Particle Swarm Optimization Variants Research Articles

Hybrid particle swarm optimizer with fitness-distance balance and individual self-exploitation strategies for numerical optimization problems

Due to the simplicity of the learning strategy, the original particle swarm optimization (PSO) has various deficiencies, such as entrapment in local optima, rapid loss of diversity and a poor balance between exploration and exploitation, especially for many complex optimization problems. To overcome these shortcomings, this paper proposes a hybrid particle swarm optimizer with fitness-distance balance and individual self-exploitation strategies, namely, HPSO-FDB-ISE. First, to reduce the probability of becoming trapped in a local optimum for the population, fitness-distance balance is employed to construct an alternative learning exemplar to the global best position. Second, individual self-exploitation is introduced to achieve intelligent exploitation by learning from individual current information for particles. Finally, a nonlinear time-varying inertia weight is used to efficiently balance the exploitation and exploration in the search process. The proposed HPSO-FDB-ISE is evaluated on the CEC 2017 test suite against six state-of-the-art meta-heuristics and seven state-of-the-art PSO variants. Experimental results and statistical analysis reveal that the proposed HPSO-FDB-ISE algorithm yields excellent performances compared to other algorithms that are considered in this paper in the majority of cases.

Fitness-Based Acceleration Coefficients Binary Particle Swarm Optimization (FACBPSO) to Solve the Discounted Knapsack Problem

The discounted {0-1} knapsack problem (D{0-1}KP) is a multi-constrained optimization and an extended form of the 0-1 knapsack problem. The DKP is composed of a set of item batches where each batch has three items and the objective is to maximize profit by selecting at most one item from each batch. Therefore, the D{0-1}KP is complex and has found many applications in real economic problems and other areas where the concept of promotional discounts exists. As DKP belongs to a binary class problem, so the novel binary particle swarm optimization variant with modifications is proposed in this paper. The acceleration coefficients are important parameters of the particle swarm optimization algorithm that keep the balance between exploration and exploitation. In conventional binary particle swarm optimization (BPSO), the acceleration coefficients of each particle remain the same in iteration, whereas in the proposed variant, fitness-based acceleration coefficient binary particle swarm optimization (FACBPSO), values of acceleration coefficients are based on the fitness of each particle. This modification enforces the least fit particles to move fast and best fit accordingly, which accelerates the convergence speed and reduces the computing time. Experiments were conducted on four instances of DKP having 10 datasets of each instance and the results of FACBPSO were compared with conventional BPSO and the new exact algorithm using a greedy repair strategy. The results demonstrate that the proposed algorithm outperforms PSO-GRDKP and the new exact algorithm in solving four instances of D{0-1}KP, with improved convergence speed and feasible solution time.

Particle swarm optimization: Stability analysis using N-informers under arbitrary coefficient distributions

This paper derives, under minimal modelling assumptions, a simple to use theorem for obtaining both order-1 and order-2 stability criteria for a common class of particle swarm optimization (PSO) variants. Specifically, PSO variants that can be rewritten as a finite sum of stochastically weighted difference vectors between a particle’s position and swarm informers are covered by the theorem. Additionally, the use of the derived theorem allows a PSO practitioner to obtain stability criteria that contains no artificial restriction on the relationship between control coefficients. The majority of previous stability results for PSO variants provided stability criteria under the restriction that certain control coefficients are equal; such restrictions are not present when using the derived theorem. Using the derived theorem, as demonstration of its ease of use, stability criteria are derived without the imposed restriction on the relation between the control coefficients for four popular PSO variants.

Differential Elite Learning Particle Swarm Optimization for Global Numerical Optimization

Although particle swarm optimization (PSO) has been successfully applied to solve optimization problems, its optimization performance still encounters challenges when dealing with complicated optimization problems, especially those with many interacting variables and many wide and flat local basins. To alleviate this issue, this paper proposes a differential elite learning particle swarm optimization (DELPSO) by differentiating the two guiding exemplars as much as possible to direct the update of each particle. Specifically, in this optimizer, particles in the current swarm are divided into two groups, namely the elite group and non-elite group, based on their fitness. Then, particles in the non-elite group are updated by learning from those in the elite group, while particles in the elite group are not updated and directly enter the next generation. To comprise fast convergence and high diversity at the particle level, we let each particle in the non-elite group learn from two differential elites in the elite group. In this way, the learning effectiveness and the learning diversity of particles is expectedly improved to a large extent. To alleviate the sensitivity of the proposed DELPSO to the newly introduced parameters, dynamic adjustment strategies for parameters were further designed. With the above two main components, the proposed DELPSO is expected to compromise the search intensification and diversification well to explore and exploit the solution space properly to obtain promising performance. Extensive experiments conducted on the widely used CEC 2017 benchmark set with three different dimension sizes demonstrated that the proposed DELPSO achieves highly competitive or even much better performance than state-of-the-art PSO variants.

Optimal design of cascaded Wiener-Hammerstein system using a heuristically supervised discrete Kalman filter with application on benchmark problems

Block oriented models are recurrently employed to describe the dynamic characteristics of nonlinear systems. This paper adopts an efficacious block-oriented model called cascaded Wiener-Hammerstein (W-H) structure to model a nonlinear system. The parameters of the W-H model are identified using a nature-inspired evolution algorithm-supported Kalman filter (KF). In the proposed technique, the utility of the employed optimisation algorithm named Harris Hawks optimiser (HHO) is to acquire the optimal global solution of initial state KF parameters for the W-H system identification problem. Then, the conventional KF algorithm utilises these optimised KF parameters to beget the near-global estimated W-H system parameters. The effectiveness of the proposed HHO-based KF algorithm is verified through a comparison study with other variants of particle swarm optimisation (PSO) and harmony search (HS) algorithms-supported KF methods on two numerical W-H problems with different nonlinearity levels and two practical benchmark plants, namely, real electronic diode switching network and flutter clearance of F-18 systems research aircraft. The simulation results ensure that the proposed HHO-KF approach offers significantly improved results over other competing methods in terms of various well known standard metrics. The hypothesis test verifies the stability and consistency of the proposed identification method. Moreover, the proposed approach provides a faster convergence rate and the lowest estimation precision compared with other reported techniques.

Constrained self regulating particle swarm optimization

Self regulating particle swarm optimization (SRPSO) is a variant of particle swarm optimization (PSO) which has proved to be a very efficient algorithm for unconstrained optimization compared with other evolutionary algorithms (EAs) and utilized recently by the researchers for solving real-world problems. However, SRPSO has not been evaluated and analyzed for constrained optimization. In this work, SRPSO has been evaluated exhaustively for constrained optimization using the 24 constrained benchmark problems by coupling it with four efficient constraint handling techniques (CHTs). The results of constrained SRPSO algorithm have been compared with two other algorithms i.e. Differential evolution (DE) and PSO. DE and PSO have also been coupled with same four CHTs and evaluated on the 24 constrained benchmark problems. Statistical analysis on performance evaluation of three algorithms on the benchmark problems shows that constrained SRPSO algorithm performance is better than constrained PSO but it is found to be deficient when compared with constrained DE with 95% confidence level. Therefore, the objective of this work is to evaluate the SRPSO algorithm comprehensively for constrained optimization with different views to come up with suitability of constrained SRPSO algorithm when coupled with particular CHT for solving specific type of problems.

An Improved particle swarm optimization based on lévy flight and simulated annealing for high dimensional optimization problem

Particle swarm optimization (PSO) is a simple metaheuristic method to implement with robust performance. PSO is regarded as one of the numerous researchers' most well-studied algorithms. However, two of its most fundamental problems remain unresolved. PSO converges onto the local optimum for high-dimensional optimization problems, and it has slow convergence speeds. This paper introduces a new variant of a particle swarm optimization algorithm utilizing Lévy flight-McCulloch, and fast simulated annealing (PSOLFS). The proposed algorithm uses two strategies to address high-dimensional problems: hybrid PSO to define the global search area and fast simulated annealing to refine the visited search region. In this paper, PSOLFS is designed based on a balance between exploration and exploitation. We evaluated the algorithm on 16 benchmark functions for 500 and 1,000 dimension experiments. On 500 dimensions, the algorithm obtains the optimal value on 14 out of 16 functions. On 1,000 dimensions, the algorithm obtains the optimal value on eight benchmark functions and is close to optimal on four others. We also compared PSOLFS with another five PSO variants regarding convergence accuracy and speed. The results demonstrated higher accuracy and faster convergence speed than other PSO variants. Moreover, the results of the Wilcoxon test show a significant difference between PSOLFS and the other PSO variants. Our experiments' findings show that the proposed method enhances the standard PSO by avoiding the local optimum and improving the convergence speed.

Stochastic Triad Topology Based Particle Swarm Optimization for Global Numerical Optimization

Particle swarm optimization (PSO) has exhibited well-known feasibility in problem optimization. However, its optimization performance still encounters challenges when confronted with complicated optimization problems with many local areas. In PSO, the interaction among particles and utilization of the communication information play crucial roles in improving the learning effectiveness and learning diversity of particles. To promote the communication effectiveness among particles, this paper proposes a stochastic triad topology to allow each particle to communicate with two random ones in the swarm via their personal best positions. Then, unlike existing studies that employ the personal best positions of the updated particle and the neighboring best position of the topology to direct its update, this paper adopts the best one and the mean position of the three personal best positions in the associated triad topology as the two guiding exemplars to direct the update of each particle. To further promote the interaction diversity among particles, an archive is maintained to store the obsolete personal best positions of particles and is then used to interact with particles in the triad topology. To enhance the chance of escaping from local regions, a random restart strategy is probabilistically triggered to introduce initialized solutions to the archive. To alleviate sensitivity to parameters, dynamic adjustment strategies are designed to dynamically adjust the associated parameter settings during the evolution. Integrating the above mechanism, a stochastic triad topology-based PSO (STTPSO) is developed to effectively search complex solution space. With the above techniques, the learning diversity and learning effectiveness of particles are largely promoted and thus the developed STTPSO is expected to explore and exploit the solution space appropriately to find high-quality solutions. Extensive experiments conducted on the commonly used CEC 2017 benchmark problem set with different dimension sizes substantiate that the proposed STTPSO achieves highly competitive or even much better performance than state-of-the-art and representative PSO variants.

Pyramid particle swarm optimization with novel strategies of competition and cooperation

Particle swarm optimization (PSO) has shown its advantages in various optimization problems. Topology and updating strategies are among its key concepts and have significant impacts on optimization ability. This paper proposes a pyramid PSO (PPSO) with novel competitive and cooperative strategies to update particles’ information. PPSO builds a pyramid and assigns each particle to a specific layer according to its fitness. The particles at the same layer will make a pairwise comparison to determine the winners and the losers. The losers will cooperate with their corresponding winners, while the winners will cooperate with the particles at the upper layer and those at the top layer. Each particle in PPSO has its own learning behavior, having more than one exemplar rather than the only global best to learn from. The diversity of the swarm is enhanced and it positively affects the performance of PSO. Extensive experiments demonstrate that the PPSO has superior performance in terms of accuracy, Wilcoxon signed-rank test and convergence speed, yet achieves comparable running time in most cases, when compared with the canonical PSO and eight state-of-the-art PSO variants. Furthermore, we analyze the influence of parameters for the PPSO. All these illustrate that the PPSO is promising for numerical optimization.

Coverage Optimization of Wireless Sensor Networks Using Combinations of PSO and Chaos Optimization

The coverage rate is the most crucial index in wireless sensor networks (WSNs) design; it involves making the sensors with a reasonable distribution, which closely relates to the quality of service (QoS) and survival period of the entire network. This article proposes to use particle swarm optimization (PSO) and chaos optimization in conjunction for the coverage optimization. All sensor locations are encoded together as a particle position. PSO was used first to make sensors move close to their optimal positions; furthermore, a variable domain chaos optimization algorithm (VDCOA) was employed to reach a higher coverage rate, along with improved evenness and average moving distance. Six versions of VDCOA, taking circle, logistic, Gaussian, Chebyshev, sinusoidal and cubic maps, respectively, were investigated. The simulation experiment tested three cases: square, rectangular and circular regions using nine algorithms: six versions of PSO plus VDCOA, PSO and other two PSO variants. All six versions showed better performance than PSO and CPSO, with coverage all exceeding 90% for the first two cases. Moreover, one version, PSO plus circle map (PSO-Circle), increased the coverage rate by 3.17%, 2.41% and 12.94% compared with PSO in three cases, respectively, and outperformed the other eight algorithms.

Subpopulation Particle Swarm Optimization with a Hybrid Mutation Strategy.

With the large-scale optimization problems in the real world becoming more and more complex, they also require different optimization algorithms to keep pace with the times. Particle swarm optimization algorithm is a good tool that has been proved to deal with various optimization problems. Conventional particle swarm optimization algorithms learn from two particles, namely, the best position of the current particle and the best position of all particles. This particle swarm optimization algorithm is simple to implement, simple, and easy to understand, but it has a fatal defect. It is hard to find the global optimal solution quickly and accurately. In order to deal with these defects of standard particle swarm optimization, this paper proposes a particle swarm optimization algorithm (SHMPSO) based on the hybrid strategy of seed swarm optimization (using codes available from https://gitee.com/mr-xie123234/code/tree/master/). In SHMPSO, a subpopulation coevolution particle swarm optimization algorithm is adopted. In SHMPSO, an elastic candidate-based strategy is used to find a candidate and realize information sharing and coevolution among populations. The mean dimension learning strategy can be used to make the population converge faster and improve the solution accuracy of SHMPSO. Twenty-one benchmark functions and six industries-recognized particle swarm optimization variants are used to verify the advantages of SHMPSO. The experimental results show that SHMPSO has good convergence speed and good robustness and can obtain high-precision solutions.

A Comparison on PSO Optimized PID Controller for Inter-Area Oscillation Control in an Interconnected Power System

This paper emphasizes on the development of control strategy for inter area oscillation suppression for a unified two-area hydro-thermal deregulated power system. A particle swarm optimization (PSO) optimized Proportional Integral Derivative (PID) controller is proposed for automatic generation control (AGC). Further comparison between different variants of PSO are carried out, where 6 different variants have been explored, which are success rate based PSO, evolution speed and aggregation degree factors based PSO, global-local best inertia weight based PSO, distance from global best based PSO, fixed inertia weight based PSO and varying acceleration coefficients based PSO. A comprehensive analysis of these optimization techniques are presented on the basis of major dynamic performance parameters, i.e. settling time and peak overshoot. Successive rate based PSO variant found best among these six variants.

Boolean Particle Swarm Optimization with various Evolutionary Population Dynamics approaches for feature selection problems

In the feature selection process, reaching the best subset of features is considered a difficult task. To deal with the complexity associated with this problem, a sophisticated and robust optimization approach is needed. This paper proposes an efficient feature selection approach based on a Boolean variant of Particle Swarm Optimization (BPSO) boosted with Evolutionary Population Dynamics (EPD). The proposed improvement assists the BPSO to avoid local optima obstacles via boosting its exploration ability. In the BPSO-EPD, the worst half of the solutions are discarded by repositioning them around the optimal solutions selected from the best half. Six natural selection mechanisms comprising Best-based, Tournament, Roulette wheel, Stochastic universal sampling, Linear rank, and Random-based are employed to select guiding solutions. To assess the performance of the proposed improvement, 22 well-regarded datasets collected from the UCI repository are employed. The experimental results demonstrate the superiority of the proposed EPD-based feature selection approaches, especially the BPSO-TEPD variant when compared with conventional BPSO and other five EPD-based variants. Taking SpecEW dataset as an example, an increment of 6.7% accuracy can be achieved for BSPO-TEPD. Consequently, BPSO-TEPD approach also outperformed other well-known optimizers, including two binary variants of PSO using S-shaped transfer function (SBPSO) and V-shaped transfer function (VBPSO), Binary Grasshopper Optimization Algorithm (BGOA), Binary Gravitational Search Algorithm (BGSA), Binary Ant Lion Optimizer (BALO), Binary Bat algorithm (BBA), Binary Salp Swarm Algorithm (BSSA), Binary Whale Optimization Algorithm (BWOA), and Binary Teaching-Learning Based Optimization (BTLBO). The result emphasizes the excellent behavior of EPD strategies in evolving the ability of BPSO when dealing with feature selection problems.

Distribution network energy loss reduction under EV charging schedule

This article deals with the problem of energy losses in distribution networks (DNs) under electric vehicle (EV) penetration. The problem of charging overlaps causing severe power losses and voltage drops is faced under appropriate EV charging. An optimized EV charging schedule is proposed under EV time-of-arrival consideration. The solution algorithm is based on a particle swarm optimization (PSO) variant, and both grid-to-vehicle (G2V) and vehicle-to-grid (V2G) schemes are included regarding the power interactions of the EVs with the grid. The goal is to optimally allocate the charging and/or discharging time periods of the EVs in order to minimize energy losses while delivering fully charges EVs to the owners. New departures after the first EVs' arrival are also handled. The results indicate that with the proposed scheduling, daily energy loss reduction could be reached up to 25% under an improved voltage profile that indicates more uniform loading for the DN.

Random walk autonomous groups of particles for particle swarm optimization

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.

Intelligent fault diagnosis for power distribution system-comparative studies

Short circuit is one of the most popular types of permanent fault in power distribution system. Thus, fast and accuracy diagnosis of short circuit failure is very important so that the power system works more effectively. In this paper, a newly enhanced support vector machine (SVM) classifier has been investigated to identify ten short-circuit fault types, including single line-to-ground faults (XG, YG, ZG), line-to-line faults (XY, XZ, YZ), double line-to-ground faults (XYG, XZG, YZG) and three-line faults (XYZ). The performance of this enhanced SVM model has been improved by using three different versions of particle swarm optimization (PSO), namely: classical PSO (C-PSO), time varying acceleration coefficients PSO (T-PSO) and constriction factor PSO (K-PSO). Further, utilizing pseudo-random binary sequence (PRBS)-based time domain reflectometry (TDR) method allows to obtain a reliable dataset for SVM classifier. The experimental results performed on a two-branch distribution line show the most optimal variant of PSO for short fault diagnosis.

An evolving ensemble model of multi-stream convolutional neural networks for human action recognition in still images

Still image human action recognition (HAR) is a challenging problem owing to limited sources of information and large intra-class and small inter-class variations which requires highly discriminative features. Transfer learning offers the necessary capabilities in producing such features by preserving prior knowledge while learning new representations. However, optimally identifying dynamic numbers of re-trainable layers in the transfer learning process poses a challenge. In this study, we aim to automate the process of optimal configuration identification. Specifically, we propose a novel particle swarm optimisation (PSO) variant, denoted as EnvPSO, for optimal hyper-parameter selection in the transfer learning process with respect to HAR tasks with still images. It incorporates Gaussian fitness surface prediction and exponential search coefficients to overcome stagnation. It optimises the learning rate, batch size, and number of re-trained layers of a pre-trained convolutional neural network (CNN). To overcome bias of single optimised networks, an ensemble model with three optimised CNN streams is introduced. The first and second streams employ raw images and segmentation masks yielded by mask R-CNN as inputs, while the third stream fuses a pair of networks with raw image and saliency maps as inputs, respectively. The final prediction results are obtained by computing the average of class predictions from all three streams. By leveraging differences between learned representations within optimised streams, our ensemble model outperforms counterparts devised by PSO and other state-of-the-art methods for HAR. In addition, evaluated using diverse artificial landscape functions, EnvPSO performs better than other search methods with statistically significant difference in performance.

A Bio-Inspired Multi-Population-Based Adaptive Backtracking Search Algorithm.

Backtracking search algorithm (BSA) is a nature-based optimization technique extensively used to solve various real-world global optimization problems for the past few years. The present work aims to introduce an improved BSA (ImBSA) based on a multi-population approach and modified control parameter settings to apprehend an ensemble of various mutation strategies. In the proposed ImBSA, a new mutation strategy is suggested to enhance the algorithm’s performance. Also, for all mutation strategies, the control parameters are updated adaptively during the algorithm’s execution. Extensive experiments have been performed on CEC2014 and CEC2017 single-objective benchmark functions, and the results are compared with several state-of-the-art algorithms, improved BSA variants, efficient differential evolution (DE) variants, particle swarm optimization (PSO) variants, and some other hybrid variants. The nonparametric Friedman rank test has been conducted to examine the efficiency of the proposed algorithm statistically. Moreover, six real-world engineering design problems have been solved to examine the problem-solving ability of ImBSA. The experimental results, statistical analysis, convergence graphs, complexity analysis, and the results of real-world applications confirm the superior performance of the suggested ImBSA.

A Novel UAV Path Planning Algorithm Based on Double-Dynamic Biogeography-Based Learning Particle Swarm Optimization

Particle swarm optimization (PSO), one of the classical path planning algorithms, has been considered for unmanned aerial vehicle (UAV) path planning more frequently in recent years. A large amount of studies on UAV path planning based on modified PSO have been reported. However, most UAV path planning algorithms still optimize only one kind terrain problem which is mountain terrain. At the same time, many modified PSO algorithms also have some problems, such as insufficient convergence and unsatisfactory efficiency. In this paper, six kinds of terrain functions of UAV path planning are proposed to simulate real-world application. The terrain functions contain city, village without houses, village with houses, mountainous area without houses, mountainous area with houses, and mountainous area with a huge building. Inspired by CLPSO and BLPSO, we proposed a new double-dynamic biogeography-based learning particle swarm optimization (DDBLPSO) algorithm to solve these problems. The double-dynamic biogeography-based learning strategy replacing the traditional learning mechanism from the personal and global best particles is used to select the learning particles. In this strategy, each particle will learn from the better one of two selected particles which are not worse than itself. However, one random component of particle will replaced by corresponding component of other particle if all components of the particle only learn from itself. In this way, particles sufficiently learn from better objects and maintain the ability of jumping out of local optimality. The superiority of our algorithm is verified with four relevant algorithms, a PSO variant, and a BBO variant on the benchmark suite of CEC2015. Real-world application demonstrates that the algorithm we proposed outperforms four relevant algorithms, a PSO variant, and a BBO variant both in small-scale problems and large-scale problems. This paper shows a good application of our novel algorithm.

New Particle Swarm Optimization Variant with Modified Neighborhood Structure

New Particle Swarm Optimization Variant with Modified Neighborhood Structure