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。

基于改进GSA-SVM算法的电能质量扰动分类方法

针对不同类型电能质量扰动信号分类准确率不高的问题,通过MATLAB/simulink搭建常见的9种不同的电能质量扰动信号的模型进行仿真分析,提出一种改进的万有引力搜索算法(improved gravitational search algorithm,IGSA)对支持向量机(support vector machine,SVM)的惩罚因子和核函数参数进行寻优的方法,通过优化SVM的惩罚因子和核函数参数,构建IGSA-SVM分类器,再把提取到的特征向量进行归一化之后输入到所构造好IGSA-SVM分类器中进行训练与分类。仿真结果表明,IGSA-SVM分类器的分类准确率比SVM和GSA-SVM这2种分类器都要好,可以实现对9种不同的电能质量扰动信号的快速准确分类,有利于解决实际的工程问题。

基于CPSOGSA算法的威布尔参数估计及其在民机设备可靠性评估中的应用

为了解决小样本条件下民机装备可靠性模型参数的估计问题,本文提出一种基于收缩系数的粒子群万有引力搜索算法(Contraction factor Particle Swarm Optimization-Gravitational Search Algorithm,CPSOGSA)的参数估计算法。该方法提升了粒子群算法寻优性能,有效提升威布尔模型的参数估计精度。通过算例证明:该方法可以很好地用于民机设备的小样本可靠性参数估计,估计结果具有较高的精度,且耗时更短,表明了该方法的有效性和可行性。

基于GSA-SVR算法的MEMS温度漂移补偿方法

针对微机电系统(MEMS)仪表零偏受温度变化影响较大的问题,该文提出了一种基于引力搜索算法-支持向量回归(GSA-SVR)的MEMS零偏温度漂移补偿方法。先通过小波变换对MEMS陀螺和MEMS加速度计输出信号进行预处理,再采用GSA-SVR算法对MEMS在不同工作状态下进行温度建模并补偿。实验结果表明,在稳定工作阶段,与补偿前相比,补偿后加速度计和陀螺的输出标准差分别降低了90%和85%。与传统SVR相比,该文方法准确性较高,实用性较好,GSA-SVR算法将加速度计和陀螺输出的标准差分别降低了6%和10%。

基于改进引力搜索算法的水轮机调节系统仿真

针对现阶段水电机组存在多种复杂工况、工程计算受限于算法本身的复杂性等问题,提出一种改进的引力搜索算法(改进PSOGSA),以此提高水轮机控制参数的优化性能,弥补传统控制策略难以满足动态需求的不足.首先,结合PSO算法,在GSA的速度更新公式中引入学习因子进行改进.其次,应用一种权重系数优化其位置更新公式,提高算法的自适应性.最后,结合相关仿真建模试验,使用所提改进PSOGSA对水轮机调节系统PID参数进行优化调节.仿真结果表明,在5%空载频率扰动下,改进PSOGSA的PID控制器明显优于上述传统算法,所调节的模型系统能在更短时间内趋于稳定,此时的超调量远低于传统算法,表明此改进PSOGSA在后续迭代中具备更高的迭代效率,并且改善了常规算法中易陷入局部最优的问题,从而证明了改进PSOGSA的合理有效性,水轮机调节系统的控制效果在一定程度上得到优化.

基于改进GSA算法的多能源移动电源车优化配置

传统能源供给模式很难覆盖高原高寒地区的能源孤岛,而多能源移动电源车因其机动灵活、环境适应性强的特点成为较好的解决手段。现有多能源移动电源车尚缺乏针对高原高寒独特背景下的应用研究,且当前研究中的多能源配置算法存在收敛速度慢、易陷入局部最优等问题。本文提出一种基于改进型万有引力算法的多能源配置算法,以多能源移动电源车年经济成本为目标,在万有引力算法的基础上,引入粒子群算法的思想,将个体历史最优和全局最优位置赋权,引入粒子群速度迭代计算,提高粒子群收敛的速度和方向性。依据西藏某地区实际应用算例,该算法在收敛速度和全局搜索能力的优越性得到验证。结果表明,本文设计的移动电源车多能源配置具有更好的经济性,可为高原高寒地区多能源移动电源车的优化配置提供设计依据。

计及工况预测误差的主动配电网日前无功优化调度策略

为解决工况预测误差较大时,日前无功优化调度方案优化效果不佳的问题,提出了计及工况预测误差的主动配电网日前无功优化调度策略。首先,使用轻量级梯度提升机算法建立日前工况功率预测模型;其次,考虑大规模高比例分布式电源接入主动配电网,以调度时段内所有时间断面的多目标加权累加和为目标函数建立日前无功优化调度模型;最后,设计了一种变寻优粒子空间的改进引力搜索算法对日前无功优化调度模型进行求解,该算法根据历史工况预测误差评价指标调整寻优粒子空间各维度的上下限矩阵,从而抑制了当无功区域内工况预测误差较大时可控设备调度异常的缺陷。最后采用拓展的IEEE 33节点系统算例进行有效性验证。

基于混沌万有引力算法对APSIM模型中旱地春小麦产量形成参数的优化

为了解决APSIM模型中春小麦产量形成参数本土化率定过程中所面临的耗时长、精度差、效率低等问题,采用混沌万有引力(chaotic gravitational search algorithm, CGSA)算法,基于1971-2014和2018-2021年甘肃省定西市统计年鉴中的产量数据以及2015-2017年定西市安定区凤翔镇安家沟村的大田试验数据、1971-2021年定西市安定区的产量和气象资料,对春小麦产量形成参数进行优化。结果表明,采用CGSA优化参数后,均方根误差(RMSE)、归一化均方根误差(NRMSE)和模型有效性指数(ME)的平均值分别为22.98 kg·hm^(-2)、1.393%和0.995,说明模型在甘肃省定西市春小麦产量的评估中表现出较好的适应性。此外,CGSA具有较好的全局寻优性能和较快的收敛性,为APSIM模型的参数优化提供了一种高效、精准的方法。

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。