基于改进引力搜索算法的桁架结构优化设计

引力搜索算法是近几年提出的较有竞争力的群智能优化算法,然而,标准引力搜索算法存在后期收敛速度慢的缺点。为有效利用优化算法来解决结构优化的问题,提出一种改进的引力搜索算法(improved gravitational search algorithm,IGSA)。通过引入Logistic映射,使GSA初始种群遍历整个搜索空间,提高算法找出最优解的可能性。通过引入粒子群算法(particle swarm optimization,PSO)的信息交互机制,利用个体粒子历史最佳位置和种群历史最佳位置动态调整粒子的速度和位置,使个体粒子更快地向适应度值更高的位置移动,使算法搜索能力加强。对6个经典测试函数进行寻优,结果表明改进后算法收敛速度快,收敛精度高,稳定性较佳,跳出局部最佳解的能力较强。用IGSA和GSA对72杆空间桁架进行尺寸优化,与其他算法相比,结果表明IGSA得到最优值的迭代次数明显减少,得到的最优解明显优于通用算法。     

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.     

工业机器人时间-能量最优轨迹规划

针对工业机器人时间最优、能耗最优的多目标轨迹优化问题,提出了一种基于改进引力搜索算法的最优轨迹规划方法。将引力搜索算法的种群按照惯性质量的大小均分为两组。首先引领组的粒子进行小范围的邻域搜索。然后引领组通过施加引力来引导跟随组的粒子进行位置更新。同时引入人工蜂群算法的贪婪选择策略,每次更新保留较优解。以自主研发的150 kg重载机器人为实验对象,将所提算法与标准人工蜂群算法和引力搜索算法进行比较,结果表明所提算法具有更优性能。     

Convergence analysis and performance of an improved gravitational search algorithm

Gravitational search algorithm (GSA) has been shown to yield good performance for solving various optimization problems. However, it tends to suffer from premature convergence and loses the abilities of exploration and exploitation when solving complex problems. This paper presents an improved gravitational search algorithm (IGSA) that first employs chaotic perturbation operator and then considers memory strategy to overcome the aforementioned problems. The chaotic operator can enhance its global convergence to escape from local optima, and the memory strategy provides a faster convergence and shares individual's best fitness history to improve the exploitation ability. After that, convergence analysis of the proposed IGSA is presented based on discrete-time linear system theory and results show that IGSA is not only guaranteed to converge under the conditions, but can converge to the global optima with the probability 1. Finally, choice of reasonable parameters for IGSA is discussed on four typical benchmark test functions based on sensitivity analysis. Moreover, IGSA is tested against a suite of benchmark functions with excellent results and is compared to GA, PSO, HS, WDO, CFO, APO and other well-known GSA variants presented in the literatures. The results obtained show that IGSA converges faster than GSA and other heuristic algorithms investigated in this paper with higher global optimization performance.     

带有引力搜索算子的烟花算法

针对烟花算法(FA) 寻优过程中粒子间信息交流少、对最优点位置不在原点和原点附近的目标函数求解能力差的缺点, 提出带有引力搜索算子的烟花算法(FAGSO). 算子利用粒子间相互引力作用对粒子维度信息进行改善, 以提高算法的优化性能. 6 个标准和增加位置偏移测试函数的仿真结果表明, FAGSO相比于FA、粒子群算法和引力搜索算法, 在寻优速度和寻优精度方面有更好的优化性能.

     

Strategic bidding using fuzzy adaptive gravitational search algorithm in a pool based electricity market

A novel stochastic optimization approach to solve optimal bidding strategy problem in a pool based electricity market using fuzzy adaptive gravitational search algorithm (FAGSA) is presented. Generating companies (suppliers) participate in the bidding process in order to maximize their profits in an electricity market. Each supplier will bid strategically for choosing the bidding coefficients to counter the competitors bidding strategy. The gravitational search algorithm (GSA) is tedious to solve the optimal bidding strategy problem because, the optimum selection of gravitational constant (G). To overcome this problem, FAGSA is applied for the first time to tune the gravitational constant using fuzzy “IF/THEN” rules. The fuzzy rule-based systems are natural candidates to design gravitational constant, because they provide a way to develop decision mechanism based on specific nature of search regions, transitions between their boundaries and completely dependent on the problem. The proposed method is tested on IEEE 30-bus system and 75-bus Indian practical system and compared with GSA, particle swarm optimization (PSO) and genetic algorithm (GA). The results show that, fuzzification of the gravitational constant, improve search behavior, solution quality and reduced computational time compared against standard constant parameter algorithms.     

改进引力搜索算法用于工控系统入侵检测

为提高引力搜索算法的全局搜索能力和收敛速度,提出改进引力搜索算法(IGSA)。为引力常量嵌入混沌映射,使其在减小的同时可以混沌地变化,快速地跳出局部极小值,扩展搜索区域;引入细菌觅食算法(BFA)的趋化算子,利用最优个体信息对当前最佳粒子进行调整,提高收敛速度。4种基准函数的测试结果对比表明,IGSA有着更好的搜索能力和收敛速度。利用IGSA对孪生支持向量机(TWSVM)的参数进行寻优,将寻优后的TWSVM分类器应用于工控标准入侵检测数据集。实验结果表明,IGSA-TWSVM对整体入侵的误报率、漏报率和对各类入侵的检测率都优于其它算法。     

PSOGSA-Explore: A new hybrid metaheuristic approach for beampattern optimization in collaborative beamforming

A conventional collaborative beamforming (CB) system suffers from high sidelobes due to the random positioning of the nodes. This paper introduces a hybrid metaheuristic optimization algorithm called the Particle Swarm Optimization and Gravitational Search Algorithm-Explore (PSOGSA-E) to suppress the peak sidelobe level (PSL) in CB, by the means of finding the best weight for each node. The proposed algorithm combines the local search ability of the gravitational search algorithm (GSA) with the social thinking skills of the legacy particle swarm optimization (PSO) and allows exploration to avoid premature convergence. The proposed algorithm also simplifies the cost of variable parameter tuning compared to the legacy optimization algorithms. Simulations show that the proposed PSOGSA-E outperforms the conventional, the legacy PSO, GSA and PSOGSA optimized collaborative beamformer by obtaining better results faster, producing up to 100% improvement in PSL reduction when the disk size is small.     

改进的万有引力搜索算法在函数优化中的应用

万有引力搜索算法应用于函数优化问题时易陷入局部最优解且优化精度不高。针对这些问题,提出了一种改进的万有引力搜索算法。该算法通过引入反向学习策略、精英策略和边界变异策略,显著地提高了万有引力搜索算法中粒子的探索能力与开发能力,获得了较强的全局优化能力和局部优化能力。通过对6个非线性基准函数进行仿真实验,结果表明：与基本的万有引力搜索算法、加权的万有引力搜索算法和人工蜂群算法相比,改进的万有引力搜索算法在求解复杂函数的优化问题时具有更好的优化性能。     

基数约束投资组合问题的一种混合元启发式算法求解

针对资产数目和投资资金比例受约束的投资组合选择这一NP难问题,基于混沌搜索、粒子群优化和引力搜索算法提出了一种新的混合元启发式搜索算法。该算法能很好地平衡开发能力和勘探能力,有效抑制了算法早熟收敛现象。标准测试函数的测试结果表明混合算法与标准的粒子群优化和引力搜索算法相比具有更好的寻优效率;实证分析进一步对混合算法与遗传算法及粒子群优化算法在求解这类投资组合选择问题的性能进行了比较。数值结果表明,混合算法在搜索具有高预期回报的非支配投资组合方面表现更好,取得了更为满意的结果。     

A memory-based gravitational search algorithm for enhancing minimum variance distortionless response beamforming

This paper introduces a memory-based version of gravitational search algorithm (MBGSA) to improve the beamforming performance by preventing loss of optimal trajectory. The conventional gravitational search algorithm (GSA) is a memory-less heuristic optimization algorithm based on Newton’s laws of gravitation. Therefore, the positions of agents only depend on the optimal solutions of previous iteration. In GSA, there is always a chance to lose optimal trajectory because of not utilizing the best solution from previous iterations of the optimization process. This drawback reduces the performance of GSA when dealing with complicated optimization problems. However, the MBGSA uses the overall best solution of the agents from previous iterations in the calculation of agents’ positions. Consequently, the agents try to improve their positions by always searching around overall best solutions. The performance of the MBGSA is evaluated by solving fourteen standard benchmark optimization problems and the results are compared with GSA and modified GSA (MGSA). It is also applied to adaptive beamforming problems to improve the weight vectors computed by Minimum Variance Distortionless Response (MVDR) algorithm as a real world optimization problem. The proposed algorithm demonstrates high performance of convergence compared to GSA and Particle Swarm Optimization (PSO).     

Binary optimization using hybrid particle swarm optimization and gravitational search algorithm

The PSOGSA is a novel hybrid optimization algorithm, combining strengths of both particle swarm optimization (PSO) and gravitational search algorithm (GSA). It has been proven that this algorithm outperforms both PSO and GSA in terms of improved exploration and exploitation. The original version of this algorithm is well suited for problems with continuous search space. Some problems, however, have binary parameters. This paper proposes a binary version of hybrid PSOGSA called BPSOGSA to solve these kinds of optimization problems. The paper also considers integration of adaptive values to further balance exploration and exploitation of BPSOGSA. In order to evaluate the efficiencies of the proposed binary algorithm, 22 benchmark functions are employed and divided into three groups: unimodal, multimodal, and composite. The experimental results confirm better performance of BPSOGSA compared with binary gravitational search algorithm (BGSA), binary particle swarm optimization (BPSO), and genetic algorithm in terms of avoiding local minima and convergence rate.     

A Solution to the Combined Economic and Emission Dispatch Using Hybrid PSOGSA Algorithm

This article presents a new hybrid algorithm based on particle swarm optimization (PSO) and the gravitational search algorithm (GSA) for solving the combined economic and emission dispatch (CEED) problem in power systems. Performance of this approach for the CEED problem is studied and evaluated on three test systems with 3, 6, and 40 generating units, with various cost curve nature and different constraints. The results obtained are compared to those reported in the recent literature. Those results show that the proposed algorithm provides an effective and robust high-quality solution of the CEED problem.     

基于IGSA优化的LSSVM制冷系统故障诊断研究

为提高制冷系统故障诊断的准确率,提出一种基于改进引力搜索算法(IGSA)优化的最小二乘支持向量机(LSSVM)的制冷系统故障诊断方法。首先,引入粒子群算法的速度更新机制对引力搜索算法进行改进,增加粒子的记忆性和信息共享能力,提高了算法的收敛速度和搜索精度;其次,利用IGSA对LSSVM的核参数与正则化参数进行优化,得到最优的IGSA-LSSVM故障诊断模型。最后,利用故障模拟实验台模拟制冷系统的四种典型故障,将优化好的LSSVM模型对其进行分类识别,并与标准LSSVM、GSA-LSSVM和PSO-LSSVM模型进行比较。仿真结果表明,基于IGSA优化的LSSVM方法具有良好的辨识能力和泛化能力,能够更好地对制冷系统故障进行诊断。     

CGSA scheduler: A multi-objective-based hybrid approach for task scheduling in cloud environment

In cloud computing task scheduling is one of the important processes. The key problem of scheduling is how to allocate the entire task to a corresponding virtual machine while maximizing profit. The main objective of this paper is to execute the entire task with low cost, less resource use, and less energy consumption. To obtain the multi-objective function for scheduling, in this paper we propose a hybridization of cuckoo search and gravitational search algorithm (CGSA). The vital design of our approach is to exploit the merits of both cuckoo search (CS) and gravitational search algorithms (GSA) while avoiding their drawbacks. The performance of the algorithm is analyzed based on the different evaluation measures. The algorithms like GSA, CS, Particle swarm optimization (PSO), and genetic algorithm (GA) are used as a comparative analysis. The experimental results show that our proposed algorithm achieves the better result compare to the existing approaches.     

A novel hybrid gravitational search and pattern search algorithm for load frequency control of nonlinear power system

In this paper, a hybrid gravitational search algorithm (GSA) and pattern search (PS) technique is proposed for load frequency control (LFC) of multi-area power system. Initially, various conventional error criterions are considered, the PI controller parameters for a two-area power system are optimized employing GSA and the effect of objective function on system performance is analyzed. Then GSA control parameters are tuned by carrying out multiple runs of algorithm for each control parameter variation. After that PS is employed to fine tune the best solution provided by GSA. Further, modifications in the objective function and controller structure are introduced and the controller parameters are optimized employing the proposed hybrid GSA and PS (hGSA-PS) approach. The superiority of the proposed approach is demonstrated by comparing the results with some recently published modern heuristic optimization techniques such as firefly algorithm (FA), differential evolution (DE), bacteria foraging optimization algorithm (BFOA), particle swarm optimization (PSO), hybrid BFOA-PSO, NSGA-II and genetic algorithm (GA) for the same interconnected power system. Additionally, sensitivity analysis is performed by varying the system parameters and operating load conditions from their nominal values. Also, the proposed approach is extended to two-area reheat thermal power system by considering the physical constraints such as reheat turbine, generation rate constraint (GRC) and governor dead band (GDB) nonlinearity. Finally, to demonstrate the ability of the proposed algorithm to cope with nonlinear and unequal interconnected areas with different controller coefficients, the study is extended to a nonlinear three unequal area power system and the controller parameters of each area are optimized using proposed hGSA-PS technique.     

求解流水线调度问题的万有引力搜索算法

研究了以最大完工时间为目标的流水线调度问题,使用万有引力算法求解调度问题,提出了一种最大排序规则,利用物体间各个位置分量值存在的大小次序关系,并结合随机键编码的方法产生,将物体的连续位置转变成了一个可行的调度方案;提出了一种边界变异的策略使得越界的物体不再聚集在边界上,而是分布在边界附近的可行空间内,从而增加种群的多样性;结合交换算子和插入算子提出了一种新的局部搜索算法,有效地避免了算法陷入局部最优值,进一步提高了解的质量.最后证明了算法的收敛性,并且计算了算法的时间复杂度和空间复杂度,仿真实验说明了所得算法的有效性.     

Optimal design and implementation of compact fractional order microwave integrator

The implementation of novel, stable, accurate, and wideband infinite impulse response fractional order microwave integrators (FOMIs) is presented. The formulation of FOMIs is employed with equal length line elements in cascading. The optimum values of characteristic impedances of the line elements are determined by approximation to the ideal fractional order integrator (FOI). The hybrid algorithm (HPSO‐GSA) combining particle swarm optimization (PSO) and gravitational search algorithm (GSA) which integrates PSO's exploitation and GSA's exploration ability is used. The comparison of HPSO‐GSA with PSO and GSA is carried out for the proposed FOMIs. The performance criteria used are magnitude response, absolute magnitude error, phase response, pole‐zero response, percentage improvement graph, and convergence rate. The simulation analysis affirms the superiority of proposed FOMI using HPSO‐GSA. The absolute magnitude error of proposed 0.5 order HPSO‐GSA‐based FOMI is as low as 0.9436. The structure of the designed FOI is implemented with microstrip configuration on RT/Duroid substrate with permittivity 2.2 and thickness 0.762 mm that is eligible for wideband microwave integrator. The designed FOMI is compact in size and suitable to cover microwave applications. The measured results are established in fine agreement with simulation results in the frequency range of 2‐9 GHz in MATLAB and Advanced Design Software environment.     

Gravitational search algorithm: a comprehensive analysis of recent variants

Gravitational search algorithm is a nature-inspired algorithm based on the mathematical modelling of the Newton’s law of gravity and motion. In a decade, researchers have presented many variants of gravitational search algorithm by modifying its parameters to efficiently solve complex optimization problems. This paper conducts a comparative analysis among ten variants of gravitational search algorithm which modify three parameters, namely Kbest, velocity, and position. Experiments are conducted on two sets of benchmark categories, namely standard functions and CEC2015 functions, including problems belonging to different categories such as unimodal, multimodal, and unconstrained optimization functions. The performance comparison is evaluated and statistically validated in terms of mean fitness value and convergence graph. In experiments, IGSA has achieved better precision with balanced trade-off between exploration and exploitation. Moreover, triple negative breast cancer dataset has been considered to analysis the performance of GSA variants for the nuclei segmentation. The variants performance has been analysed in terms of both qualitative and quantitive with aggregated Jaccard index as performance measure. Experiments affirm that IGSA-based method has outperformed other methods.

     

基于混合算法的含分布式电源的配电网优化

考虑到分布式电源的选址与定容对配电网有着重要影响意义,针对分布式电源的接入对配电网系统能量损耗和各节点电压影响的问题,首先建立了以有功功率损耗和系统节点电压的目标函数优化模型,提出了充分整合引力搜索算法(GSA)的勘探能力和粒子群(PSO)的开采能力的混合算法(PSOG-SA),同时确定权重系数,最后采用IEEE-33标准节点配电网模型进行了仿真实验,通过和其他两种算法的比较,验证了配电网系统在该算法下的有效性和可靠性.算例分析表明,合理的DG接入能够一定程度上降低系统有功功率损耗,改善节点电压.