A PSO algorithm with inertia weight decay by normal distribution

This paper presents an improved particle swarm optimization (PSO) technique for global optimization. Many variants of the technique have been proposed in literature. However, two major things characterize many of these variants namely, static search space and velocity limits, which bound their flexibilities in obtaining optimal solutions for many optimization problems. Furthermore, the problem of premature convergence persists in many variants despite the introduction of additional parameters such as inertia weight and extra computation ability. This paper proposes an improved PSO algorithm without inertia weight. The proposed algorithm dynamically adjusts the search space and velocity limits for the swarm in each iteration by picking the highest and lowest values among all the dimensions of the particles, calculates their absolute values and then uses the higher of the two values to define a new search range and velocity limits for next iteration. The efficiency and performance of the proposed algorithm was shown using popular benchmark global optimization problems with low and high dimensions. Results obtained demonstrate better convergence speed and precision, stability, robustness with better global search ability when compared with six recent variants of the original algorithm.

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Pulmonary Nodule Recognition Based on Multiple Kernel Learning Support Vector Machine-PSO

Computational and Mathematical Methods in Medicine ◽

10.1155/2018/1461470 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Yang Li ◽

Zhichuan Zhu ◽

Alin Hou ◽

Qingdong Zhao ◽

Liwei Liu ◽

...

Keyword(s):

Support Vector Machine ◽

Pulmonary Nodule ◽

Multiple Kernel Learning ◽

Pso Algorithm ◽

Support Vector ◽

Training Time ◽

Inertia Weight ◽

Fitness Value ◽

Svm Algorithm ◽

Fitness Curve

Pulmonary nodule recognition is the core module of lung CAD. The Support Vector Machine (SVM) algorithm has been widely used in pulmonary nodule recognition, and the algorithm of Multiple Kernel Learning Support Vector Machine (MKL-SVM) has achieved good results therein. Based on grid search, however, the MKL-SVM algorithm needs long optimization time in course of parameter optimization; also its identification accuracy depends on the fineness of grid. In the paper, swarm intelligence is introduced and the Particle Swarm Optimization (PSO) is combined with MKL-SVM algorithm to be MKL-SVM-PSO algorithm so as to realize global optimization of parameters rapidly. In order to obtain the global optimal solution, different inertia weights such as constant inertia weight, linear inertia weight, and nonlinear inertia weight are applied to pulmonary nodules recognition. The experimental results show that the model training time of the proposed MKL-SVM-PSO algorithm is only 1/7 of the training time of the MKL-SVM grid search algorithm, achieving better recognition effect. Moreover, Euclidean norm of normalized error vector is proposed to measure the proximity between the average fitness curve and the optimal fitness curve after convergence. Through statistical analysis of the average of 20 times operation results with different inertial weights, it can be seen that the dynamic inertial weight is superior to the constant inertia weight in the MKL-SVM-PSO algorithm. In the dynamic inertial weight algorithm, the parameter optimization time of nonlinear inertia weight is shorter; the average fitness value after convergence is much closer to the optimal fitness value, which is better than the linear inertial weight. Besides, a better nonlinear inertial weight is verified.

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Impact of Various Chaotic Maps on the Performance of Chaos Enhanced PSO Algorithm with Inertia Weight – An Initial Study

Advances in Intelligent Systems and Computing - Nostradamus: Modern Methods of Prediction, Modeling and Analysis of Nonlinear Systems ◽

10.1007/978-3-642-33227-2_18 ◽

2013 ◽

pp. 153-166 ◽

Cited By ~ 9

Author(s):

Michal Pluhacek ◽

Roman Senkerik ◽

Ivan Zelinka

Keyword(s):

Chaotic Maps ◽

Pso Algorithm ◽

Initial Study ◽

Inertia Weight

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The determination of the most suitable inertia weight strategy for particle swarm optimization via the minimax mixed-integer linear programming model

Engineering Computations ◽

10.1108/ec-05-2020-0272 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Volkan Soner Özsoy

Keyword(s):

Linear Programming ◽

Integer Linear Programming ◽

Mixed Integer Linear Programming ◽

Pso Algorithm ◽

Complex Problem ◽

Mixed Integer ◽

Swarm Optimization ◽

Content Type ◽

Inertia Weight

Purpose This paper aims to consider each strategy of the particle swarm optimization (PSO) as a unit in data envelopment analysis (DEA) and uses the minimax mixed-integer linear programming DEA approach to find the most suitable inertia weight strategy. A total of 15 inertia weight strategies were empirically examined in a suite of 42 benchmark problems in the view of DEA. Design/methodology/approach PSO is very sensitive to inertia weight strategies, and therefore, an important amount of research attempts has been concentrated on these strategies. There is no research into the determination of the most suitable inertia weight strategy; however, there are a large number of comparisons related to the inertia weight strategies. DEA is one of the performance evaluation methods, and its models classify the set of strategies into two distinct sets as efficient and inefficient. However, only one of the strategies should be used in the PSO algorithm. Some effective models were proposed to find the most efficient strategy. Findings The experimental studies demonstrate that an approach is a useful tool in the determination of the most suitable strategy. Besides, if the author encounters a new complex problem whose properties are known, it will help the author to choose the best strategy. Practical implications A heavy oil thermal cracking three lumps model for the simplification of the reaction system was used because it is an important complicated chemical process. In addition, the soil water retention curve (SWRC) plays an important role in diverse facets of agricultural engineering. As the SWRC can be regarded as a nonlinear function between the water content and the soil water potential, Van Genuchten model is proposed to describe this function. To determinate these model parameters, an optimization problem is formulated, which minimizes the difference between the measured and modeled data. Originality/value In this paper, the PSO algorithm is integrated with minimax mixed-integer linear programming to find the most suitable inertia weight strategy. In this way, the best strategy could be chosen for a new more complex problem.

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An Improved Particle Swarm Optimization Algorithm with Adaptive Inertia Weights

International Journal of Information Technology & Decision Making ◽

10.1142/s0219622019500147 ◽

2019 ◽

Vol 18 (03) ◽

pp. 833-866 ◽

Cited By ~ 8

Author(s):

Mi Li ◽

Huan Chen ◽

Xiaodong Wang ◽

Ning Zhong ◽

Shengfu Lu

Keyword(s):

Particle Swarm Optimization ◽

Particle Swarm ◽

Pso Algorithm ◽

Local Optimum ◽

Random Mutation ◽

Swarm Optimization ◽

Inertia Weight ◽

Fitness Value ◽

The One ◽

Individual Particles

The particle swarm optimization (PSO) algorithm is simple to implement and converges quickly, but it easily falls into a local optimum; on the one hand, it lacks the ability to balance global exploration and local exploitation of the population, and on the other hand, the population lacks diversity. To solve these problems, this paper proposes an improved adaptive inertia weight particle swarm optimization (AIWPSO) algorithm. The AIWPSO algorithm includes two strategies: (1) An inertia weight adjustment method based on the optimal fitness value of individual particles is proposed, so that different particles have different inertia weights. This method increases the diversity of inertia weights and is conducive to balancing the capabilities of global exploration and local exploitation. (2) A mutation threshold is used to determine which particles need to be mutated. This method compensates for the inaccuracy of random mutation, effectively increasing the diversity of the population. To evaluate the performance of the proposed AIWPSO algorithm, benchmark functions are used for testing. The results show that AIWPSO achieves satisfactory results compared with those of other PSO algorithms. This outcome shows that the AIWPSO algorithm is conducive to balancing the abilities of the global exploration and local exploitation of the population, while increasing the diversity of the population, thereby significantly improving the optimization ability of the PSO algorithm.

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On the Performance of Linear Decreasing Inertia Weight Particle Swarm Optimization for Global Optimization

The Scientific World JOURNAL ◽

10.1155/2013/860289 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 30

Author(s):

Martins Akugbe Arasomwan ◽

Aderemi Oluyinka Adewumi

Keyword(s):

Global Optimization ◽

Particle Swarm Optimization ◽

Optimization Problems ◽

Particle Swarm ◽

Pso Algorithm ◽

Search Space ◽

Terminal Point ◽

Simulation Experiments ◽

Swarm Optimization ◽

Inertia Weight

Linear decreasing inertia weight (LDIW) strategy was introduced to improve on the performance of the original particle swarm optimization (PSO). However, linear decreasing inertia weight PSO (LDIW-PSO) algorithm is known to have the shortcoming of premature convergence in solving complex (multipeak) optimization problems due to lack of enough momentum for particles to do exploitation as the algorithm approaches its terminal point. Researchers have tried to address this shortcoming by modifying LDIW-PSO or proposing new PSO variants. Some of these variants have been claimed to outperform LDIW-PSO. The major goal of this paper is to experimentally establish the fact that LDIW-PSO is very much efficient if its parameters are properly set. First, an experiment was conducted to acquire a percentage value of the search space limits to compute the particle velocity limits in LDIW-PSO based on commonly used benchmark global optimization problems. Second, using the experimentally obtained values, five well-known benchmark optimization problems were used to show the outstanding performance of LDIW-PSO over some of its competitors which have in the past claimed superiority over it. Two other recent PSO variants with different inertia weight strategies were also compared with LDIW-PSO with the latter outperforming both in the simulation experiments conducted.

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Speech Recognition Method Based on Linear Descending Inertia Weight PSO Algorithm Optimizing SVM Kernel Parameters

2009 Fifth International Conference on Natural Computation ◽

10.1109/icnc.2009.261 ◽

2009 ◽

Cited By ~ 1

Author(s):

Jing Bai ◽

Yueling Guo

Keyword(s):

Speech Recognition ◽

Pso Algorithm ◽

Recognition Method ◽

Inertia Weight ◽

Kernel Parameters

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Particle Swarm Optimization with Team Spirit Inertia Weight

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.383-390.5744 ◽

2011 ◽

Vol 383-390 ◽

pp. 5744-5750

Author(s):

Xi Zhen Wang ◽

Yan Li ◽

Gang Hu Cheng

Keyword(s):

Particle Swarm Optimization ◽

Particle Swarm ◽

Pso Algorithm ◽

Convergence Problem ◽

Swarm Optimization ◽

Inertia Weight ◽

Standard Particle Swarm Optimization ◽

Decline Curves ◽

Team Spirit ◽

Global And Local

A PSO Algorithm with Team Spirit Inertia weight (TSWPSO) is presented based on the study of the effect of inertia weight on Standard Particle Swarm Optimization (SPSO). Due to the theory of group in organization psychology, swarm is divided into multiple sub-swarms and search is run in a number of different sub-swarms which are parallel performed. Try to find or modify a curve which is compatible with optimized object within many inertia weight decline curves, in order to balance the global and local explorations ability in particle swarm optimization and to avoid the premature convergence problem effectively. The testes by five classical functions show that, TSWPSO has a better performance in both the convergence rate and the precision.

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Parameter Identification Model with the Control Term in Batch Anaerobic Fermentation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.217-219.1535 ◽

2012 ◽

Vol 217-219 ◽

pp. 1535-1540 ◽

Cited By ~ 1

Author(s):

Hong Li Xiao ◽

Shu Xi Zhang ◽

Zhi Long Xiu ◽

En Min Feng

Keyword(s):

Experimental Data ◽

Parameter Identification ◽

Batch Fermentation ◽

Anaerobic Fermentation ◽

Optimal Parameter ◽

Dynamical Behavior ◽

Pso Algorithm ◽

Anaerobic Culture ◽

Inertia Weight ◽

Identification Model

In this paper, according to the characteristics, dynamical behavior and the experimental data of the batch anaerobic culture, a parameter identification model was improved to describe the dynamical system for microorganism in batch fermentation. And some relative characters were introduced. Finally, a PSO algorithm with the inertia weight was used to get the best optimal parameter of the identification model. The results show that the model reduces the errors between the experimental data and computational values, and they can simulate the process of batch fermentation better.

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A Particle Swarm Optimization with Variety Factor

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.239-240.1291 ◽

2012 ◽

Vol 239-240 ◽

pp. 1291-1297 ◽

Cited By ~ 1

Author(s):

Hai Sheng Qin ◽

Deng Yue Wei ◽

Jun Hui Li ◽

Lei Zhang ◽

Yan Qiang Feng

Keyword(s):

Particle Swarm Optimization ◽

Convergence Property ◽

Particle Swarm ◽

Pso Algorithm ◽

Premature Convergence ◽

Simulation Experiments ◽

Swarm Optimization ◽

Inertia Weight ◽

Previous Algorithm ◽

Modified Pso

A new particle swarm optimization (PSO) algorithm (a PSO with Variety Factor, VFPSO) based on the PSO was proposed. Compared with the previous algorithm, the proposed algorithm is to update the Variety Factor and to improve the inertia weight of the PSO. The target of the improvement is that the new algorithm could go on enhancing the robustness as before and should reduce the risk of premature convergence. The simulation experiments show that it has great advantages of convergence property over some other modified PSO algorithms, and also avoids algorithm being trapped in local minimum effectively. So it can avoid the phenomenon of premature convergence.

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