A Study of Normalized Population Diversity in Particle Swarm Optimization

2013 ◽  
Vol 4 (1) ◽  
pp. 1-34 ◽  
Author(s):  
Shi Cheng ◽  
Yuhui Shi ◽  
Quande Qin
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Population Diversity ◽  
Matrix Elements ◽  
Swarm Optimization ◽  
Multimodal Function ◽  
The Matrix ◽  
The Relationship ◽  
Solution Matrix

The values and velocities of a Particle swarm optimization (PSO) algorithm can be recorded as series of matrix and its population diversity can be considered as an observation of the distribution of matrix elements. Each dimension is measured separately in the dimension-wise diversity, on the contrary, the element-wise diversity measures all dimension together. In this paper, PSO algorithm is first represented in the matrix format, then based on the analysis of the relationship between pairs of vectors in PSO solution matrix, different normalization strategies are utilized for dimension-wise and element-wise population diversity, respectively. Experiments on benchmark functions are conducted. Based on the simulation results of ten benchmark functions (include unimodal/multimodal function, separable/non-separable function), the properties of normalized population diversities are analyzed and discussed.

A Study of Normalized Population Diversity in Particle Swarm Optimization

2020 ◽  
pp. 345-381
Author(s):  
Shi Cheng ◽  
Yuhui Shi ◽  
Quande Qin
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Population Diversity ◽  
Swarm Optimization ◽  
Multimodal Function ◽  
The Matrix ◽  
Simulation Results ◽  
The Relationship ◽  
Solution Matrix

The values and velocities of a Particle swarm optimization (PSO) algorithm can be recorded as a series of matrix and its population diversity can be considered as an observation of the distribution of matrix elements. Each dimension is measured separately in the dimension-wise diversity. On the contrary, the element-wise diversity measures all dimensions together. In this chapter, the PSO algorithm is first represented in the matrix format. Then, based on the analysis of the relationship between pairs of vectors in the PSO solution matrix, different normalization strategies are utilized for dimension-wise and element-wise population diversity, respectively. Experiments on benchmark functions are conducted. Based on the simulation results of 10 benchmark functions (including unimodal/multimodal function, separable/non-separable function), the properties of normalized population diversities are analyzed and discussed.

Design and Simulation of an Improved Particle Swarm Optimization

2010 ◽  
Vol 20-23 ◽  
pp. 1280-1285
Author(s):  
Jian Xiang Wei ◽  
Yue Hong Sun
Keyword(s):  
Particle Swarm Optimization ◽  
Dimensional Space ◽  
Numerical Test ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Population Diversity ◽  
Test Problems ◽  
Local Optimum ◽  
Swarm Optimization ◽  
Improved Pso

The particle swarm optimization (PSO) algorithm is a new population search strategy, which has exhibited good performance through well-known numerical test problems. However, it is easy to trap into local optimum because the population diversity becomes worse during the evolution. In order to overcome the shortcoming of the PSO, this paper proposes an improved PSO based on the symmetry distribution of the particle space position. From the research of particle movement in high dimensional space, we can see: the more symmetric of the particle distribution, the bigger probability can the algorithm be during converging to the global optimization solution. A novel population diversity function is put forward and an adjustment algorithm is put into the basic PSO. The steps of the proposed algorithm are given in detail. With two typical benchmark functions, the experimental results show the improved PSO has better convergence precision than the basic PSO.

Bacterial Particle Swarm Optimization Algorithm

2011 ◽  
Vol 211-212 ◽  
pp. 968-972
Author(s):  
Ming Li ◽  
Xue Ling Ji
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm Optimization Algorithm ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Global Optimum ◽  
Population Diversity ◽  
Swarm Optimization ◽  
Bacterial Colony ◽  
Evolutionary Mechanism ◽  
Basic Law

The loss of the population diversity leads to the premature convergence in existing particle swarm optimization(PSO) algorithm. In order to solve this problem, a novel version of PSO algorithm called bacterial PSO(BacPSO), was proposed in this paper. In the new algorithm, the individuals were replaced by bacterial, and a new evolutionary mechanism was designed by the basic law of evolution of bacterial colony. Such evolutionary mechanism also generated a new natural termination criterion. Propagation and death operators were used to keep the population diversity of BacPSO. The simulation results show that BacPSO algorithm not only significantly improves convergence speed ,but also can converge to the global optimum.

scholarly journals A novel PID-like particle swarm optimizer: on terminal convergence analysis

2021 ◽  
Author(s):  
Chuang Wang ◽  
Zidong Wang ◽  
Fei Han ◽  
Hongli Dong ◽  
Hongjian Liu
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Future Trend ◽  
Population Diversity ◽  
Particle Swarm Optimizer ◽  
Swarm Optimization ◽  
Local Optima ◽  
Convergence Conditions ◽  
Searching Ability

AbstractIn this paper, a novel proportion-integral-derivative-like particle swarm optimization (PIDLPSO) algorithm is presented with improved terminal convergence of the particle dynamics. A derivative control term is introduced into the traditional particle swarm optimization (PSO) algorithm so as to alleviate the overshoot problem during the stage of the terminal convergence. The velocity of the particle is updated according to the past momentum, the present positions (including the personal best position and the global best position), and the future trend of the positions, thereby accelerating the terminal convergence and adjusting the search direction to jump out of the area around the local optima. By using a combination of the Routh stability criterion and the final value theorem of the Z-transformation, the convergence conditions are obtained for the developed PIDLPSO algorithm. Finally, the experiment results reveal the superiority of the designed PIDLPSO algorithm over several other state-of-the-art PSO variants in terms of the population diversity, searching ability and convergence rate.

scholarly journals A New Approach to Sequence Construction With Good Correlation by Particle Swarm Optimization

2015 ◽  
Vol 11 (3) ◽  
pp. 127 ◽  
Author(s):  
Mahdiyar Sarayloo ◽  
Ennio Gambi ◽  
Susanna Spinsante
Keyword(s):  
Particle Swarm Optimization ◽  
Fitness Function ◽  
Binary Sequence ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Binary Sequences ◽  
Swarm Optimization ◽  
Variable Population ◽  
Relationship Of ◽  
The Relationship

In this paper, a novel computationally affordable method to generate long binary sequences featuring desired properties is presented, based on the use of a number of shorter non linear binary sub-sequences. The paper shows the relationship of the Auto- and Cross-Correlation (AC, CC) ofthe generated long binary sequences with the AC and CC ofconstituent sub-sequences. It is also shown that the starting bit position of sub-sequences has an important role on AC and CC of the generated sequences. To generate the optimal long binary sequence from correlation points of view, Particle Swarm Optimization (PSO) algorithm is employed. All the techniques stated in the literature to improve the PSO are implemented and it is clearly shown that the constriction factor and the variable population size turn out to have a great impact on minimizing the fitness function (RMS of AC) representing the target Correlationproperties expected for the resulting long sequence. Possible application scenarios for the long sequences generated by the proposed method are also discussed and evaluated.

scholarly journals Particle Swarm Optimization for Multimodal Functions: A Clustering Approach

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Alessandro Passaro ◽  
Antonina Starita
Keyword(s):  
Particle Swarm Optimization ◽  
Clustering Algorithm ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Pso Algorithm ◽  
Neighborhood Structure ◽  
Swarm Optimization ◽  
Multimodal Functions ◽  
Multimodal Function ◽  
Computation Algorithms

The particle swarm optimization (PSO) algorithm is designed to find a single optimal solution and needs some modifications to be able to locate multiple optima on a multimodal function. In parallel with evolutionary computation algorithms, these modifications can be grouped in the framework of niching. In this work, we present a new approach to niching in PSO based on clustering particles to identify niches. The neighborhood structure, on which particles rely for communication, is exploited together with the niche information to locate multiple optima in parallel. Our approach was implemented in the k-means-based PSO (kPSO), which employs the standard k-means clustering algorithm, improved with a mechanism to adaptively identify the number of clusters. kPSO proved to be a competitive solution when compared with other existing algorithms, since it showed better performance on a benchmark set of multimodal functions.

scholarly journals Virtual Angle Boundary-Aware Particle Swarm Optimization to Maximize the Coverage of Directional Sensor Networks

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2868
Author(s):  
Gong Cheng ◽  
Huangfu Wei
Keyword(s):  
Particle Swarm Optimization ◽  
Sensor Networks ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
The Internet ◽  
Directional Sensor Networks ◽  
Swarm Optimization ◽  
Coverage Optimization ◽  
Boundary Constraint ◽  
Directional Sensor

With the transition of the mobile communication networks, the network goal of the Internet of everything further promotes the development of the Internet of Things (IoT) and Wireless Sensor Networks (WSNs). Since the directional sensor has the performance advantage of long-term regional monitoring, how to realize coverage optimization of Directional Sensor Networks (DSNs) becomes more important. The coverage optimization of DSNs is usually solved for one of the variables such as sensor azimuth, sensing radius, and time schedule. To reduce the computational complexity, we propose an optimization coverage scheme with a boundary constraint of eliminating redundancy for DSNs. Combined with Particle Swarm Optimization (PSO) algorithm, a Virtual Angle Boundary-aware Particle Swarm Optimization (VAB-PSO) is designed to reduce the computational burden of optimization problems effectively. The VAB-PSO algorithm generates the boundary constraint position between the sensors according to the relationship among the angles of different sensors, thus obtaining the boundary of particle search and restricting the search space of the algorithm. Meanwhile, different particles search in complementary space to improve the overall efficiency. Experimental results show that the proposed algorithm with a boundary constraint can effectively improve the coverage and convergence speed of the algorithm.

scholarly journals Knowledge-guided multiobjective particle swarm optimization with fusion learning strategies

2021 ◽  
Author(s):  
Wei Li ◽  
Xiang Meng ◽  
Ying Huang ◽  
Soroosh Mahmoodi
Keyword(s):  
Particle Swarm Optimization ◽  
Learning Strategies ◽  
Learning Strategy ◽  
Particle Swarm ◽  
Population Diversity ◽  
Selection Strategy ◽  
Rapid Loss ◽  
Solution Quality ◽  
Swarm Optimization ◽  
Multiobjective Particle Swarm Optimization

AbstractMultiobjective particle swarm optimization (MOPSO) algorithm faces the difficulty of prematurity and insufficient diversity due to the selection of inappropriate leaders and inefficient evolution strategies. Therefore, to circumvent the rapid loss of population diversity and premature convergence in MOPSO, this paper proposes a knowledge-guided multiobjective particle swarm optimization using fusion learning strategies (KGMOPSO), in which an improved leadership selection strategy based on knowledge utilization is presented to select the appropriate global leader for improving the convergence ability of the algorithm. Furthermore, the similarity between different individuals is dynamically measured to detect the diversity of the current population, and a diversity-enhanced learning strategy is proposed to prevent the rapid loss of population diversity. Additionally, a maximum and minimum crowding distance strategy is employed to obtain excellent nondominated solutions. The proposed KGMOPSO algorithm is evaluated by comparisons with the existing state-of-the-art multiobjective optimization algorithms on the ZDT and DTLZ test instances. Experimental results illustrate that KGMOPSO is superior to other multiobjective algorithms with regard to solution quality and diversity maintenance.

Adaptive particle swarm optimization algorithm based long short-term memory networks for sentiment analysis

2021 ◽  
pp. 1-17
Author(s):  
J. Shobana ◽  
M. Murali
Keyword(s):  
Particle Swarm Optimization ◽  
Sentiment Analysis ◽  
Language Processing ◽  
Short Term Memory ◽  
Contextual Information ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Swarm Optimization ◽  
Adaptive Particle Swarm Optimization ◽  
Proposed Model

Text Sentiment analysis is the process of predicting whether a segment of text has opinionated or objective content and analyzing the polarity of the text’s sentiment. Understanding the needs and behavior of the target customer plays a vital role in the success of the business so the sentiment analysis process would help the marketer to improve the quality of the product as well as a shopper to buy the correct product. Due to its automatic learning capability, deep learning is the current research interest in Natural language processing. Skip-gram architecture is used in the proposed model for better extraction of the semantic relationships as well as contextual information of words. However, the main contribution of this work is Adaptive Particle Swarm Optimization (APSO) algorithm based LSTM for sentiment analysis. LSTM is used in the proposed model for understanding complex patterns in textual data. To improve the performance of the LSTM, weight parameters are enhanced by presenting the Adaptive PSO algorithm. Opposition based learning (OBL) method combined with PSO algorithm becomes the Adaptive Particle Swarm Optimization (APSO) classifier which assists LSTM in selecting optimal weight for the environment in less number of iterations. So APSO - LSTM ‘s ability in adjusting the attributes such as optimal weights and learning rates combined with the good hyper parameter choices leads to improved accuracy and reduces losses. Extensive experiments were conducted on four datasets proved that our proposed APSO-LSTM model secured higher accuracy over the classical methods such as traditional LSTM, ANN, and SVM. According to simulation results, the proposed model is outperforming other existing models.

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