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1
Gonsalves, Tad, and Akira Egashira. "Parallel Swarms Oriented Particle Swarm Optimization." Applied Computational Intelligence and Soft Computing 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/756719.
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The particle swarm optimization (PSO) is a recently invented evolutionary computation technique which is gaining popularity owing to its simplicity in implementation and rapid convergence. In the case of single-peak functions, PSO rapidly converges to the peak; however, in the case of multimodal functions, the PSO particles are known to get trapped in the local optima. In this paper, we propose a variation of the algorithm called parallel swarms oriented particle swarm optimization (PSO-PSO) which consists of a multistage and a single stage of evolution. In the multi-stage of evolution, individual subswarms evolve independently in parallel, and in the single stage of evolution, the sub-swarms exchange information to search for the global-best. The two interweaved stages of evolution demonstrate better performance on test functions, especially of higher dimensions. The attractive feature of the PSO-PSO version of the algorithm is that it does not introduce any new parameters to improve its convergence performance. The strategy maintains the simple and intuitive structure as well as the implemental and computational advantages of the basic PSO.
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Borowska, Bożena. "Learning Competitive Swarm Optimization." Entropy 24, no. 2 (February 16, 2022): 283. http://dx.doi.org/10.3390/e24020283.
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Particle swarm optimization (PSO) is a popular method widely used in solving different optimization problems. Unfortunately, in the case of complex multidimensional problems, PSO encounters some troubles associated with the excessive loss of population diversity and exploration ability. This leads to a deterioration in the effectiveness of the method and premature convergence. In order to prevent these inconveniences, in this paper, a learning competitive swarm optimization algorithm (LCSO) based on the particle swarm optimization method and the competition mechanism is proposed. In the first phase of LCSO, the swarm is divided into sub-swarms, each of which can work in parallel. In each sub-swarm, particles participate in the tournament. The participants of the tournament update their knowledge by learning from their competitors. In the second phase, information is exchanged between sub-swarms. The new algorithm was examined on a set of test functions. To evaluate the effectiveness of the proposed LCSO, the test results were compared with those achieved through the competitive swarm optimizer (CSO), comprehensive particle swarm optimizer (CLPSO), PSO, fully informed particle swarm (FIPS), covariance matrix adaptation evolution strategy (CMA-ES) and heterogeneous comprehensive learning particle swarm optimization (HCLPSO). The experimental results indicate that the proposed approach enhances the entropy of the particle swarm and improves the search process. Moreover, the LCSO algorithm is statistically and significantly more efficient than the other tested methods.
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Shen, Yuanxia, Linna Wei, Chuanhua Zeng, and Jian Chen. "Particle Swarm Optimization with Double Learning Patterns." Computational Intelligence and Neuroscience 2016 (2016): 1–19. http://dx.doi.org/10.1155/2016/6510303.
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Particle Swarm Optimization (PSO) is an effective tool in solving optimization problems. However, PSO usually suffers from the premature convergence due to the quick losing of the swarm diversity. In this paper, we first analyze the motion behavior of the swarm based on the probability characteristic of learning parameters. Then a PSO with double learning patterns (PSO-DLP) is developed, which employs the master swarm and the slave swarm with different learning patterns to achieve a trade-off between the convergence speed and the swarm diversity. The particles in the master swarm and the slave swarm are encouraged to explore search for keeping the swarm diversity and to learn from the global best particle for refining a promising solution, respectively. When the evolutionary states of two swarms interact, an interaction mechanism is enabled. This mechanism can help the slave swarm in jumping out of the local optima and improve the convergence precision of the master swarm. The proposed PSO-DLP is evaluated on 20 benchmark functions, including rotated multimodal and complex shifted problems. The simulation results and statistical analysis show that PSO-DLP obtains a promising performance and outperforms eight PSO variants.
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Aziz, Nor Azlina Ab, Zuwairie Ibrahim, Marizan Mubin, Sophan Wahyudi Nawawi, and Nor Hidayati Abdul Aziz. "Transitional Particle Swarm Optimization." International Journal of Electrical and Computer Engineering (IJECE) 7, no. 3 (June 1, 2017): 1611. http://dx.doi.org/10.11591/ijece.v7i3.pp1611-1619.
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A new variation of particle swarm optimization (PSO) termed as transitional PSO (T-PSO) is proposed here. T-PSO attempts to improve PSO via its iteration strategy. Traditionally, PSO adopts either the synchronous or the asynchronous iteration strategy. Both of these iteration strategies have their own strengths and weaknesses. The synchronous strategy has reputation of better exploitation while asynchronous strategy is stronger in exploration. The particles of T-PSO start with asynchronous update to encourage more exploration at the start of the search. If no better solution is found for a number of iteration, the iteration strategy is changed to synchronous update to allow fine tuning by the particles. The results show that T-PSO is ranked better than the traditional PSOs.
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Sousa-Ferreira, Ivo, and Duarte Sousa. "A review of velocity-type PSO variants." Journal of Algorithms & Computational Technology 11, no. 1 (September 18, 2016): 23–30. http://dx.doi.org/10.1177/1748301816665021.
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This paper presents a review of the particular variants of particle swarm optimization, based on the velocity-type class. The original particle swarm optimization algorithm was developed as an unconstrained optimization technique, which lacks a model that is able to handle constrained optimization problems. The particle swarm optimization and its inapplicability in constrained optimization problems are solved using the dynamic-objective constraint-handling method. The dynamic-objective constraint-handling method is originally developed for two variants of the basic particle swarm optimization, namely restricted velocity particle swarm optimization and self-adaptive velocity particle swarm optimization. Also on the subject velocity-type class, a review of three other variants is given, specifically: (1) vertical particle swarm optimization; (2) velocity limited particle swarm optimization; and (3) particle swarm optimization with scape velocity. These velocity-type particle swarm optimization variants all have in common a velocity parameter which determines the direction/movements of the particles.
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Fan, Shu-Kai S., and Chih-Hung Jen. "An Enhanced Partial Search to Particle Swarm Optimization for Unconstrained Optimization." Mathematics 7, no. 4 (April 17, 2019): 357. http://dx.doi.org/10.3390/math7040357.
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Particle swarm optimization (PSO) is a population-based optimization technique that has been applied extensively to a wide range of engineering problems. This paper proposes a variation of the original PSO algorithm for unconstrained optimization, dubbed the enhanced partial search particle swarm optimizer (EPS-PSO), using the idea of cooperative multiple swarms in an attempt to improve the convergence and efficiency of the original PSO algorithm. The cooperative searching strategy is particularly devised to prevent the particles from being trapped into the local optimal solutions and tries to locate the global optimal solution efficiently. The effectiveness of the proposed algorithm is verified through the simulation study where the EPS-PSO algorithm is compared to a variety of exiting “cooperative” PSO algorithms in terms of noted benchmark functions.
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Ma, Zi Rui. "Particle Swarm Optimization Based on Multiobjective Optimization." Applied Mechanics and Materials 263-266 (December 2012): 2146–49. http://dx.doi.org/10.4028/www.scientific.net/amm.263-266.2146.
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PSO will population each individual as the search space without a volume and quality of particle. These particles in the search space at a certain speed flight, the speed according to its own flight experience and the entire population of flight experience dynamic adjustment. We describe the standard PSO, multi-objective optimization and MOPSO. The main focus of this thesis is several PSO algorithms which are introduced in detail and studied. MOPSO algorithm introduced adaptive grid mechanism of the external population, not only to groups of particle on variation, but also to the value scope of the particles and variation, and the variation scale and population evolution algebra in proportion.
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Xu, Yu Fa, Jie Gao, Guo Chu Chen, and Jin Shou Yu. "Quantum Particle Swarm Optimization Algorithm." Applied Mechanics and Materials 63-64 (June 2011): 106–10. http://dx.doi.org/10.4028/www.scientific.net/amm.63-64.106.
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Based on the problem of traditional particle swarm optimization (PSO) easily trapping into local optima, quantum theory is introduced into PSO to strengthen particles’ diversities and avoid the premature convergence effectively. Experimental results show that this method proposed by this paper has stronger optimal ability and better global searching capability than PSO.
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Lenin, K. "CROWDING DISTANCE BASED PARTICLE SWARM OPTIMIZATION ALGORITHM FOR SOLVING OPTIMAL REACTIVE POWER DISPATCH PROBLEM." International Journal of Research -GRANTHAALAYAH 6, no. 6 (June 30, 2018): 226–37. http://dx.doi.org/10.29121/granthaalayah.v6.i6.2018.1369.
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In this paper, Crowding Distance based Particle Swarm Optimization (CDPSO) algorithm has been proposed to solve the optimal reactive power dispatch problem. Particle Swarm Optimization (PSO) is swarm intelligence-based exploration and optimization algorithm which is used to solve global optimization problems. In PSO, the population is referred as a swarm and the individuals are called particles. Like other evolutionary algorithms, PSO performs searches using a population of individuals that are updated from iteration to iteration. The crowding distance is introduced as the index to judge the distance between the particle and the adjacent particle, and it reflects the congestion degree of no dominated solutions. In the population, the larger the crowding distance, the sparser and more uniform. In the feasible solution space, we uniformly and randomly initialize the particle swarms and select the no dominated solution particles consisting of the elite set. After that by the methods of congestion degree choosing (the congestion degree can make the particles distribution more sparse) and the dynamic e infeasibility dominating the constraints, we remove the no dominated particles in the elite set. Then, the objectives can be approximated. Proposed crowding distance based Particle Swarm Optimization (CDPSO) algorithm has been tested in standard IEEE 30 bus test system and simulation results shows clearly the improved performance of the projected algorithm in reducing the real power loss and static voltage stability margin has been enhanced.
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YEN, GARY G., and MOAYED DANESHYARI. "DIVERSITY-BASED INFORMATION EXCHANGE AMONG MULTIPLE SWARMS IN PARTICLE SWARM OPTIMIZATION." International Journal of Computational Intelligence and Applications 07, no. 01 (March 2008): 57–75. http://dx.doi.org/10.1142/s1469026808002144.
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This paper proposes a method to exchange information among multiple swarms in particle swarm optimization (PSO) to facilitate evolutionary search. The algorithm is developed to solve problems having landscapes with a large number of local optima. Each swarm maintains two sets of particles; one set includes the particles to be shared with other swarms, while the other involves the particles to be replaced by individuals from other swarms. The proposed algorithm also provides a new design to search for neighboring swarms in order to share common interests among the swarm's neighborhood. The particle's movement is according to one variation of PSO with three basic terms, each one to lead the particles toward the best particle in the swarm, in the neighborhood, and in the whole population. Demonstrated through a suite of benchmark test functions, the proposed algorithm shows competitive performance with improved convergence speed.
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Spears, William M., Derek T. Green, and Diana F. Spears. "Biases in Particle Swarm Optimization." International Journal of Swarm Intelligence Research 1, no. 2 (April 2010): 34–57. http://dx.doi.org/10.4018/jsir.2010040103.
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The most common versions of particle swarm optimization (PSO) algorithms are rotationally variant. It has also been pointed out that PSO algorithms can concentrate particles along paths parallel to the coordinate axes. In this paper, the authors explicitly connect these two observations by showing that the rotational variance is related to the concentration along lines parallel to the coordinate axes. Based on this explicit connection, the authors create fitness functions that are easy or hard for PSO to solve, depending on the rotation of the function.
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Rossides, George, Benjamin Metcalfe, and Alan Hunter. "Particle Swarm Optimization—An Adaptation for the Control of Robotic Swarms." Robotics 10, no. 2 (April 8, 2021): 58. http://dx.doi.org/10.3390/robotics10020058.
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Particle Swarm Optimization (PSO) is a numerical optimization technique based on the motion of virtual particles within a multidimensional space. The particles explore the space in an attempt to find minima or maxima to the optimization problem. The motion of the particles is linked, and the overall behavior of the particle swarm is controlled by several parameters. PSO has been proposed as a control strategy for physical swarms of robots that are localizing a source; the robots are analogous to the virtual particles. However, previous attempts to achieve this have shown that there are inherent problems. This paper addresses these problems by introducing a modified version of PSO, as well as introducing new guidelines for parameter selection. The proposed algorithm links the parameters to the velocity and acceleration of each robot, and demonstrates obstacle avoidance. Simulation results from both MATLAB and Gazebo show close agreement and demonstrate that the proposed algorithm is capable of effective control of a robotic swarm and obstacle avoidance.
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Zhou, Fei Hong, and Zi Zhen Liao. "A Particle Swarm Optimization Algorithm." Applied Mechanics and Materials 303-306 (February 2013): 1369–72. http://dx.doi.org/10.4028/www.scientific.net/amm.303-306.1369.
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The basic and improved algorithms of PSO focus on how to effectively search the optimal solution in the solution space using one of the particle swarm. However, the particles are always chasing the global optimal point and such points currently found on their way of search, rapidly leading their speed down to zero and hence being restrained in the local minimum. Consequently, the convergence or early maturity of particles exists. The improved PSO is based on the enlightenment of BP neural network while the improvement is similar to smooth the weight through low-pass filter. The test of classical functions show that the PSO provides a promotion in the convergence precision and calculation velocity to a certain extent.
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El-Shorbagy, M. A., and Aboul Ella Hassanien. "Particle Swarm Optimization from Theory to Applications." International Journal of Rough Sets and Data Analysis 5, no. 2 (April 2018): 1–24. http://dx.doi.org/10.4018/ijrsda.2018040101.
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Particle swarm optimization (PSO) is considered one of the most important methods in swarm intelligence. PSO is related to the study of swarms; where it is a simulation of bird flocks. It can be used to solve a wide variety of optimization problems such as unconstrained optimization problems, constrained optimization problems, nonlinear programming, multi-objective optimization, stochastic programming and combinatorial optimization problems. PSO has been presented in the literature and applied successfully in real life applications. In this paper, a comprehensive review of PSO as a well-known population-based optimization technique. The review starts by a brief introduction to the behavior of the PSO, then basic concepts and development of PSO are discussed, it's followed by the discussion of PSO inertia weight and constriction factor as well as issues related to parameter setting, selection and tuning, dynamic environments, and hybridization. Also, we introduced the other representation, convergence properties and the applications of PSO. Finally, conclusions and discussion are presented. Limitations to be addressed and the directions of research in the future are identified, and an extensive bibliography is also included.
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Ning, Zhou, and Zhang Jing. "Study on Mechanical Design Optimization Based on Improved Particle Swarm Optimization Algorithm." Open Mechanical Engineering Journal 9, no. 1 (October 7, 2015): 961–65. http://dx.doi.org/10.2174/1874155x01509010961.
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In view of local optimization in particle swarm optimization algorithm (PSO algorithm), chaos theory was introduced to PSO algorithm in this paper. Plenty of populations were generated by using the ergodicity of chaotic motion. The uniformly distributed initial particles of the particle swarms were extracted from the populations according to the Euclidean distance between particles, so that the particles could uniformly distribute in the solution space. Local search was carried out on the optimal position of the particles during evolution, so as to improve the development capability of PSO algorithm and prevent its prematurity, thus enhancing its global optimizing capability. Then the improved PSO algorithm was applied to mechanical design optimization. With optimization design for two-stage gear reducer as the study object, objective function and constraint conditions were determined by building a mathematical model of optimization design, thus realizing optimization design. Simulation and comparison between the improved algorithm and unimproved algorithm show that improved PSO algorithm can optimize the optimization results of PSO algorithm at a faster convergence rate.
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Moraglio, Alberto, Cecilia Di Chio, Julian Togelius, and Riccardo Poli. "Geometric Particle Swarm Optimization." Journal of Artificial Evolution and Applications 2008 (February 21, 2008): 1–14. http://dx.doi.org/10.1155/2008/143624.
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Using a geometric framework for the interpretation of crossover of recent introduction, we show an intimate connection between particle swarm optimisation (PSO) and evolutionary algorithms. This connection enables us to generalise PSO to virtually any solution representation in a natural and straightforward way. The new Geometric PSO (GPSO) applies naturally to both continuous and combinatorial spaces. We demonstrate this for the cases of Euclidean, Manhattan and Hamming spaces and report extensive experimental results. We also demonstrate the applicability of GPSO to more challenging combinatorial spaces. The Sudoku puzzle is a perfect candidate to test new algorithmic ideas because it is entertaining and instructive as well as being a nontrivial constrained combinatorial problem. We apply GPSO to solve the Sudoku puzzle.
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Bi, Ya, Anthony Lam, Huiqun Quan, Hui Liu, and Cunfa Wang. "A comprehensively improved particle swarm optimization algotithm to guarantee particle activity." Izvestiya vysshikh uchebnykh zavedenii. Fizika, no. 5 (2021): 94–101. http://dx.doi.org/10.17223/00213411/64/5/94.
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The particle swarm optimization algorithm has the disadvantages, for instance, the convergence viscosity of the algorithm is reduced at the post evolution phase, the optimization search efficiency is reduced, the algorithm is easy to be inserted with local extremum during the calculation of complex problem of high-dimensional multiple extremum, and the convergence thereof is low. As to the disadvantage of the PSO, we proposed a particle swarm optimization of comprehensive improvement strategy, which is a simple particle swarm optimization with dynamic adaptive hybridization of extremum disturbance and cross (ecds-PSO algorithm). This new comprehensive improved particle swarm algorithm discards the particle velocity and reduces the PSO from the second order to the first order difference equation. The evolutionary process is only controlled by the variables of the particles position. The hybridization operation of increasing the extremum disturbance and introducing genetic algorithm can accelerate the particles to overstep the local extremum. The mathematical derivation and a plurality of comparative experiment provide us the following information: the improved particle swarm optimization is a simple and effective optimization algorithm which can improve the algorithm accuracy, convergence viscosity and ability of avoiding the local extremum, and effectively reduce the calculation complexity.
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Kien, Chong Woon, and Neoh Siew Chin. "Improved Particle Swarm Optimization (PSO) for Performance Optimization of Electronic Filter Circuit Designs." Applied Mechanics and Materials 229-231 (November 2012): 1643–50. http://dx.doi.org/10.4028/www.scientific.net/amm.229-231.1643.
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This article discusses and analyzes particle swarm optimization (PSO) approach in the design and performance optimization of a 4th-order Sallen Key high pass filter. Three types of particle swarm features are studied: basic PSO, PSO with regrouped particles (PSO-RP) and PSO with diversity embedded regrouped particles (PSO-DRP). PSO-RP and PSO-DRP are proposed to solve the stagnation problem of basic PSO. Based on the developed PSO approaches, LTspice is employed as the circuit simulator for the performance investigation of the designed filter. In this paper, 12 design parameters of the Sallen Key high pass filter are optimized to satisfy the required constraints and specifications on gain, cut-off frequency, and pass band ripples. Overall results show that PSO with diversity embedded regrouped particles improve the conventional search of basic PSO and has managed to achieve the design objectives.
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Li, Zheng Bo. "Learning-Based Multi-Directional Adaptive PSO." Applied Mechanics and Materials 321-324 (June 2013): 2183–86. http://dx.doi.org/10.4028/www.scientific.net/amm.321-324.2183.
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Particle Swarm Optimization (PSO) is a swarm intelligence algorithm to achieve through competition and collaboration between the particles in the complex search space to find the global optimum. Basic PSO algorithm evolutionary late convergence speed is slow and easy to fall into the shortcomings of local minima, this paper presents a multi-learning particle swarm optimization algorithm, the algorithm particle at the same time to follow their own to find the optimal solution, random optimal solution and the optimal solution for the whole group of other particles with dimensions velocity update discriminate area boundary position optimization updates and small-scale perturbations of the global best position, in order to enhance the algorithm escape from local optima capacity. The test results show that several typical functions: improved particle swarm algorithms significantly improve the global search ability, and can effectively avoid the premature convergence problem. Algorithm so that the relative robustness of the search space position has been significantly improved global optimal solution in high-dimensional optimization problem, suitable for solving similar problems, the calculation results can meet the requirements of practical engineering.
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Hudaib, Amjad A., and Ahmad Kamel AL Hwaitat. "Movement Particle Swarm Optimization Algorithm." Modern Applied Science 12, no. 1 (December 31, 2017): 148. http://dx.doi.org/10.5539/mas.v12n1p148.
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Particle Swarm Optimization (PSO) ia a will known meta-heuristic that has been used in many applications for solving optimization problems. But it has some problems such as local minima. In this paper proposed a optimization algorithm called Movement Particle Swarm Optimization (MPSO) that enhances the behavior of PSO by using a random movement function to search for more points in the search space. The meta-heuristic has been experimented over 23 benchmark faction compared with state of the art algorithms: Multi-Verse Optimizer (MFO), Sine Cosine Algorithm (SCA), Grey Wolf Optimizer (GWO) and particle Swarm Optimization (PSO). The Results showed that the proposed algorithm has enhanced the PSO over the tested benchmarked functions.
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Golubovic, Ruzica, and Dragan Olcan. "Antenna optimization using Particle Swarm Optimization algorithm." Journal of Automatic Control 16, no. 1 (2006): 21–24. http://dx.doi.org/10.2298/jac0601021g.
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We present the results for two different antenna optimization problems that are found using the Particle Swarm Optimization (PSO) algorithm. The first problem is finding the maximal forward gain of a Yagi antenna. The second problem is finding the optimal feeding of a broadside antenna array. The optimization problems have 6 and 20 optimization variables, respectively. The preferred values of the parameters of the PSO algorithm are found for presented problems. The results show that the preferred parameters of PSO are somewhat different for optimization problems with different number of dimensions of the optimization space. The results that are found using the PSO algorithm are compared with the results that are found using other optimization algorithms, in order to estimate the efficiency of the PSO.
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Zhou, Xin, Shangbo Zhou, Yuxiao Han, and Shufang Zhu. "Lévy flight-based inverse adaptive comprehensive learning particle swarm optimization." Mathematical Biosciences and Engineering 19, no. 5 (2022): 5241–68. http://dx.doi.org/10.3934/mbe.2022246.
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<abstract><p>In the traditional particle swarm optimization algorithm, the particles always choose to learn from the well-behaved particles in the population during the population iteration. Nevertheless, according to the principles of particle swarm optimization, we know that the motion of each particle has an impact on other individuals, and even poorly behaved particles can provide valuable information. Based on this consideration, we propose Lévy flight-based inverse adaptive comprehensive learning particle swarm optimization, called LFIACL-PSO. In the LFIACL-PSO algorithm, First, when the particle is trapped in the local optimum and cannot jump out, inverse learning is used, and the learning step size is obtained through the Lévy flight. Second, to increase the diversity of the algorithm and prevent it from prematurely converging, a comprehensive learning strategy and Ring-type topology are used as part of the learning paradigm. In addition, use the adaptive update to update the acceleration coefficients for each learning paradigm. Finally, the comprehensive performance of LFIACL-PSO is measured using 16 benchmark functions and a real engineering application problem and compared with seven other classical particle swarm optimization algorithms. Experimental comparison results show that the comprehensive performance of the LFIACL-PSO outperforms comparative PSO variants.</p></abstract>
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Jiang, Chang Yuan, Shu Guang Zhao, Li Zheng Guo, and Chuan Ji. "An Improved Particle Swarm Optimization Algorithm." Applied Mechanics and Materials 195-196 (August 2012): 1060–65. http://dx.doi.org/10.4028/www.scientific.net/amm.195-196.1060.
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Based on the analyzing inertia weight of the standard particle swarm optimization (PSO) algorithm, an improved PSO algorithm is presented. Convergence condition of PSO is obtained through solving and analyzing the differential equation. By the experiments of four Benchmark function, the results show the performance of S-PSO improved more clearly than the standard PSO and random inertia weight PSO. Theoretical analysis and simulation experiments show that the S-PSO is efficient and feasible.
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Park, Jun-Hyuk, and Byung-In Kim. "A Modified Particle Swarm Optimization Algorithm : Information Diffusion PSO." Journal of Korean Institute of Industrial Engineers 37, no. 3 (September 1, 2011): 163–70. http://dx.doi.org/10.7232/jkiie.2011.37.3.163.
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Tang, Kezong, and Chengjian Meng. "Particle Swarm Optimization Algorithm Using Velocity Pausing and Adaptive Strategy." Symmetry 16, no. 6 (May 27, 2024): 661. http://dx.doi.org/10.3390/sym16060661.
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Particle swarm optimization (PSO) as a swarm intelligence-based optimization algorithm has been widely applied to solve various real-world optimization problems. However, traditional PSO algorithms encounter issues such as premature convergence and an imbalance between global exploration and local exploitation capabilities when dealing with complex optimization tasks. To address these shortcomings, an enhanced PSO algorithm incorporating velocity pausing and adaptive strategies is proposed. By leveraging the search characteristics of velocity pausing and the terminal replacement mechanism, the problem of premature convergence inherent in standard PSO algorithms is mitigated. The algorithm further refines and controls the search space of the particle swarm through time-varying inertia coefficients, symmetric cooperative swarms concepts, and adaptive strategies, balancing global search and local exploitation. The performance of VASPSO was validated on 29 standard functions from Cec2017, comparing it against five PSO variants and seven swarm intelligence algorithms. Experimental results demonstrate that VASPSO exhibits considerable competitiveness when compared with 12 algorithms. The relevant code can be found on our project homepage.
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Ali, Omer, Qamar Abbas, Khalid Mahmood, Ernesto Bautista Thompson, Jon Arambarri, and Imran Ashraf. "Competitive Coevolution-Based Improved Phasor Particle Swarm Optimization Algorithm for Solving Continuous Problems." Mathematics 11, no. 21 (October 24, 2023): 4406. http://dx.doi.org/10.3390/math11214406.
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Particle swarm optimization (PSO) is a population-based heuristic algorithm that is widely used for optimization problems. Phasor PSO (PPSO), an extension of PSO, uses the phase angle θ to create a more balanced PSO due to its increased ability to adjust the environment without parameters like the inertia weight w. The PPSO algorithm performs well for small-sized populations but needs improvements for large populations in the case of rapidly growing complex problems and dimensions. This study introduces a competitive coevolution process to enhance the capability of PPSO for global optimization problems. Competitive coevolution disintegrates the problem into multiple sub-problems, and these sub-swarms coevolve for a better solution. The best solution is selected and replaced with the current sub-swarm for the next competition. This process increases population diversity, reduces premature convergence, and increases the memory efficiency of PPSO. Simulation results using PPSO, fuzzy-dominance-based many-objective particle swarm optimization (FMPSO), and improved competitive multi-swarm PPSO (ICPPSO) are generated to assess the convergence power of the proposed algorithm. The experimental results show that ICPPSO achieves a dominating performance. The ICPPSO results for the average fitness show average improvements of 15%, 20%, 30%, and 35% over PPSO and FMPSO. The Wilcoxon statistical significance test also confirms a significant difference in the performance of the ICPPSO, PPSO, and FMPSO algorithms at a 0.05 significance level.
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Leong, Wen Fung, and Gary G. Yen. "Constraint Handling in Particle Swarm Optimization." International Journal of Swarm Intelligence Research 1, no. 1 (January 2010): 42–63. http://dx.doi.org/10.4018/jsir.2010010103.
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In this article, the authors propose a particle swarm optimization (PSO) for constrained optimization. The proposed PSO adopts a multiobjective approach to constraint handling. Procedures to update the feasible and infeasible personal best are designed to encourage finding feasible regions and convergence toward the Pareto front. In addition, the infeasible nondominated solutions are stored in the global best archive to exploit the hidden information for guiding the particles toward feasible regions. Furthermore, the number of feasible personal best in the personal best memory and the scalar constraint violations of personal best and global best are used to adapt the acceleration constants in the PSO flight equations. The purpose is to find more feasible particles and search for better solutions during the process. The mutation procedure is applied to encourage global and fine-tune local searches. The simulation results indicate that the proposed constrained PSO is highly competitive, achieving promising performance.
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Li, Yun Zhi, Quan Yuan, Yang Zhao, and Qian Hui Gang. "A Novel Reactive Power Compensation Approach Based on Particle Swarm Optimization." Applied Mechanics and Materials 740 (March 2015): 401–4. http://dx.doi.org/10.4028/www.scientific.net/amm.740.401.
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The particle swarm optimization (PSO) algorithm as a stochastic search algorithm for solving reactive power optimization problem. The PSO algorithm converges too fast, easy access to local convergence, leading to convergence accuracy is not high, to study the particle swarm algorithm improvements. The establishment of a comprehensive consideration of the practical constraints and reactive power regulation means no power optimization mathematical model, a method using improved particle swarm algorithm for reactive power optimization problem, the algorithm weighting coefficients and inactive particles are two aspects to improve. Meanwhile segmented approach to particle swarm algorithm improved effectively address the shortcomings evolution into local optimum and search accuracy is poor, in order to determine the optimal reactive power optimization program.
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Zeng, Guang Pu, and Hui Lian Fan. "Two-Subpopulation Particle Swarm Optimization Based on Pheromone Diffusion." Applied Mechanics and Materials 667 (October 2014): 300–308. http://dx.doi.org/10.4028/www.scientific.net/amm.667.300.
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The particle swarm optimization (PSO) algorithm is a new population based search strat-egy, which has exhibited good performance on well-known numerical test problems. However, conventional algorithm of particle swarm optimization (PSO) is often trapped in local optima in global optimization of multimodal high-dimensional function. Analysis of the main causes of the premature convergence, proposes an improved two-subpopulation PSO algorithm, based on the mechanism of pheromone diffusion and diversity feedback. The population is divided into main subpopulation particle swarm and assistant subpopulation particle swarm, whose search direction is inversed completely. A pheromone diffusion function, which can control the degree of convergence of particles move to the best position, is designed by both taking into account these particles distribution and their fitness value. Adjusting inertial weight and numbers of sub-populations adaptively with diversity feedback greatly contribute to breaking away from local optima. Experiments on optimization of high-dimension benchmark functions show that, comparing with some other PSO variants, the improved algorithm can find better optima with converges faster, and prevent more effectively the premature convergence.
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Li, Ming, and Xue Ling Ji. "Bacterial Particle Swarm Optimization Algorithm." Advanced Materials Research 211-212 (February 2011): 968–72. http://dx.doi.org/10.4028/www.scientific.net/amr.211-212.968.
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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.
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Yamanaka, Yoshikazu, and Katsutoshi Yoshida. "Simple gravitational particle swarm algorithm for multimodal optimization problems." PLOS ONE 16, no. 3 (March 18, 2021): e0248470. http://dx.doi.org/10.1371/journal.pone.0248470.
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In real world situations, decision makers prefer to have multiple optimal solutions before making a final decision. Aiming to help the decision makers even if they are non-experts in optimization algorithms, this study proposes a new and simple multimodal optimization (MMO) algorithm called the gravitational particle swarm algorithm (GPSA). Our GPSA is developed based on the concept of “particle clustering in the absence of clustering procedures”. Specifically, it simply replaces the global feedback term in classical particle swarm optimization (PSO) with an inverse-square gravitational force term between the particles. The gravitational force mutually attracts and repels the particles, enabling them to autonomously and dynamically generate sub-swarms in the absence of algorithmic clustering procedures. Most of the sub-swarms gather at the nearby global optima, but a small number of particles reach the distant optima. The niching behavior of our GPSA was tested first on simple MMO problems, and then on twenty MMO benchmark functions. The performance indices (peak ratio and success rate) of our GPSA were compared with those of existing niching PSOs (ring-topology PSO and fitness Euclidean-distance ratio PSO). The basic performance of our GPSA was comparable to that of the existing methods. Furthermore, an improved GPSA with a dynamic parameter delivered significantly superior results to the existing methods on at least 60% of the tested benchmark functions.
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Zhang, Guan Yu, Xiao Ming Wang, Rui Guo, and Guo Qiang Wang. "An Improved Particle Swarm Optimization Algorithm." Applied Mechanics and Materials 394 (September 2013): 505–8. http://dx.doi.org/10.4028/www.scientific.net/amm.394.505.
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This paper presents an improved particle swarm optimization (PSO) algorithm based on genetic algorithm (GA) and Tabu algorithm. The improved PSO algorithm adds the characteristics of genetic, mutation, and tabu search into the standard PSO to help it overcome the weaknesses of falling into the local optimum and avoids the repeat of the optimum path. By contrasting the improved and standard PSO algorithms through testing classic functions, the improved PSO is found to have better global search characteristics.
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Xu, Xinliang, and Fu Yan. "Random walk autonomous groups of particles for particle swarm optimization." Journal of Intelligent & Fuzzy Systems 42, no. 3 (February 2, 2022): 1519–45. http://dx.doi.org/10.3233/jifs-210867.
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Autonomous groups of particles swarm optimization (AGPSO), inspired by individual diversity in biological swarms such as insects or birds, is a modified particle swarm optimization (PSO) variant. The AGPSO method is simple to understand and easy to implement on a computer. It has achieved an impressive performance on high-dimensional optimization tasks. However, AGPSO also struggles with premature convergence, low solution accuracy and easily falls into local optimum solutions. To overcome these drawbacks, random-walk autonomous group particle swarm optimization (RW-AGPSO) is proposed. In the RW-AGPSO algorithm, Levy flights and dynamically changing weight strategies are introduced to balance exploration and exploitation. The search accuracy and optimization performance of the RW-AGPSO algorithm are verified on 23 well-known benchmark test functions. The experimental results reveal that, for almost all low- and high-dimensional unimodal and multimodal functions, the RW-AGPSO technique has superior optimization performance when compared with three AGPSO variants, four PSO approaches and other recently proposed algorithms. In addition, the performance of the RW-AGPSO has also been tested on the CEC’14 test suite and three real-world engineering problems. The results show that the RW-AGPSO is effective for solving high complexity problems.
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Yang, Xiang Jun, Yi Long Zhao, Yu Chuang Chen, and Xin Chao Zhao. "A Multi-Swarm Cooperative Perturbed Particle Swarm Optimization." Advanced Materials Research 225-226 (April 2011): 619–22. http://dx.doi.org/10.4028/www.scientific.net/amr.225-226.619.
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Combined with a variety of ideas a Multi-swarm cooperative Perturbed Particle Swarm Optimization algorithm (MpPSO) is presented to improve the performance and to reduce the premature convergence of PSO. This algorithm includes the idea of multiple swarms to improve the evolution efficiency by information sharing between populations to avoid falling into local optimum caused by single population. It also includes the idea of perturbing the swarms beside the global best solution, which can escape from local optimum. Experiments show that the proposed algorithm MpPSO has better performance, better convergence and stability when comparing with the traditional and the recently improved particle swarm optimization.
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Ni, Hong Mei, and Wei Gang Wang. "An Improved Particle Swarm Optimization Algorithm." Advanced Materials Research 850-851 (December 2013): 809–12. http://dx.doi.org/10.4028/www.scientific.net/amr.850-851.809.
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Niche is an important technique for multi-peak function optimization. When the particle swarm optimization (PSO) algorithm is used in multi-peak function optimization, there exist some problems, such as easily falling into prematurely, having slow convergence rate and so on. To solve above problems, an improved PSO algorithm based on niche technique is brought forward. PSO algorithm utilizes properties of swarm behavior to solve optimization problems rapidly. Niche techniques have the ability to locate multiple solutions in multimodal domains. The improved PSO algorithm not only has the efficient parallelism but also increases the diversity of population because of the niche technique. The simulation result shows that the new algorithm is prior to traditional PSO algorithm, having stronger adaptability and convergence, solving better the question on multi-peak function optimization.
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Liu, Hao, Gang Xu, Gui-yan Ding, and Yu-bo Sun. "Human Behavior-Based Particle Swarm Optimization." Scientific World Journal 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/194706.
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Particle swarm optimization (PSO) has attracted many researchers interested in dealing with various optimization problems, owing to its easy implementation, few tuned parameters, and acceptable performance. However, the algorithm is easy to trap in the local optima because of rapid losing of the population diversity. Therefore, improving the performance of PSO and decreasing the dependence on parameters are two important research hot points. In this paper, we present a human behavior-based PSO, which is called HPSO. There are two remarkable differences between PSO and HPSO. First, the global worst particle was introduced into the velocity equation of PSO, which is endowed with random weight which obeys the standard normal distribution; this strategy is conducive to trade off exploration and exploitation ability of PSO. Second, we eliminate the two acceleration coefficientsc1andc2in the standard PSO (SPSO) to reduce the parameters sensitivity of solved problems. Experimental results on 28 benchmark functions, which consist of unimodal, multimodal, rotated, and shifted high-dimensional functions, demonstrate the high performance of the proposed algorithm in terms of convergence accuracy and speed with lower computation cost.
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Zhu, Yong Bin. "Overview of Particle Swarm Optimization." Applied Mechanics and Materials 543-547 (March 2014): 1597–600. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.1597.
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Particle swarm optimization (PSO) is a new optimization algorithm based on swarm intelligence. Firstly, the paper briefly introduces the origin of the PSO, the basic algorithm and the basic model, but an overview on the basic principle of the algorithm and its improved algorithm is also provided. Then, the research status and the current application of the algorithm as well as the development direction in the future are reviewed.
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Marini, Federico, and Beata Walczak. "Particle swarm optimization (PSO). A tutorial." Chemometrics and Intelligent Laboratory Systems 149 (December 2015): 153–65. http://dx.doi.org/10.1016/j.chemolab.2015.08.020.
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Yao, Hai Tao, Hai Qiang Chen, and Tuan Fa Qin. "Niche PSO Particle Filter with Particles Fusion for Target Tracking." Applied Mechanics and Materials 239-240 (December 2012): 1368–72. http://dx.doi.org/10.4028/www.scientific.net/amm.239-240.1368.
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An improved particle filter algorithm is proposed to track a randomly moving target in video. In particle filter framework, a particle swarm optimization improved by niche technique which implemented by restricted competition selection is integrated. It can move particles into high likelihood area of target and form multi-population distribution, so that the searching capability of particles is enhanced and then the adaptation to the change of dynamic target state is improved. The particles of niching particle swarm optimization and the particles of particle filter are integrated for new particle weight calculation and finally realize a new particle filter for target tracking in video sequence.
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Lenin, K. "AMELIORATED PARTICLE SWARM OPTIMIZATION ALGORITHM FOR SOLVING OPTIMAL REACTIVE POWER DISPATCH PROBLEM." International Journal of Research -GRANTHAALAYAH 6, no. 2 (February 28, 2018): 202–13. http://dx.doi.org/10.29121/granthaalayah.v6.i2.2018.1563.
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In this paper, an Ameliorated Particle Swarm Optimization (APSO) algorithm has been proposed to solve the optimal reactive power dispatch problem. Particle Swarm Optimization (PSO) is swarm intelligence-based exploration and optimization algorithm which is used to solve global optimization problems. But due to deficiency of population diversity and early convergence it is often stuck into local optima. Diversity upsurges and avoids premature convergence by using evolutionary operators in PSO. In this paper the intermingling crossover operator is used to upsurge the exploration capability of the swarm in the exploration space. Particle Swarm Optimization uses this crossover method to converge optimum solution in quick manner. Thus the intermingling crossover operator is united with particle swarm optimization to augment the performance and possess the diversity which guides the particles to the global optimum powerfully. Proposed Ameliorated Particle Swarm Optimization (APSO) algorithm has been tested in standard IEEE 30 bus test system and simulation results shows clearly the improved performance of the projected algorithm in reducing the real power loss and static voltage stability margin has been enhanced.
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Abdul-Adheem, Wameedh Riyadh. "An enhanced particle swarm optimization algorithm." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 6 (December 1, 2019): 4904. http://dx.doi.org/10.11591/ijece.v9i6.pp4904-4907.
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<p>In this paper, an enhanced stochastic optimization algorithm based on the basic Particle Swarm Optimization (PSO) algorithm is proposed. The basic PSO algorithm is built on the activities of the social feeding of some animals. Its parameters may influence the solution considerably. Moreover, it has a couple of weaknesses, for example, convergence speed and premature convergence. As a way out of the shortcomings of the basic PSO, several enhanced methods for updating the velocity such as Exponential Decay Inertia Weight (EDIW) are proposed in this work to construct an Enhanced PSO (EPSO) algorithm. The suggested algorithm is numerically simulated established on five benchmark functions with regards to the basic PSO approaches. The performance of the EPSO algorithm is analyzed and discussed based on the test results.</p>
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Ogutu, Patrick O. M., Dr Nicholas Oyie, and Dr Winston Ojenge. "Performance Analysis of an Improved Particle Swarm Optimization and the Standard Particle Swarm Optimization." International Journal of Engineering and Advanced Technology 13, no. 1 (October 30, 2023): 37–42. http://dx.doi.org/10.35940/ijeat.a4298.1013123.
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Many industries employ different modes of control when it comes to PID parameter tuning. The problem of tuning a control system for linear and nonlinear systems has been undertaken by previous authors however the level of error reduction in the system performance has not been done quite well, hence the study on improved particle swarm optimization using improved Algorithm for PID parameter tuning. This paper tackled optimization of PID parameters based on improved PSO algorithm for the non-linear system. The particle swarm optimization is used to tune the PID parameters to ensure improved system response and operation. The PSO was deployed in a nonlinear system for application and validation of results achieved through PID tuning of the standard parameters on the MATLAB Simulink platform. The study ensured that the PID parameters were effectively tuned by applying improved PSO Algorithm to the plant process. The research used a standard nonlinear system depicting the real-life situation and an Improved Particle Swarm Optimization Algorithm to analyze and compare the improved behavior on the MATLAB/Simulink toolbox as applied to the PID parameters. Finally, it was logically realized that an improved PSO Algorithm system response was much better in comparison with the non-PSO tuned system. The simulation was performed on the plant transfer function using the MATLAB and Simulink platforms at various parameter choices and situations, and realizations were made from the data obtained. As the iteration was increased from 10, 50, and 100, there was a significant reduction in ITAE error from 0.054806 to a minimum of 0.01900, which is far better than the SPSO algorithm. SPSO reduces the error from 0.065143 to 0.020476. It was noted that the system behavior was far better in terms of settling time and peak overshoot for IPSO.
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Kok, S., and J. A. Snyman. "A Strongly Interacting Dynamic Particle Swarm Optimization Method." Journal of Artificial Evolution and Applications 2008 (March 31, 2008): 1–9. http://dx.doi.org/10.1155/2008/126970.
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A novel dynamic interacting particle swarm optimization algorithm (DYN-PSO) is proposed. The algorithm can be considered to be the synthesis of two established trajectory methods for unconstrained minimization. In the new method, the minimization of a function is achieved through the dynamic motion of a strongly interacting particle swarm, where each particle in the swarm is simultaneously attracted by all other particles located at positions of lower function value. The force of attraction experienced by a particle at higher function value due to a particle at a lower function value is equal to the difference between the respective function-values divided by their stochastically perturbed position difference. The resultant motion of the particles under the influence of the attracting forces is computed by solving the associated equations of motion numerically. An energy dissipation strategy is applied to each particle. The specific chosen force law and the dissipation strategy result in the rapid collapse (convergence) of the swarm to a stationary point. Numerical results show that, in comparison to the standard particle swarm algorithm, the proposed DYN-PSO algorithm is promising.
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Nguyen, Tram, Toan Bui, and Bay Vo. "Multi-Swarm Single-Objective Particle Swarm Optimization to Extract Multiple-Choice Tests." Vietnam Journal of Computer Science 06, no. 02 (May 2019): 147–61. http://dx.doi.org/10.1142/s219688881950009x.
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This paper proposes the use of multi-swarm method in particle swarm optimization (PSO) algorithm to generate multiple-choice tests based on assumed objective levels of difficulty. The method extracts an abundance of tests at the same time with the same levels of difficulty and approximates the difficulty-level requirement given by the users. The experimental results show that the proposed method can generate many tests from question banks satisfying predefined levels of difficulty. Additionally, the proposed method is also shown to be effective in terms of many criteria when compared with other methods such as manually extracted tests, random methods and PSO-based methods in terms of execution time, standard deviation, the number of particles per swarm and the number of swarms.
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Lenin, K. "DIMENSIONED PARTICLE SWARM OPTIMIZATION FOR REACTIVE POWER OPTIMIZATION PROBLEM." International Journal of Research -GRANTHAALAYAH 6, no. 4 (April 30, 2018): 281–90. http://dx.doi.org/10.29121/granthaalayah.v6.i4.2018.1663.
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This paper present’s Dimensioned Particle Swarm Optimization (DPSO) algorithm for solving Reactive power optimization (RPO) problem. Dimensioned extension is introduced to particles in the particle swarm optimization (PSO) model in order to overcome premature convergence in interactive optimization. In the performance of basic PSO often flattens out with a loss of diversity in the search space as resulting in local optimal solution. Proposed algorithm has been tested in standard IEEE 57 test bus system and compared to other standard algorithms. Simulation results reveal about the best performance of the proposed algorithm in reducing the real power loss and voltage profiles are within the limits.
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Ji, Wei Dong, and Ke Qi Wang. "Particle Swarm Improvement Optimization Algorithm and Performance Study." Advanced Materials Research 468-471 (February 2012): 2546–49. http://dx.doi.org/10.4028/www.scientific.net/amr.468-471.2546.
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In this paper, the PSO algorithm is improved, and take mutate of idea into PSO, namely algorithm not set particle boundaries constraints to make them limited in the search interval, but produce the same number of random particle replace those particles of flying away from the search area. Put forward a kind of improved particle swarm optimization algorithm. Use three input XOR problem to improve algorithm testing, the results show that the improved algorithm in the convergence speed and global search ability is superior to the PSO and SGA algorithm, and avoid the prematurity and local convergence.
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Wei-Yan Chang, Wei-Yan Chang, Prathibha Soma Wei-Yan Chang, Huan Chen Prathibha Soma, Hsuan Chang Huan Chen, and Chun-Wei Tsai Hsuan Chang. "A Hybrid Firefly with Dynamic Multi-swarm Particle Swarm Optimization for WSN Deployment." 網際網路技術學刊 24, no. 4 (July 2023): 825–36. http://dx.doi.org/10.53106/160792642023072404001.
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<p>Enhancing the coverage area of the sensing range with the limiting resource is a critical problem in the wireless sensor network (WSN). Mobile sensors are patched coverage holes and they also have limited energy to move in large distances. Several recent studies indicated the metaheuristic algorithms can find an acceptable deployed solution in a reasonable time, especially the PSO-based algorithm. However, the speeds of convergence of most PSO-based algorithms are too fast which will lead to the premature problem to degrade the quality of deployed performance in WSN. A hybrid metaheuristic combined with dynamic multi-swarm particle swarm optimization and firefly algorithm will be presented in this paper to find an acceptable deployed solution with the maximum coverage rate and minimum energy consumption via static and mobile sensors. Moreover, a novel switch search mechanism between sub-swarms will also be presented for the proposed algorithm to avoid fall into local optimal in early convergence process. The simulation results show that the proposed method can obtain better solutions than other PSO-based deployment algorithms compared in this paper in terms of coverage rate and energy consumption.</p> <p> </p>
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Lenin, K. "POLAR PARTICLE SWARM OPTIMIZATION ALGORITHM FOR SOLVING OPTIMAL REACTIVE POWER PROBLEM." International Journal of Research -GRANTHAALAYAH 6, no. 6 (June 30, 2018): 335–45. http://dx.doi.org/10.29121/granthaalayah.v6.i6.2018.1378.
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This paper presents Polar Particle Swarm optimization (PPSO) algorithm for solving optimal reactive power problem. The standard Particle Swarm Optimization (PSO) algorithm is an innovative evolutionary algorithm in which each particle studies its own previous best solution and the group’s previous best to optimize problems. In the proposed PPSO algorithm that enhances the behaviour of PSO and avoids the local minima problem by using a polar function to search for more points in the search space in order to evaluate the efficiency of proposed algorithm, it has been tested on IEEE 30 bus system and compared to other algorithms. Simulation results demonstrate good performance of the Polar Particle Swarm optimization (PPSO) algorithm in solving an optimal reactive power problem.
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Zhao, Ren Tao, You Yu Wang, Hua De Li, and Jun Tie. "Infrared Image Contrast Enhancement Based on Modified Particle Swarm Optimization." Advanced Materials Research 760-762 (September 2013): 1389–93. http://dx.doi.org/10.4028/www.scientific.net/amr.760-762.1389.
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Adaptive infrared image contrast enhancement is presented based on modified particle swarm optimization (PSO) and incomplete Beta Function. On the basis of traditional PSO, modified PSO integrates into the theory of Multi-Particle Swarm and evolution theory algorithm. By using separate search space optimal solution of multiple particles, the global search ability is improved. And in the iteration procedures, timely adjustment of acceleration coefficients is convenient for PSO to find the global optimal solution in the later iteration. Through infrared image simulation, experimental results show that the modified PSO is better than the standard PSO in computing speed and convergence.
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Fan, Hui. "A New Combined Particle Swarm Optimization Algorithm Based Golden Section Strategy." Advanced Materials Research 308-310 (August 2011): 1099–105. http://dx.doi.org/10.4028/www.scientific.net/amr.308-310.1099.
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Based the defects of global optimal model falling into local optimum easily and local model with slow convergence speed during traditional PSO algorithm solving a complex high-dimensional and multi-peak function, a two sub-swarms particle optimization algorithm is proposed. All particles are divided into two equivalent parts. One part particles adopts global evolution model, while the other part uses local evolution model. If the global optimal fitness of the whole population stagnates for some iteration, a golden rule is introduced into local evolution model. This strategy can substitute the partial perfect particles of local evolution for the equivalent worse particles of global evolution model. So, some particles with advantage are joined into the whole population to make the algorithm keep active all the time. Compared with classic PSO and PSO-GL(A dynamic global and local combined particle swarm optimization algorithm, PSO-GL), the results show that the proposed PSO in this paper can get more effective performance over the other two algorithm in the simulation experiment for four benchmark testing function.