Opposition-based learning in the shuffled differential evolution algorithm

This paper proposes using the opposition-based learning (OBL) strategy in the shuffled differential evolution (SDE). In the SDE, population is divided into several memeplexes and each memeplex is improved by the differential evolution (DE) algorithm. The OBL by comparing the fitness of an individual to its opposite and retaining the fitter one in the population accelerates search process. The objective of this paper is to introduce new versions of the DE which, on one hand, use the partitioning and shuffling concepts of SDE to compensate for the limited amount of search moves of the original DE and, on the other hand, employ the OBL to accelerate the DE without making premature convergence. Four versions of DE algorithm are proposed based on the OBL and SDE strategies. All algorithms similarly use the opposition-based population initialization to achieve fitter initial individuals and their difference is in applying opposition-based generation jumping. Experiments on 25 benchmark functions designed for the special session on real-parameter optimization of CEC2005 and non-parametric analysis of obtained results demonstrate that the performances of the proposed algorithms are better than the SDE. The fourth version of proposed algorithm has a significant difference compared to the SDE in terms of all considered aspects. The emphasis of comparison results is to obtain some successful performances on unsolved functions for the first time, which so far have not been reported any successful runs on them. In a later part of the comparative experiments, performance comparisons of the proposed algorithm with some modern DE algorithms reported in the literature confirm a significantly better performance of our proposed algorithm, especially on high-dimensional functions.     

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.     

Enhancing particle swarm optimization using generalized opposition-based learning

Particle swarm optimization (PSO) has been shown to yield good performance for solving various optimization problems. However, it tends to suffer from premature convergence when solving complex problems. This paper presents an enhanced PSO algorithm called GOPSO, which employs generalized opposition-based learning (GOBL) and Cauchy mutation to overcome this problem. GOBL can provide a faster convergence, and the Cauchy mutation with a long tail helps trapped particles escape from local optima. The proposed approach uses a similar scheme as opposition-based differential evolution (ODE) with opposition-based population initialization and generation jumping using GOBL. Experiments are conducted on a comprehensive set of benchmark functions, including rotated multimodal problems and shifted large-scale problems. The results show that GOPSO obtains promising performance on a majority of the test problems.     

Probabilistic opposition-based particle swarm optimization with velocity clamping

A probabilistic opposition-based Particle Swarm Optimization algorithm with Velocity Clamping and inertia weights (OvcPSO) is designed for function optimization—to accelerate the convergence speed and to optimize solution’s accuracy on standard benchmark functions. In this work, probabilistic opposition-based learning for particles is incorporated with PSO to enhance the convergence rate—it uses velocity clamping and inertia weights to control the position, speed and direction of particles to avoid premature convergence. A comprehensive set of 58 complex benchmark functions including a wide range of dimensions have been used for experimental verification. It is evident from the results that OvcPSO can deal with complex optimization problems effectively and efficiently. A series of experiments have been performed to investigate the influence of population size and dimensions upon the performance of different PSO variants. It also outperforms FDR-PSO, CLPSO, FIPS, CPSO-H and GOPSO on various benchmark functions. Last but not the least, OvcPSO has also been compared with opposition-based differential evolution (ODE); it outperforms ODE on lower swarm population and higher-dimensional functions.     

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。     

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。     

Constrained differential evolution using generalized opposition-based learning

Differential evolution (DE) is a well-known optimization approach to deal with nonlinear and complex optimization problems. However, many real-world optimization problems are constrained problems that involve equality and inequality constraints. DE with constraint handling techniques, named constrained differential evolution (CDE), can be used to solve constrained optimization problems. In this paper, we propose a new CDE framework that uses generalized opposition-based learning (GOBL), named GOBL-CDE. In GOBL-CDE, firstly, the transformed population is generated using general opposition-based learning in the population initialization. Secondly, the transformed population and the initial population are merged and only half of the best individuals are selected to compose the new initial population to proceed mutation, crossover, and selection. Lastly, based on a jumping probability, the transformed population is calculated again after generating new populations, and the fittest individuals are selected to compose new population from the union of the current population and the transformed population. The GOBL-CDE framework can be applied to most CDE variants. As examples, in this study, the framework is applied to two popular representative CDE variants, i.e., rank-iMDDE and \(\varepsilon \)DEag. Experiment results on 24 benchmark functions from CEC’2006 and 18 benchmark functions from CEC’2010 show that the proposed framework is an effective approach to enhance the performance of CDE algorithms.     

A novel population initialization method for accelerating evolutionary algorithms

Population initialization is a crucial task in evolutionary algorithms because it can affect the convergence speed and also the quality of the final solution. If no information about the solution is available, then random initialization is the most commonly used method to generate candidate solutions (initial population). This paper proposes a novel initialization approach which employs opposition-based learning to generate initial population. The conducted experiments over a comprehensive set of benchmark functions demonstrate that replacing the random initialization with the opposition-based population initialization can accelerate convergence speed.     

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.     

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.     

Opposition versus randomness in binary spaces

Evolutionary algorithms start with an initial population vector, which is randomly generated when no preliminary knowledge about the solution is available. Recently, it has been claimed that in solving continuous domain optimization problems, the simultaneous consideration of randomness and opposition is more effective than pure randomness. In this paper it is mathematically proven that this scheme, called opposition-based learning, also does well in binary spaces. The proposed binary opposition-based scheme can be embedded inside many binary population-based algorithms. We applied it to accelerate the convergence rate of binary gravitational search algorithm (BGSA) as an application. The experimental results and mathematical proofs confirm each other.     

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。     

具有反向学习和自适应逃逸功能的粒子群优化算法

为克服粒子群优化算法进化后期收敛速度慢、易陷入局部最优等缺点,提出一种具有反向学习和自适应逃逸功能的粒子群优化算法.通过设定的阈值,算法将种群进化状态划分为正常状态和"早熟"状态: 若算法处于正常的进化状态,采用标准粒子群优化算法的进化模式;当粒子陷入"早熟"状态,运用反向学习和自适应逃逸功能,对个体最优位置进行反向学习,产生粒子的反向解,增加粒子的反向学习能力,增强算法逃离局部最优的能力,提高算法寻优率.在固定评估次数的情况下,对8个基准测试函数进行仿真,实验结果表明:所提算法在收敛速度、寻优精度和逃离局部最优的能力上明显优于多种经典粒子群优化算法,如充分联系的粒子群优化算法(FIPS)、基于时变加速度系数的自组织分层粒子群优化算法(HPSO-TVAC)、综合学习的粒子群优化算法(CLPSO)、自适应粒子群优化算法(APSO)、双中心粒子群优化算法(DCPSO)和具有快速收敛和自适应逃逸功能的粒子群优化算法(FAPSO)等.     

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。     

正交差分演化算法在工程优化设计中的应用

提出一种基于正交设计的快速差分演化算法,并把它应用于工程优化设计中。新算法在保留传统差分演化算法简单、有效等特性的同时,还具有以下一些特点：（1）引入一种基于正交设计的杂交算子,并结合约束统计优生法来产生最好子个体;（2）提出一种简单的多样性规则,以处理约束条件;（3）简化基本差分演化算法的缩放因子,尽量减少算法的控制参数,方便工程人员的使用。通过对2个工程优化实例进行实验,并与其他算法的结果作比较,其结果表明,新算法在解的精度、稳定性、收敛性和收敛速度上表现出很好的性能,并且对所优化的问题没有特殊的要求,具有很好的普适性。     

多策略黑猩猩优化算法研究及其工程应用

针对基本黑猩猩优化算法存在的依赖初始种群、易陷入局部最优和收敛精度低等问题,提出一种多策略黑猩猩优化算法EOSMICOA（chaotic elite opposition-based simple method improved COA）。在EOSMICOA算法中,利用混沌精英反向学习策略对黑猩猩个体位置进行初始化,提高种群的多样性和质量,同时在位置更新过程中利用单纯形法和群个体记忆机制对较差个体进行改进,进一步提高算法的局部开发能力和勘探能力,以及算法的寻优精度。为验证改进算法的寻优能力,将EOSMICOA算法与多个智能算法对20个复杂函数进行对比实验,结果表明EOSMICOA在收敛精度、寻优速度等方面都有明显优势。最后,将EOSMICOA与当前最新改进算法应用于焊接梁设计中,对比结果表明EOSMICOA可以更有效地应用于工程设计优化问题。     

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.     

基于局部搜索的反向学习竞争粒子群优化算法

为提升粒子群优化算法在复杂优化问题,特别是高维优化问题上的优化性能,提出一种基于Solis&Wets局部搜索的反向学习竞争粒子群优化算法(solis and wets-opposition based learning competitive particle swarm optimizer with local search, SW-OBLCSO). SW-OBLCSO算法采用竞争学习和反向学习两种学习机制,并设计了基于个体的局部搜索算子.利用10个常用基准测试函数和12个带有偏移旋转的复杂测试函数,在不同维度情况下将SW-OBLCSO算法与多种优化算法进行对比.实验结果表明,所提出算法在收敛速度和全局搜索能力上表现出突出的性能.对模糊认知图(fuzzy cognitive maps)学习问题的测试表明, SW-OBLCSO算法在处理实际问题时同样具有出色的性能.     

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.