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.

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.

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.

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.

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。

基于引力搜索算法的激光位移传感器参数优化

为了优化中等量程激光三角位移传感器性能及体积,以200 mm~500 mm量程为例,建立了数学模型实现结构参数优化。在传感器结构设计中,采用平面反射镜对光路进行折叠,以工作物距、透镜焦距、线阵探测器件位置以及反射镜位置为被优化量并定义了目标函数,采用引力搜索算法(gravitational search algorithm,GSA)实现对位移传感器的结构优化。经过算法迭代,相同宽度限制下所得优化后的结构参数与传统激光三角结构相比,在500 mm处灵敏度提高24.29%,非线性误差由11.40%降低为7.43%。结果表明,此结构与优化算法对激光三角位移传感器性能与体积有较大的正向优化效果。

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.

配电网智能柱上断路器优化配置策略

针对配网一二次融合柱上断路器的安装优化问题,分析配电网故障时柱上断路器和熔断器的配合动作,建立用户停电时间与柱上断路器位置之间的模型。考虑以柱上断路器投资费用、运行费用和停电损失之和为最小的优化目标模型,通过改进引力搜索算法提升寻优速度,增强算法跳出局部最优的能力。对IEEE-RBTS BUS6系统进行案例分析。结果表明,所提策略能优化柱上断路器的安装数量和位置,提升了配电网运行的经济性和可靠性。将所提方法应用到配网柱上断路器优化配置中是合理且有效的。

基于精英思想自适应改进万有引力搜索算法

为了解决万有引力搜索算法容易出现局部最优的问题,提出了一种新型改进万有引力搜索算法。该算法在质量的计算中引入随机因子;结合精英思想,基于适应度值对力进行有选择的合成,并且对更优粒子对应的力赋予更大的随机数;引入控制参数,自适应地更新粒子的位置,减小某些粒子过于随意变化带来的影响。通过以上这些操作,增强了算法的随机性,同时保证了算法的收敛性。经对10个基准函数进行仿真实验,结果表明新算法有更好的收敛速度和寻优精度,全局和局部优化能力增强。

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。

Path planning of unmanned aerial vehicle based on improved gravitational search algorithm

Path planning of Uninhabited Aerial Vehicle(UAV) is a complicated global optimum problem.In the paper,an improved Gravitational Search Algorithm(GSA) was proposed to solve the path planning problem.Gravitational Search Algorithm(GSA) is a newly presented under the inspiration of the Newtonian gravity,and it is easy to fall local best.On the basis of introducing the idea of memory and social information of Particle Swarm Optimization(PSO),a novel moving strategy in the searching space was designed,which can improve the quality of the optimal solution.Subsequently,a weighted value was assigned to inertia mass of every agent in each iteration process to accelerate the convergence speed of the search.Particle position was updated according to the selection rules of survival of the fittest.In this way,the population is always moving in the direction of the optimal solution.The feasibility and effectiveness of our improved GSA approach was verified by comparative experimental results with PSO,basic GSA and two other GSA models.

An Improved Gravitational Search Algorithm for Dynamic Neural Network Identification

Gravitational search algorithm(GSA) is a newly developed and promising algorithm based on the law of gravity and interaction between masses. This paper proposes an improved gravitational search algorithm(IGSA) to improve the performance of the GSA, and first applies it to the field of dynamic neural network identification. The IGSA uses trial-and-error method to update the optimal agent during the whole search process. And in the late period of the search, it changes the orbit of the poor agent and searches the optimal agent s position further using the coordinate descent method. For the experimental verification of the proposed algorithm,both GSA and IGSA are testified on a suite of four well-known benchmark functions and their complexities are compared. It is shown that IGSA has much better efficiency, optimization precision, convergence rate and robustness than GSA. Thereafter, the IGSA is applied to the nonlinear autoregressive exogenous(NARX) recurrent neural network identification for a magnetic levitation system.Compared with the system identification based on gravitational search algorithm neural network(GSANN) and other conventional methods like BPNN and GANN, the proposed algorithm shows the best performance.

Hypersonic reentry trajectory planning by using hybrid fractional-order particle swarm optimization and gravitational search algorithm

This paper proposes a novel hybrid algorithm called Fractional-order Particle Swarm optimization Gravitational Search Algorithm(FPSOGSA)and applies it to the trajectory planning of the hypersonic lifting reentry flight vehicles.The proposed method is used to calculate the control profiles to achieve the two objectives,namely a smoother trajectory and enforcement of the path constraints with terminal accuracy.The smoothness of the trajectory is achieved by scheduling the bank angle with the aid of a modified scheme known as a Quasi-Equilibrium Glide(QEG)scheme.The aerodynamic load factor and the dynamic pressure path constraints are enforced by further planning of the bank angle with the help of a constraint enforcement scheme.The maximum heating rate path constraint is enforced through the angle of attack parameterization.The Common Aero Vehicle(CAV)flight vehicle is used for the simulation purpose to test and compare the proposed method with that of the standard Particle Swarm Optimization(PSO)method and the standard Gravitational Search Algorithm(GSA).The simulation results confirm the efficiency of the proposed FPSOGSA method over the standard PSO and the GSA methods by showing its better convergence and computation efficiency.