An improved Opposition-Based Sine Cosine Algorithm for global optimization

Real life optimization problems require techniques that properly explore the search spaces to obtain the best solutions. In this sense, it is common that traditional optimization algorithms fail in local optimal values. The Sine Cosine Algorithms (SCA) has been recently proposed; it is a global optimization approach based on two trigonometric functions. SCA uses the sine and cosine functions to modify a set of candidate solutions; such operators create a balance between exploration and exploitation of the search space. However, like other similar approaches, SCA tends to be stuck into sub-optimal regions that it is reflected in the computational effort required to find the best values. This situation occurs due that the operators used for exploration do not work well to analyze the search space. This paper presents an improved version of SCA that considers the opposition based learning (OBL) as a mechanism for a better exploration of the search space generating more accurate solutions. OBL is a machine learning strategy commonly used to increase the performance of metaheuristic algorithms. OBL considers the opposite position of a solution in the search space. Based on the objective function value, the OBL selects the best element between the original solution and its opposite position; this task increases the accuracy of the optimization process. The hybridization of concepts from different fields is crucial in intelligent and expert systems; it helps to combine the advantages of algorithms to generate more efficient approaches. The proposed method is an example of this combination; it has been tested over several benchmark functions and engineering problems. Such results support the efficacy of the proposed approach to find the optimal solutions in complex search spaces.     

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.     

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.     

An extended teaching-learning based optimization algorithm for solving no-wait flow shop scheduling problem

The no-wait flow shop scheduling problem (NWFSSP) performs an important function in the manufacturing industry. Inspired by the overall process of teaching-learning, an extended framework of meta-heuristic based on the teaching-learning process is proposed, which consists of four parts, i.e. previewing before class, teaching phase, learning phase, reviewing after class. This paper implements a hybrid meta-heuristic based on probabilistic teaching-learning mechanism (mPTLM) to solve the NWFSSP with the makespan criterion. In previewing before class, an initial method that combines a modified Nawaz-Enscore-Ham (NEH) heuristic and the opposition-based learning (OBL) is introduced. In teaching phase, the Gaussian distribution is employed as the teacher to guide learners to search more promising areas. In learning phase, this paper presents a new means of communication with crossover. In reviewing after class, an improved speed-up random insert local search based on simulated annealing (SA) is developed to enhance the local searching ability. The computational results and comparisons based on Reeves, Taillard and VRF’s benchmarks demonstrate the effectiveness of mPTLM for solving the NWFSSP.     

基于粒子群优化算法的并行模拟退火算法

针对模拟退火（simulated annealing,SA）算法收敛速度慢,随机采样策略缺乏记忆能力,算法内在的串行性使其具有并行化问题依赖等缺点,提出了基于粒子群优化（particle swarm optimization,PSO）算法的并行模拟退火算法。该算法利用粒子群优化算法中个体的记忆功能引导算法在解空间中开展精细搜索,在反向学习算法基础上设计新的反向转动操作机制增加了算法的多样性,借助PSO的天然并行性克服了SA的并行问题依赖性,并在集群上实现了多Agent协同进化的改进算法。对Toy模型的蛋白质结构预测问题进行了仿真实验,结果表明该算法能有效提高求解问题的质量和效率。     

Multi-workflow scheduling and resource provisioning in Mobile Edge Computing using opposition-based Marine-Predator Algorithm

Workflow Scheduling in Mobile Edge Computing (MEC) tries to allocate the best possible set of resources for the workflows, considering objectives such as deadline, cost, energy, Quality of Service (QoS), and so on. However, MEC may be under different workloads from the IoT and this may not have the required amount of resources to efficiently handle the workflows. To mitigate this problem, in this paper, we use proactive resource provisioning and workload prediction methods. For this purpose, we present a workload prediction method using a multilayer feed-forward Artificial Neural Network (ANN) model and apply its results for resource provisioning. Afterward, we present an opposition-based version of the Marine-Predator Algorithm (MPA) algorithm, denoted as OMPA. In this algorithm, we present a probabilistic opposition-based learning (OBL) method, which benefits from the OBL, Quasi OBL, and dynamic OBL methods. Afterward, the OMPA algorithm is used for training the multi-layer feed-forward ANN model and multi-workflow scheduling by taking into account factors such as the makespan and number of Virtual Machines (VMs). Extensive experiments conducted in the iFogSim simulator and on the NASA and Saskatchewan datasets indicate that the proposed scheme can achieve better results compared to other metaheuristic algorithms and scheduling schemes.     

基于多目标烟花算法的关联规则挖掘*

针对量化关联规则的特点,提出基于多目标烟花算法和反向学习的量化关联规则挖掘算法.该算法通过多目标烟花算法全面搜索关联规则,引入反向学习提高算法收敛速度并降低算法陷入局部最优的概率,使用基于相似度的冗余淘汰机制保持库中关联规则的多样性,经过多次迭代最终获得关联规则集合.文中算法无需人为指定支持度、置信度等阈值,实验表明,算法在不同数据集上均获得稳定结果,能充分覆盖数据集,在可靠性、相关性及可理解性之间获得较好的均衡.     

Optimal reactive power dispatch by improved GSA-based algorithm with the novel strategies to handle constraints

Optimal reactive power dispatch (ORPD) is well known as a complex mixed integer nonlinear optimization problem where many constraints are required to handle. In the last decades, many artificial intelligence-based optimization methods have been used to solve ORPD problem. But, these optimization methods lack an effective means to handle constraints on state variables. Thus, in this paper, the novel and feasible conditional selection strategies (CSS) are devised to handle constraints efficiently in the proposed improved gravitational search algorithm (GSA-CSS). In addition, considering the weakness of GSA itself, the improved GSA-CSS (IGSA-CSS) is presented which employs the memory property of particle swarm optimization (PSO) to enhance global searching ability and utilizes the concept of opposition-based learning (OBL) for optimizing initial population. The presented GSA-CSS and IGSA-CSS methods are applied to ORPD problem on IEEE14-bus, IEEE30-bus and IEEE57-bus test systems for minimization of power transmission losses (P_loss) and voltage deviation (V_d), respectively. The comparisons of simulation results reveal that IGSA-CSS provides better results and the improvements of algorithm in this work are feasible and effective.     

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.     

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.     

基于混合采样机制的互信息分布估计算法

针对二阶分布估计算法的早熟收敛问题,提出一种基于混合采样机制的互信息分布估计算法(MIEDA). MIEDA利用互信息度量变量之间的相关性,形成互信息树的概率模型;采用稀疏模型构建的思想,并基于自私基因理论建立信息奖惩机制,以加快算法的收敛速度;结合反向学习、最优解变异和随机采样形成混合采样机制,以提高算法的采样效率.仿真结果表明,MIEDA比常见的二阶分布估计算法具有更高的稳定性和更强的寻优能力.     

基于改进KH算法优化ELM的目标威胁估计

为了提高目标威胁度估计的精确度,建立了反向学习磷虾群算法（OKH）优化极限学习机的目标威胁估计模型（OKH-ELM）,提出基于此模型的算法。该模型使用反向学习策略优化磷虾群算法,并通过改进后的磷虾群算法优化极限学习机初始输入权重和偏置,使优化后的极限学习机能够对威胁度测试样本集做更好的预测。实验结果显示,OKH算法能够更好地优化极限学习机的权值与阈值,使建立的极限学习机目标威胁估计模型具有更高的预测精度和更强的泛化能力,能够精准、有效地实现目标威胁估计。     

Optimal design of nonlinear model predictive controller based on new modified multitracker optimization algorithm

The controller design for the robotic manipulator faces different challenges such as the system's nonlinearities and the uncertainties of the parameters. Furthermore, the tracking of different linear and nonlinear trajectories represents a vital role by the manipulator. This paper suggests an optimal design for the nonlinear model predictive control (NLMPC) based on a new improved intelligent technique and it is named modified multitracker optimization algorithm (MMTOA). The proposed modification of the MTOA is carried out based on opposition-based learning (OBL) and quasi OBL approaches. This modification improves the exploration behavior of the MTOA to prevent it from becoming trapped in a local optimum. The proposed method is applied on the robotic manipulator to track different linear and nonlinear trajectories. The NLMPC parameters are tuned by the MMTOA rather than the trial and error method of the designer. The proposed NLMPC based on MMTOA is compared with the original MTOA, genetic algorithm, and cuckoo search algorithm in literature. The superiority and effectiveness of the proposed controller are confirmed to track different linear and nonlinear trajectories. Furthermore, the robustness of the proposed method is emphasized against the uncertainties of the parameters.     

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.     

An orthogonal opposition-based-learning Yin–Yang-pair optimization algorithm for engineering optimization

Yin–Yang-pair Optimization (YYPO) is a recently developed philosophy-inspired meta-heuristic algorithm, which works with two main points for exploitation and exploration, respectively, and then generates more points via splitting to search the global optimum. However, it suffers from low quality of candidate solutions in its exploration process owing to the lack of elitism. Inspired by this, a new modified algorithm named orthogonal opposition-based-learning Yin–Yang-pair Optimization (OOYO) is proposed to enhance the performance of YYPO. First, the OOYO retains the normalization operation in YYPO and starts with a single point to exploit. A set of opposite points is designed by a method of opposition-based learning with split points generated from the current optimum for exploration. Then, the points, i.e., candidate solutions, are constructed by the randomly selected split point and opposite points through the idea of orthogonal experiment design to make full use of information from the space. The proposed OOYO does not add additional time complexity and eliminates a user-defined parameter in YYPO, which facilitates parameter adjustment. The novel orthogonal opposition-based learning strategy can provide inspirations for the improvement of other optimization algorithms. Extensive test functions containing a classic test suite of 23 standard benchmark functions and 2 test suites of Swarm Intelligence Symposium 2005 and Congress on Evolutionary Computation 2020 from Institute of Electrical and Electronics Engineers are employed to evaluate the proposed algorithm. Non-parametric statistical results demonstrate that OOYO outperforms YYPO and furnishes strong competitiveness compared with other state-of-the-art algorithms. In addition, we apply OOYO to solve four well-known constrained engineering problems and a practical problem of parameters optimization in a rainstorm intensity model.

     

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。     

一种精英反向学习的萤火虫优化算法

为了提高传统萤火虫算法的收敛速度和求解精度,提出了一种精英反向学习的萤火虫优化算法。通过反向学习策略构造精英群体,在精英群体构成的区间上求普通群体的反向解,增加了群体的多样性,提高了算法的收敛速度;同时,为了避免最优个体陷入局部最优,使整个群体在搜索过程中出现停滞,提出了差分演化变异策略;最后,提出了一种线性递减的自适应步长来平衡算法的开发能力。实验结果表明,算法在收敛速度和收敛精度上有更好的效果。     

具有学习机制的正弦余弦算法

针对标准正余弦算法在求解函数优化问题时易陷入局部最优、收敛精度较差等问题,提出了一种具有学习机制的正弦余弦算法。该算法引入精英反向学习策略构造精英及反向群体,对其混合群体进行择优保留,从而优化了种群中的个体位置、提高了算法的寻优精度;同时,利用个体的反思学习能力防止个体盲目地向当前最优解学习,使算法停滞在局部最优,从而有效地避免了算法的未成熟收敛。在13个标准测试函数进行仿真实验,实验结果证明,该算法相比于对比算法具有较强的鲁棒性和函数优化能力。     

融合动态反向学习的阿奎拉鹰与哈里斯鹰混合优化算法

阿奎拉鹰优化算法(Aquila optimizer, AO)和哈里斯鹰优化算法(Harris hawks optimization, HHO)是近年提出的优化算法。AO算法全局寻优能力强,但收敛精度低,容易陷入局部最优,而HHO算法具有较强的局部开发能力,但存在全局探索能力弱,收敛速度慢的缺陷。针对原始算法存在的局限性,本文将两种算法混合并引入动态反向学习策略,提出一种融合动态反向学习的阿奎拉鹰与哈里斯鹰混合优化算法。首先,在初始化阶段引入动态反向学习策略提升混合算法初始化性能与收敛速度。此外,混合算法分别保留了AO的探索机制与HHO的开发机制,提高算法的寻优能力。仿真实验采用23个基准测试函数和2个工程设计问题测试混合算法优化性能,并对比了几种经典反向学习策略,结果表明引入动态反向学习的混合算法收敛性能更佳,能够有效求解工程设计问题。