A Multi-Layered Gravitational Search Algorithm for Function Optimization and Real-World Problems

A gravitational search algorithm(GSA)uses gravitational force among individuals to evolve population.Though GSA is an effective population-based algorithm,it exhibits low search performance and premature convergence.To ameliorate these issues,this work proposes a multi-layered GSA called MLGSA.Inspired by the two-layered structure of GSA,four layers consisting of population,iteration-best,personal-best and global-best layers are constructed.Hierarchical interactions among four layers are dynamically implemented in different search stages to greatly improve both exploration and exploitation abilities of population.Performance comparison between MLGSA and nine existing GSA variants on twenty-nine CEC2017 test functions with low,medium and high dimensions demonstrates that MLGSA is the most competitive one.It is also compared with four particle swarm optimization variants to verify its excellent performance.Moreover,the analysis of hierarchical interactions is discussed to illustrate the influence of a complete hierarchy on its performance.The relationship between its population diversity and fitness diversity is analyzed to clarify its search performance.Its computational complexity is given to show its efficiency.Finally,it is applied to twenty-two CEC2011 real-world optimization problems to show its practicality.

A multi-objective gravitational search algorithm based approach of power system stability enhancement with UPFC

On the basis of the theoretical analysis of a single-machine infinite-bus （SMIB）, using the modified linearized Phil- lips-Heffron model installed with unified power flow controller （UPFC）, the potential of the UPFC supplementary controller to enhance the dynamic stability of a power system is evaluated by measuring the electromechanical controllability through singular value decomposition （SVD） analysis. This controller is tuned to simultaneously shift the undamped electromeehanical modes to a prescribed zone in the s-plane. The problem of robust UPFC based damping controller is formulated as an optimization problem according to the eigenvalue-based multi-objective function comprising the damping factor, and the damping ratio of the undamped electromechanical modes to be solved using gravitational search algorithm （GSA） that has a strong ability to find the most optimistic results. The different loading conditions are simulated on a SMIB system and the rotor speed deviation, internal voltage deviation, DC voltage deviation and electrical power deviation responses are studied with the effect of this flexible AC transmission systems （FACTS） controller. The results reveal that the tuned GSA based UPFC controller using the proposed multi-objective function has an excellent capability in damping power system with low frequency oscillations and greatly enhances the dynamic stability of the power systems.

Improved gravitational search algorithm based on free search differential evolution

This paper presents an improved gravitational search algorithm （IGSA） as a hybridization of a relatively recent evolutionary algorithm called gravitational search algorithm （GSA）, with the free search differential evolution （FSDE）. This combination incorporates FSDE into the optimization process of GSA with an attempt to avoid the premature convergence in GSA. This strategy makes full use of the exploration ability of GSA and the exploitation ability of FSDE. IGSA is tested on a suite of benchmark functions. The experimental results demonstrate the good performance of IGSA.

Gravitational search algorithm for coordinated design of PSS and TCSC as damping controller

A newly developed heuristic global optimization algorithm, called gravitational search algorithm （GSA）, was introduced and applied for simultaneously coordinated designing of power system stabilizer （PSS） and thyristor controlled series capacitor （TCSC） as a damping controller in the multi-machine power system. The coordinated design problem of PSS and TCSC controllers over a wide range of loading conditions is formulated as a multi-objective optimization problem which is the aggregation of two objectives related to damping ratio and damping factor. By minimizing the objective function with oscillation, the characteristics between areas are contained and hence the interactions among the PSS and TCSC controller under transient conditions are modified. For evaluation of effectiveness and robustness of proposed controllers, the performance was tested on a weakly connected power system subjected to different disturbances, loading conditions and system parameter variations. The cigenvalues analysis and nonlinear simulation results demonstrate the high performance of proposed controllers which is able to provide efficient damping of low frequency oscillations.

Development of hybrid optimization algorithm for structures furnished with seismic damper devices using the particle swarm optimization method and gravitational search algorithm

Previous studies about optimizing earthquake structural energy dissipation systems indicated that most existing techniques employ merely one or a few parameters as design variables in the optimization process,and thereby are only applicable only to simple,single,or multiple degree-of-freedom structures.The current approaches to optimization procedures take a specific damper with its properties and observe the effect of applying time history data to the building;however,there are many different dampers and isolators that can be used.Furthermore,there is a lack of studies regarding the optimum location for various viscous and wall dampers.The main aim of this study is hybridization of the particle swarm optimization(PSO) and gravitational search algorithm(GSA) to optimize the performance of earthquake energy dissipation systems(i.e.,damper devices) simultaneously with optimizing the characteristics of the structure.Four types of structural dampers device are considered in this study:(ⅰ) variable stiffness bracing(VSB) system,(ⅱ) rubber wall damper(RWD),(ⅲ) nonlinear conical spring bracing(NCSB) device,(iv) and multi-action stiffener(MAS) device.Since many parameters may affect the design of seismic resistant structures,this study proposes a hybrid of PSO and GSA to develop a hybrid,multi-objective optimization method to resolve the aforementioned problems.The characteristics of the above-mentioned damper devices as well as the section size for structural beams and columns are considered as variables for development of the PSO-GSA optimization algorithm to minimize structural seismic response in terms of nodal displacement(in three directions) as well as plastic hinge formation in structural members simultaneously with the weight of the structure.After that,the optimization algorithm is implemented to identify the best position of the damper device in the structural frame to have the maximum effect and minimize the seismic structure response.To examine the performance of the proposed PSO-GSA optimization method,it has been applied to a three-story reinforced structure equipped with a seismic damper device.The results revealed that the method successfully optimized the earthquake energy dissipation systems and reduced the effects of earthquakes on structures,which significantly increase the building’s stability and safety during seismic excitation.The analysis results showed a reduction in the seismic response of the structure regarding the formation of plastic hinges in structural members as well as the displacement of each story to approximately 99.63%,60.5%,79.13% and 57.42% for the VSB device,RWD,NCSB device,and MAS device,respectively.This shows that using the PSO-GSA optimization algorithm and optimized damper devices in the structure resulted in no structural damage due to earthquake vibration.

Reliability improvement in distribution systems employing an integrated voltage sag mitigation method using binary gravitational search algorithm

A method for improving the level of reliability of distribution systems is presented by employing an integrated voltage sag mitigation method that comprises a two-staged strategy,namely,distribution network reconfiguration(DNR)followed by DSTATCOM placement.Initially,an optimal DNR is applied to reduce the propagated voltage sags during the test period.The second stage involves optimal placement of the DSTATCOM to assist the already reconfigured network.The gravitational search algorithm is used in the process of optimal DNR and in placing DSTATCOM.Reliability assessment is performed using the well-known indices.The simulation results show that the proposed method is efficient and feasible for improving the level of system reliability.

Binary Gravitational Search based Algorithm for Optimum Siting and Sizing of DG and Shunt Capacitors in Radial Distribution Systems

This paper presents a binary gravitational search algorithm (BGSA) is applied to solve the problem of optimal allotment of DG sets and Shunt capacitors in radial distribution systems. The problem is formulated as a nonlinear constrained single-objective optimization problem where the total line loss (TLL) and the total voltage deviations (TVD) are to be minimized separately by incorporating optimal placement of DG units and shunt capacitors with constraints which include limits on voltage, sizes of installed capacitors and DG. This BGSA is applied on the balanced IEEE 10 Bus distribution network and the results are compared with conventional binary particle swarm optimization.

Optimal Energy Consumption Optimization in a Smart House by Considering Electric Vehicles and Demand Response via a Hybrid Gravitational Search and Particle Swarm Optimization Algorithm

Buildings are the main energy consumers across the world,especially in urban communities.Building smartization,or the smartification of housing,therefore,is a major step towards energy grid smartization too.By controlling the energy consumption of lighting,heating,and cooling systems,energy consumption can be optimized.All or some part of the energy consumed in future smart buildings must be supplied by renewable energy sources(RES),which mitigates environmental impacts and reduces peak demand for electrical energy.In this paper,a new optimization algorithm is applied to solve the optimal energy consumption problem by considering the electric vehicles and demand response in smart homes.In this way,large power stations that work with fossil fuels will no longer be developed.The current study modeled and evaluated the performance of a smart house in the presence of electric vehicles(EVs)with bidirectional power exchangeability with the power grid,an energy storage system(ESS),and solar panels.Additionally,the solar RES and ESS for predicting solar-generated power prediction uncertainty have been considered in this work.Different case studies,including the sales of electrical energy resulting from PV panels’generated power to the power grid,time-variable loads such as washing machines,and different demand response(DR)strategies based on energy price variations were taken into account to assess the economic and technical effects of EVs,BESS,and solar panels.The proposed model was simulated in MATLAB.A hybrid particle swarm optimization(PSO)and gravitational search(GS)algorithm were utilized for optimization.Scenario generation and reduction were performed via LHS and backward methods,respectively.Obtained results demonstrate that the proposed model minimizes the energy supply cost by considering the stochastic time of use(STOU)loads,EV,ESS,and PV system.Based on the results,the proposed model markedly reduced the electricity costs of the smart house.

Investigation Effects of Selection Mechanisms for Gravitational Search Algorithm

The gravitational search algorithm (GSA) is a population-based heuristic optimization technique and has been proposed for solving continuous optimization problems. The GSA tries to obtain optimum or near optimum solution for the optimization problems by using interaction in all agents or masses in the population. This paper proposes and analyzes fitness-based proportional (rou- lette-wheel), tournament, rank-based and random selection mechanisms for choosing agents which they act masses in the GSA. The proposed methods are applied to solve 23 numerical benchmark functions, and obtained results are compared with the basic GSA algorithm. Experimental results show that the proposed methods are better than the basic GSA in terms of solution quality.

基于CEEMDAN-GSA-LSTM和SVR的光伏功率短期区间预测

针对光伏输出功率存在间歇性和波动性的问题,提出一种光伏功率短期区间预测模型.首先,该模型采用自适应噪声完备集合经验模态分解将历史光伏出力数据分解为不同的分量并按照其与赤纬角、时角等时序特征量的相关性定义为时序分量和随机分量.其次,分别使用经过引力搜索算法优化的长短期记忆神经网络和支持向量回归模型对时序分量和随机分量进行预测.再次,叠加时序分量和随机分量的预测结果得到点预测结果.然后,对误差进行Johnson变换及正态分布建模后得到光伏功率区间预测结果.最后,利用算例验证该模型的有效性.结果表明:在不同天气情况下,上述模型比现有预测模型精度更高,具有较好的鲁棒性,能够基于预测值提供较为精准的置信区间.

基于GSA的水轮机调速器PID控制参数优化方法

针对现有水轮机调速器控制参数优化研究依赖系统特征参数值、忽视发电机模型的不确定性以及控制策略较落后等问题,以引力搜索算法(GSA)为基础,对水轮机调速器PID控制参数优化模型和优化方法等进行分析,仿真模拟优化中国某水电机组,比较不同状态下水轮机调速器的组合控制效果。结果表明,在孤网运行条件下,基于GSA的水轮机调速器PID控制参数优化方法对水轮机组动态运行品质的提升效果最佳。

基于PSO-GSA优化的井下加权质心人员定位算法

针对煤矿复杂环境中,接收信号强度指示的人员定位精度较低,难以动态跟踪参数变化的问题,提出一种利用改进的引力搜索算法应用于加权质心定位中进行井下人员定位的方法。先采用对数距离路径损耗模型得到信标节点到未知节点的距离,然后通过加权质心定位算法对未知节点进行定位,最后利用粒子群万有引力混合算法对相关参数和估计的位置信息进行优化。实验结果表明,该方法能够增强对环境变化的自适应能力,更有效地提高了定位精度。

基于Grid-GSA算法的植保无人机路径规划方法

为了提高植保无人机的作业效率,研究了一种路径规划方法。运用栅格法构建环境模型,根据实际的作业区域规模、形状等环境信息和无人机航向,为相应栅格赋予概率,无人机优先选择概率高的栅格行进。基于上述机制实现了在形状不规则的作业区域内进行往复回转式全覆盖路径规划;以每次植保作业距离为变量,根据仿真算法得出返航点数量与位置来确定寻优模型中的变量维数范围,以往返飞行、电池更换与药剂装填等非植保作业耗费时间最短为目标函数,通过采用引力搜索算法,实现对返航点数量与位置的寻优;为无人机设置必要的路径纠偏与光顺机制,使无人机能够按既定路线与速度飞行。对提出的路径规划方法进行了实例检验,结果显示,相比于简单规划与未规划的情况,运用Grid-GSA规划方法得出的结果中往返飞行距离总和分别减少了14%与68%,非植保作业时间分别减少了21%与36%,其它各项指标也均有不同程度的提高。在验证测试试验中,实际的往返距离总和减少了322 m,实际路径与规划路径存在较小偏差。验证了路径规划方法具有合理性、可行性以及一定的实用性。

基于双层聚类与GSA-LSSVM的汽轮机热耗率多模型预测

针对单模型难以精确描述具有复杂非线性特性的汽轮机热耗率的问题,提出一种新的热耗率多模型建模方法。首先应用GK算法分析出最优聚类个数以及初始聚类中心,避免了聚类数确定的盲目性;然后利用核模糊C均值算法对热耗率样本集做出聚类划分,在每个子空间中利用最小二乘支持向量机(LSSVM)辨识出相应子模型,同时,为了保证子模型精确度,采用引力搜索算法来解决LSSVM参数优化问题;最后,将子模型通过隶属度值加权融合得到精确的热耗率预测模型。以某600MW超临界汽轮机组为研究对象,基于现场数据建立汽轮机热耗率预报模型,仿真结果验证了提出的多模型建模方法具有较高的预报精确度和泛化能力。

FCM融合改进的GSA算法在医学图像分割中的研究

医学图像由于具有复杂性,在对其进行图像分割时存在很大的不确定性,为了提高模糊c均值聚类算法(FCM)在处理医学图像分割时的性能,提出一种新的混合方法进行图像分割。利用FCM算法将图像像素分成均匀的区域,融合引力搜索算法,将改进的引力搜索算法纳入模糊c均值聚类算法中,以找到最优聚类中心,使模糊c均值聚类的适应度函数值最小,从而提高分割效果。实验结果表明,相对于传统的聚类算法,所提算法在分割复杂的医学图像方面更具有效性。

融合FAST特征选择与ABQGSA-SVM的网络入侵检测

为进一步提升网络入侵检测效果,提出一种融合FAST特征选择与自适应二进制量子引力搜索支持向量机的(FAST-ABQGSA-SVM)网络入侵检测算法。利用FAST算法过滤掉原始特征集中冗余无关的特征形成候选特征子集,基于组合优化策略采用自适应二进制量子引力搜索算法对候选特征子集与SVM分类器参数进行组合优化。在ABQGSA反复学习寻优过程中,采取动态自适应波动式调整策略更新量子旋转角以平衡算法全局搜索能力和局部搜索能力;同时为提升算法的自适应变异能力,设计与进化程度及个体适应度值相关的自适应变异概率,当种群进化出现停滞时及时引入量子位离散交叉操作帮助种群摆脱局部极值。通过KDD CUP 99仿真实验表明,所提出的FAST-ABQGSA-SVM算法较其他同类型检测算法具有更好的鲁棒性、学习精度以及检测效果。

基于PSOGSA前向神经网络的石化控制系统入侵检测

针对日趋严峻的石化行业工业控制系统(ICS)安全形势,提出一种基于粒子群优化(PSO)和万有引力搜索算法(GSA)的前向神经网络(FNNPSOGSA),用于解决其中的入侵检测问题。分别利用GSA的全局寻优能力和PSO快速局部收敛优势,提出了一种基于PSO和GSA的混合算法PSOGSA,并将其用于前向神经网络(FNNs)的训练。通过多组基准测试数据集,将FNNPSOGSA预测结果同FNNPSO、FNNGSA和参考文献中改进的FRGNN(K-NN)和FRGNN(Naive Bayes)预测结果相比较,验证了PSOGSA在训练FNNs中是可行的,并且FNNPSOGSA具有更高的预测准确率和更强的泛化能力。更进一步,对工控入侵检测标准数据集的仿真结果表明其在工控系统入侵检测中的可行性和有效性。

基于PSO和GSA的神经网络轴承故障诊断

针对原始BP神经网络诊断方法存在初始权值和阈值随机选取而导致识别率低的问题,提出了一种基于粒子群优化算法(PSO)与引力搜索算法(GSA)优化的神经网络诊断方法。上述方法先从原始信号中提取特征向量,再利用PSO的记忆能力和信息共享能力对GSA进行改进,并以此双优化算法来优化BP神经网络的初始权值及阈值,形成一种适用于轴承故障诊断的双优化神经网络模型。实验结果表明,上述方法与原始BP法、GSA-BP法相比,能准确地识别出多种滚动轴承故障,具有比较理想的诊断效果。

基于GSA-VMD和自适应CNN的滚动轴承故障诊断

针对轴承故障诊断中,变分模态分解(VMD)的参数选择与卷积神经网络架构难以确定的问题,研究一种GSA-VMD和自适应CNN的滚动轴承故障诊断方法。首先,采用引力搜索算法(GSA)优化VMD的参数,接着利用优化的VMD分解轴承的振动信号得到若干模态分量;然后,将模态分量与振动信号结合构建特征矩阵,作为自适应CNN的输入;最后,自适应CNN采用粒子群算法(PSO)解决CNN架构难以确定的问题,适应性地构建CNN故障诊断模型,判断轴承的故障类型。实验结果表明:与ANN、CNN-SVM、WDCNN、GA-CNN诊断方法对比,所提方法 准确率更高、稳定性好、适应性强。

车辆磁流变半主动悬架GSA-LQG控制研究

针对传统的线性二次型高斯(Linear Quadratic Gaussian,LQG)控制器存在各加权矩阵系数不易确定等问题,对于车辆磁流变半主动悬架设计了基于引力搜索算法(Gravity Search Algorithm,GSA)的线性二次型高斯(GSA-LQG)控制。以悬架各性能指标为目标函数,采用引力搜索算法对加权矩阵系数进行寻优。选用磁流变阻尼器(Magnetorheological Damper,MRD)作为悬架的半主动部件,同时建立二自由度的1/4车辆磁流变半主动悬架系统模型。以随机路面激励作为输入,在MATLAB/Simulink软件中分别对被动悬架控制、基于LQG控制的车辆磁流变半主动悬架和基于GSA-LQG控制的车辆磁流变半主动悬架进行仿真分析,结果表明,基于GSA-LQG控制的车辆磁流变半主动悬架具有更好的舒适性能和安全性能。