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.

     

带有Levy Flight机制的引力搜索算法

引力搜索算法（gravitational search algorithm,GSA）是模拟万有引力定律进行搜索的一种新颖的优化算法,已有研究表明GSA算法相比一些传统的优化算法拥有较好的收敛性能,但其缺乏有效的全局寻优机制,易于被局部极值吸引,从而陷入早熟收敛。因此提出了一种基于Levy Flight和权值惯性递减的引力搜索算法QmuGSA,以加强算法的全局寻优能力。该算法通过Levy Flight独特的不均匀随机游走的机制扩大粒子的搜索范围,增加种群多样性,从而更容易跳出局部最优点。通过4个标准测试函数对所提算法进行了仿真测试,结果表明所提算法能够有效克服基本引力搜索算法易早熟、收敛精度低等缺陷,具有较好的寻优精度和全局收敛性能,能够解决一些复杂函数的优化问题。     

融合混沌反学习与蜂群搜索算子的引力搜索算法

引力搜索算法是最近提出的一种较有竞争力的群智能优化技术,然而,标准引力算法存在的收敛速度慢、容易在进化过程中陷入停滞状态.针对上述问题,提出一种改进的引力搜索算法.该算法采用混沌反学习策略初始化种群,以便获得遍历整个解空间的初始种群,进而提高算法的收敛速度和解的精度.此外,该算法利用人工蜂群搜索策略很强的探索能力,对种群进行引导以帮助算法快速跳出局部最优点.通过对13个非线性基准函数进行仿真实验,验证了改进的引力搜索算法的有效性和优越性.     

基于改进的Tent混沌万有引力搜索算法

万有引力搜索算法(gravitational search algorithm,GSA)相比于传统的优化算法具有收敛速度快、开拓性能强等特点,但GSA易陷入早熟收敛和局部最优,搜索能力较弱.为此,提出一种基于改进的Tent混沌万有引力搜索算法(gravitational search algorithm based on improved tent chaos,ITC-GSA).首先,改进Tent混沌映射来初始化种群,利用Tent混沌序列随机性、遍历性和规律性的特性使得初始种群随机性和遍历性在可行域内,具有加强算法的全局搜索能力;其次,引入引力常数G的动态调整策略提高算法的收敛速度和收敛精度;再次,设计成熟度指标判断种群成熟度,并使用Tent混沌搜索有效抑制算法早熟收敛,帮助种群跳出局部最优;最后,对10个基准函数进行仿真实验,结果表明所提算法能够有效克服GSA易陷入早熟收敛和局部最优的缺点,提高算法的收敛速度和寻优精度.     

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.     

基于信息熵的混合引力搜索算法

针对基本引力搜索算法搜索速度慢和容易出现早熟的缺点,本文提出了一种基于信息熵的混合引力搜索算法. 受粒子群算法的启发,所提算法首先通过改进基本引力搜索算法的速度和位置更新公式来提高搜索速度;其次,通过惯性质量构造了信息熵模型来刻画种群的寻优程度,并采用不同的信息熵阈值动态选择权重,平衡了算法的全局搜索能力和局部搜索能力. 用8个标准测试函数的仿真实验和基本引力搜索算法与记忆改进的引力搜索算法的比较表明了所提算法收敛速度快,鲁棒性强且效率高.     

一种基于数据场的多目标引力搜索算法

提出一种基于数据场的多目标引力搜索算法(DFMOGSA). 该算法利用外部档案存储非支配解, 同时将外部档案视为目标空间的数据场, 通过计算非支配解的势能来判断每个解的密度; 密度最低的解被选为第1类引导粒子, 直接吸引粒子向低密度区域收敛, 提高解分布的均匀性; 另外, 为了确保算法收敛 在种群内, 选择较优粒子作为第2类引导粒子, 通过引力引导粒子搜索. 对比实验结果表明了DFMOGSA算法的有效性和优越性.     

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.     

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).     

Research on a new optimization algorithm simulating multi- states of matter inspired by finite element analysis approach

A new optimization algorithm is proposed, since a huge problem that many algorithms faced was not being able to effectively balance the global and local search ability. Matter exists in three states: solid, liquid, and gas, which presents different motion characteristics. Inspired by multi- states of matter, individuals of optimization algorithm have different motion characteristics of matter, which could present different search ability. The Finite Element Analysis (FEA) approach can simulate multi- states of matter, which can be adopted to effectively balance the global search ability and local search ability in new optimization algorithm. The new algorithm is creative application of Finite Element Analysis at optimization algorithm field. Artificial Physics Optimization (APO) and Gravitational Search Algorithm (GSA) belongs to the algorithm types defined by force and mass. According to FEA approach, node displacement caused by force and stiffness could be equivalent to motion caused by force and mass of APO and GSA. In the new algorithm framework, stiffness replaces mass of APO and GSA algorithm. This paper performs research on two different algorithms based on APO and GSA respectively. The individuals of new optimization algorithm are divided into solid state, liquid state, and gas state. The effects of main parameters on the performance were studied through experiments of 6 static test functions. The performance is compared with PSO, basic APO, or GSA for four complex models which made up of solid individual, liquid individual, and gas individual in iterative process. The reasonable complex model can be confirmed experimentally. Based on the reasonable complex model, the article conducted complete experiments against Enhancing artificial bee colony algorithm with multi-elite guidance (MGABC), Artificial bee colony algorithm with an adaptive greedy position update strategy (AABC), Multi-strategy ensemble artificial bee colony (MEABC), Self-adaptive heterogeneous PSO (fk-PSO), and APO with 28 CEC2013 test problem. Experimental results show that the proposed method achieves a good performance in comparison to its counterparts as a consequence of its better exploration– exploitation balance. The algorithm supplies a new method to improve physics optimization algorithm.

     

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.     

GSA-LA: gravitational search algorithm based on learning automata

ABSTRACT

Regardless of the performance of gravitational search algorithm (GSA), it is nearly incapable of avoiding local optima in high-dimension problems. To improve the accuracy of GSA, it is necessary to fine tune its parameters. This study introduces a gravitational search algorithm based on learning automata (GSA-LA) for optimisation of continuous problems. Gravitational constant G(t) is a significant parameter that is used to adjust the accuracy of the search. In this work, learning capability is utilised to select G(t) based on spontaneous reactions. To measure the performance of the introduced algorithm, numerical analysis is conducted on several well-designed test functions, and the results are compared with the original GSA and other evolutionary-based algorithms. Simulation results demonstrate that the learning automata-based gravitational search algorithm is more efficient in finding optimum solutions and outperforms the existing algorithms.     

Adaptive gbest-guided gravitational search algorithm

One heuristic evolutionary algorithm recently proposed is the gravitational search algorithm (GSA), inspired by the gravitational forces between masses in nature. This algorithm has demonstrated superior performance among other well-known heuristic algorithms such as particle swarm optimisation and genetic algorithm. However, slow exploitation is a major weakness that might result in degraded performance when dealing with real engineering problems. Due to the cumulative effect of the fitness function on mass in GSA, masses get heavier and heavier over the course of iteration. This causes masses to remain in close proximity and neutralise the gravitational forces of each other in later iterations, preventing them from rapidly exploiting the optimum. In this study, the best mass is archived and utilised to accelerate the exploitation phase, ameliorating this weakness. The proposed method is tested on 25 unconstrained benchmark functions with six different scales provided by CEC 2005. In addition, two classical, constrained, engineering design problems, namely welded beam and tension spring, are also employed to investigate the efficiency of the proposed method in real constrained problems. The results of benchmark and classical engineering problems demonstrate the performance of the proposed method.     

多策略融合的改进万有引力搜索算法

为解决传统万有引力搜索算法（GSA）易陷入局部最优和开发能力弱等问题,提出了一种多策略融合的改进万有引力搜索算法（MFGSA）。首先,提出动态调整引力常数G的更新策略,以增强算法的探索能力和收敛精度;其次,为保留粒子的多样性,提出了基于对称思想的粒子越界处理策略,以提高算法的收敛精度;为适应前两个策略,还引入精英思想,用最优粒子改善最差粒子位置策略,以避免算法陷入局部最优;同时,提出了自适应因子更新粒子速度和位置策略,以提高算法的收敛速度。为验证改进算法的性能,将改进算法与传统万有引力搜索算法和其他四种改进万有引力搜索算法在10个基准函数上进行了对比实验,结果表明MFGSA在收敛速度、搜索精度方面优势较大,表明MFGSA性能的优越性。     

基于斥力的引力搜索算法

针对引力搜索算法(Gravitational Search Algorithm,GSA)收敛速度较快、易陷入局部最优的缺点,提出一种加入斥力的引力搜索算法RFGSA(Repulsion Force based Gravitational Search Algorithm)。该算法在引力搜索算法中引入斥力,即将一部分引力变为斥力,从而增加种群的多样性,有利于寻找全局最优。对10个基准测试函数进行优化的结果表明:该算法的收敛结果明显优于遗传算法、粒子群算法及原始的引力搜索算法。     

基于自适应正态云模型的引力樽海鞘群算法

针对樽海鞘群算法(salp swarm algorithm,SSA)在求解复合问题时存在收敛速度慢和容易陷入局部最优等缺点,提出一种结合引力搜索技术与正态云发生器的樽海鞘群算法(cloud gravitational SSA,CGSSA).在更新樽海鞘领导者位置阶段引入引力搜索算法(gravitational sear...     

引力搜索算法中粒子记忆性改进的研究

针对引力搜索算法(GSA)对一些复杂问题的搜索精度不高的问题,特别是高维函数优化性能不佳、优化过程容易出现早熟的现象,因此考虑将粒子群优化(PSO)算法中关于局部最优解和全局最优解的概念引入引力搜索算法中,对引力搜索算法中粒子的记忆性进行改进,这样使得粒子的进化不仅受空间中其他粒子的影响,还受到自身记忆的约束,以此来提高算法的搜索能力。通过对选用的10个基准函数测试,证明了该方法的有效性。     

融合多策略的增强海鸥优化算法

针对海鸥优化算法(SOA)求解精度低、种群多样性差、易陷入早熟收敛的缺点,提出了一种融合多策略的海鸥优化算法(ESOA)。首先,在每次迭代的过程中,引入改进的自适应差分变异策略,对单个海鸥个体进行差分变异操作并通过自适应机制扩大海鸥的全局搜索范围及提高种群的多样性;其次,设置了基于粒子群算法的机制来处理最差的海鸥个体位置;最后,针对海鸥的最优位置,采用了动态透镜映射的策略增加算法跳出局部最优的能力。采用CEC2017测试函数中的14个函数作为基准测试函数,将ESOA与麻雀算法(SSA)、飞蛾扑火算法(MFO)、灰狼算法(GWO),以及改进的GSCSOA、CCSOA进行性能对比。实验结果表明ESOA在统计学意义上具有显著的性能优势。     

一种多策略协同改进的海鸥算法及其应用

海鸥优化算法(SOA)作为一种随机搜索算法具有显著的优化性能,但仍然存在种群多样性程度较低、易陷入局部最优而导致寻优精度变低的问题。为了改善海鸥算法的缺陷,提出了一种多种策略协同改进的海鸥算法(CMSOA)。首先,在迭代过程中使用正余弦算法(SCA)对停滞的海鸥种群个体扰动更新,改善了整体种群的多样性;然后引入缩放因子,动态调整当前海鸥个体与最优个体之间的相对位移,提高了算法的探索与开发能力;最后,采取随机对立学习的方式对最优海鸥个体位置微调,领导整个海鸥移动至给定搜索空间的正确位置,提高跳出局部最优的能力,进一步增加寻优精度。为了测试改进的CMSOA的寻优性能,利用14个CEC2017测试函数作为测试基准,将CMSOA与对比算法进行性能测试。实验表明,CMSOA在以Freidman检验为标准的统计学意义上具有寻优优势;在三维无人机路径规划问题中,CMSOA也取得了最佳效果。