等性能优于SDE、双种群差分进化（BGDE）和非均匀变异进化规划（NUMEP）等4种算法。     

Parameter identification of chaotic systems by hybrid Nelder–Mead simplex search and differential evolution algorithm

Parameter identification of chaotic systems is an important issue in nonlinear science and has attracted increasing interest from a variety of research and application fields. Essentially, parameter identification can be formulated as a multi-dimensional optimization problem. By combining differential evolution (DE) and Nelder–Mead (NM) simplex search, an effective hybrid algorithm named NMDE is proposed in this paper. By suitably fusing the DE-based evolutionary search and NM simplex-based local search, exploration and exploitation abilities can be well balanced and satisfactory optimization performances can be achieved. The NMDE hybrid algorithm is applied to parameter identification of several typical chaotic systems. Numerical simulation and comparisons with some typical existing algorithms demonstrate the effectiveness and robustness of the proposed hybrid NMDE algorithm. Moreover, the effects of noise and population size on the performances of NMDE are investigated as well.     

Enhanced opposition-based differential evolution for solving high-dimensional continuous optimization problems

This paper presents a novel algorithm based on generalized opposition-based learning (GOBL) to improve the performance of differential evolution (DE) to solve high-dimensional optimization problems efficiently. The proposed approach, namely GODE, employs similar schemes of opposition-based DE (ODE) for opposition-based population initialization and generation jumping with GOBL. Experiments are conducted to verify the performance of GODE on 19 high-dimensional problems with D = 50, 100, 200, 500, 1,000. The results confirm that GODE outperforms classical DE, real-coded CHC (crossgenerational elitist selection, heterogeneous recombination, and cataclysmic mutation) and G-CMA-ES (restart covariant matrix evolutionary strategy) on the majority of test problems.     

一种改进的微分进化算法

相对于其他优化算法来说,微分进化算法具有控制参数少、易于使用以及鲁棒性强等特点,但在搜索过程中存在着局部搜索能力弱的缺点。针对微分进化算法局部搜索能力弱的缺点,提出了一种基于局部变异的微分进化算法,该算法使个体具有良好快速收敛能力。使用典型优化函数对比较算法进行了测试,算法分析和仿真结果表明,改进以后的算法具有寻优能力...     

Distributed memetic differential evolution with the synergy of Lamarckian and Baldwinian learning

As a population-based optimizer, the differential evolution (DE) algorithm has a very good reputation for its competence in global search and numerical robustness. In view of the fact that each member of the population is evaluated individually, DE can be easily parallelized in a distributed way. This paper proposes a novel distributed memetic differential evolution algorithm which integrates Lamarckian learning and Baldwinian learning. In the proposed algorithm, the whole population is divided into several subpopulations according to the von Neumann topology. In order to achieve a better tradeoff between exploration and exploitation, the differential evolution as an evolutionary frame is assisted by the Hooke–Jeeves algorithm which has powerful local search ability. We incorporate the Lamarckian learning and Baldwinian learning by analyzing their characteristics in the process of migration among subpopulations as well as in the hybridization of DE and Hooke–Jeeves local search. The proposed algorithm was run on a set of classic benchmark functions and compared with several state-of-the-art distributed DE schemes. Numerical results show that the proposed algorithm has excellent performance in terms of solution quality and convergence speed for all test problems given in this study.