Popular Particle Swarm Optimization Research Articles

Piecewise combinatorial particle swarm optimization

The particle swarm optimization (PSO) is easy to fall into local optima in the search process, and usually the optimum stops updating at the later stage of the iteration, especially for complex problems. In this paper, a novel piecewise combinatorial particle swarm optimization is proposed, where a new piecewise combinatorial strategy and a new exploitation space search strategy are designed. The piecewise combinatorial strategy increases population diversity through copying, crossover, and mutation operations. The exploitation space search strategy improves particles search speed by setting the exploitation particle. This algorithm is tested and compared with 11 popular PSO variants on 30 benchmark functions. The results show that the performance of this algorithm is better than many existing PSO variants, especially for complex optimization problems. In addition, the piecewise combinatorial strategy provides a new idea for integrating excellent algorithms with different focuses. In the end, the algorithm is applied to a traveling salesman problem, and it is found that the algorithm exhibits excellent performance.

Consensus based optimization with memory effects: Random selection and applications

In this work we extend the class of Consensus-Based Optimization (CBO) metaheuristic methods by considering memory effects and a random selection strategy. The proposed algorithm iteratively updates a population of particles according to a consensus dynamics inspired by social interactions among individuals. The consensus point is computed taking into account the past positions of all particles. While sharing features with the popular Particle Swarm Optimization (PSO) method, the exploratory behavior is fundamentally different and allows better control over the convergence of the particle system. We discuss some implementation aspects which lead to increased efficiency while preserving the success rate in the optimization process. In particular, we show how employing a random selection strategy to discard particles during the computation improves the overall performance. Several benchmark problems and applications to image segmentation and Neural Networks training are used to validate and test the proposed method. A theoretical analysis allows to recover convergence guarantees under mild assumptions on the objective function. This is done by first approximating the evolution of the particles with a continuous-in-time dynamics, and then by taking the mean-field limit of such dynamics. Convergence to a global minimizer is finally proved at the mean-field level.

Reinforcement learning-based particle swarm optimization with neighborhood differential mutation strategy

The particle swarm optimization (PSO) algorithm has been one of the most effective methods for solving various engineering optimization problems. Most existing PSO variants frequently use fixed operators, the adoption of a fixed operator learning mode may restrict the intelligence level of each particle, thus reducing the performance of PSO in solving optimization issues with complicated fitness landscapes. To address single goal real-parameter numerical optimization while overcoming the above shortcoming, this paper proposes a reinforcement learning-based particle swarm optimization with neighborhood differential mutation strategy (NRLPSO). In NRLPSO, a dynamic oscillation inertial weight (DOW) strategy that provides particles with dynamic adjustment ability in different situations is designed. To resolve the operator selection conundrum of exploration and exploitation, a reinforcement learning-based velocity vector generation (VRL) strategy is developed. At each iteration, particles select the velocity update model based on reinforcement learning, and VRL helps to thoroughly search the problem space. A velocity updating mechanism based on cosine similarity (VCS) is applied to control the velocity learning mode to determine more promising solutions. Furthermore, to alleviate the problem of premature convergence, a local update strategy with neighborhood differential mutation (NDM) is employed to increase the diversity of the algorithm. To verify the efficiency of the proposed algorithm, the CEC2017 and CEC2022 test suites are implemented, and nine classic or state-of-the-art PSO variants are comprehensively tested. The experimental results show that NRLPSO outperforms the popular PSO variants in terms of convergence speed and accuracy. Since NRLPSO utilizes the DE mutations, it is compared with the representative LSHADE variant algorithm - LSHADE_SPACMA. Although LSHADE_SPACMA is better than NRLPSO concerning algorithm stability and convergence accuracy, we will refine our work in the future to enhance the performance in all aspects.

A novel sequential switching quadratic particle swarm optimization scheme with applications to fast tuning of PID controllers

In this work, a sequential switching quadratic particle swarm optimization (SSQPSO) scheme is investigated, where the velocity update mechanism is improved to enhance the convergence performance. Considering the sequential characteristics (related to evolution factors) of the evolution process, a Markov chain with special probability transition matrix is employed to characterize the switching of evolution state. With the help of the mean distance, the concept of population density is first put forward in the dynamic search region enclosed by all particles. Then, taking into account the change of the population density in different generations, two quadratic acceleration terms are introduced into the velocity update model based on the Hadamard product, where four evolution-state-dependent acceleration coefficients are also adopted. The positivity or negativity of the quadratic acceleration terms is retained by resorting to the matrix sign functions. Several widely utilized benchmark functions (including two unimodal and multimodal functions) are employed to evaluate the search capability of the studied SSQPSO scheme. The experimental consequences illustrate that the performance of the developed SSQPSO scheme is superior to that of some popular particle swarm optimization (PSO) schemes. To further demonstrate the effectiveness in practical engineering, the addressed SSQPSO scheme is successfully applied to achieve the fast parameter tuning of the proportional-integral-derivative controller in a spring-mass-damper system.

A Fast-Converging Particle Swarm Optimization through Targeted, Position-Mutated, Elitism (PSO-TPME)

We improve convergence speed by two orders of magnitude and the global exploration capabilities of particle swarm optimization (PSO) through targeted position-mutated elitism (TPME). The proposed fast-converging TPME operator requires a fitness-based classification technique to categorize the particles. The introduced classification is motivated by its simplicity, low memory requirements, and automated termination criteria based on convergence. The three key innovations address particle classification, elitism, and mutation in the cognitive and social model. PSO-TPME is benchmarked against five popular PSO variants for multi-dimensional functions, which are extensively adopted in the optimization field, In particular, the convergence accuracy, convergence speed, and the capability to find global minima are investigated. The statistical error is assessed by numerous repetitions. The simulations confirmed that in ten of the thirteen investigated functions, the proposed PSO variant outperforms other variants in terms of convergence rate and accuracy by at least two orders of magnitude. On the other hand, the simulations demonstrated the early exploration capabilities of PSO-TPME in all tested functions. In the first ten iterations, PSO-TPME outperformed all the investigated PSO variants by at least two orders of magnitude.

Research on the MPPT of Photovoltaic Power Generation Based on the CSA-INC Algorithm

The existing Maximum Power Point Tracking (MPPT) method has low tracking efficiency and poor stability. It is easy to fall into the Local Maximum Power Point (LMPP) in Partial Shading Condition (PSC), resulting in the degradation of output power quality and efficiency. It was found that various bio-inspired MPPT based optimization algorithms employ different mechanisms, and their performance in tracking the Global Maximum Power Point (GMPP) varies. Thus, a Cuckoo search algorithm (CSA) combined with the Incremental conductance Algorithm (INC) is proposed (CSA-INC) is put forward for the MPPT method of photovoltaic power generation. The method can improve the tracking speed by more than 52% compared with the traditional Cuckoo Search Algorithm (CSA), and the results of the study using this algorithm are compared with the popular Particle Swarm Optimization (PSO) and the Gravitational Search Algorithm (GSA). CSA-INC has an average tracking efficiency of 99.99% and an average tracking time of 0.19 s when tracking the GMPP, which improves PV power generation’s efficiency and power quality.

Automatic Data Clustering by Hybrid Enhanced Firefly and Particle Swarm Optimization Algorithms

Data clustering is a process of arranging similar data in different groups based on certain characteristics and properties, and each group is considered as a cluster. In the last decades, several nature-inspired optimization algorithms proved to be efficient for several computing problems. Firefly algorithm is one of the nature-inspired metaheuristic optimization algorithms regarded as an optimization tool for many optimization issues in many different areas such as clustering. To overcome the issues of velocity, the firefly algorithm can be integrated with the popular particle swarm optimization algorithm. In this paper, two modified firefly algorithms, namely the crazy firefly algorithm and variable step size firefly algorithm, are hybridized individually with a standard particle swarm optimization algorithm and applied in the domain of clustering. The results obtained by the two planned hybrid algorithms have been compared with the existing hybridized firefly particle swarm optimization algorithm utilizing ten UCI Machine Learning Repository datasets and eight Shape sets for performance evaluation. In addition to this, two clustering validity measures, Compact-separated and David–Bouldin, have been used for analyzing the efficiency of these algorithms. The experimental results show that the two proposed hybrid algorithms outperform the existing hybrid firefly particle swarm optimization algorithm.

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.

A Hybrid Particle Swarm Optimizer for Curriculum Sequencing Problem

Curriculum sequencing problem is crucial to e‐learning system, which is a NP‐hard optimization problem and commonly solved by swarm intelligence. As a form of swarm intelligence, particle swarm optimization (PSO) is widely used in various kinds of optimization problems. However, PSO is found ineffective in complex optimization problems. The main reason is that PSO is ineffective in diversity preservation, leading to high risks to be trapped by the local optima. To solve this problem, a novel hybrid PSO algorithm is proposed in this study. First, a competitive‐genetic crossover strategy is proposed for PSO to balance the convergence and diversity. Second, an adaptive polynomial mutation is introduced in PSO to further improve its diversity preservation ability. Furthermore, a curriculum scheduling model is proposed, where several constraints are taken into considerations to ensure the practicability of the curriculum sequencing. The numerical comparison experiments show that the proposed algorithm is effective in solving function optimization in comparison to several popular PSO variants; furthermore, for the optimization of the designed curriculum sequencing problem, the proposed algorithm shows significant advantages over the compared algorithms with respect to the degree of the satisfaction of the objectives, i.e., 20, 14, and 5 percentages higher, respectively.

Optimal allocation of product reliability using novel multi-population particle swarm optimization algorithm

Reliability optimal allocation is a critical method in engineering and operation fields to improve and ensure product quality. However, conventional model generally uses the single objective with research and development (R & D) cost or product reliability. Moreover, the popular particle swarm optimization (PSO) algorithm solving the model has insufficient global search ability. In this paper, a novel reliability optimal allocation method is developed based on double-objective model and multi-population PSO (MPPSO) algorithm. The cost function is established considering all the cost related to reliability using analytical hierarchical process (AHP) and ordered weighted averaging (OWA) operator. Multi-population particle swarm optimization algorithm is developed based on information exchange mechanism among subpopulations. In the algorithm, the inertia weight is optimized by chaotic map, and different mutation operations are carried out on the subpopulations. An illustrative example, which implements to computer numerical control (CNC) grinding machine, is presented to illustrate the practicality and application of the proposed method. Finally, the comparison and analysis are implemented to show the advantage of proposed model and MPPSO algorithm.

An N-State Markovian Jumping Particle Swarm Optimization Algorithm

Optimization is an important research field, especially in engineering, physical sciences, and economics. The main purpose of optimization is to maximize the profit and minimize the cost of production as well as the loss of the system. Evolutionary computation algorithms, such as the genetic algorithm and the particle swarm optimization (PSO) algorithm have been successfully employed in solving various optimization problems. Owing to its application potential and promising performance in discovering the optimal solution, the PSO algorithm has been recognized as a powerful optimization technique and attracted an ever-increasing interest in the evolutionary computation community. In this article, a novel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> -state Markovian jumping PSO (NS-MJPSO) algorithm is presented where the velocity updating equation is adjusted based on the state evolution governed by a Markov chain. The performance of the proposed NS-MJPSO algorithm is evaluated via some widely used mathematical benchmark functions. The experimental results demonstrate that the developed NS-MJPSO algorithm outperforms some currently popular PSO algorithms on the widely used benchmark functions.

From particle swarm optimization to consensus based optimization: Stochastic modeling and mean-field limit

In this paper, we consider a continuous description based on stochastic differential equations of the popular particle swarm optimization (PSO) process for solving global optimization problems and derive in the large particle limit the corresponding mean-field approximation based on Vlasov–Fokker–Planck-type equations. The disadvantage of memory effects induced by the need to store the local best position is overcome by the introduction of an additional differential equation describing the evolution of the local best. A regularization process for the global best permits to formally derive the respective mean-field description. Subsequently, in the small inertia limit, we compute the related macroscopic hydrodynamic equations that clarify the link with the recently introduced consensus based optimization (CBO) methods. Several numerical examples illustrate the mean field process, the small inertia limit and the potential of this general class of global optimization methods.

An effective meta-heuristic based multi-objective hybrid optimization method for workflow scheduling in cloud computing environment

Cloud computing is an emerging distributed computing model that offers computational capability over internet. Cloud provides a huge level collection of powerful and scalable computational resources for computation and data-intensive large scale workflow deployment. For business as well as scientific applications, optimal scheduling of workflow is emerged as a major concern. Optimization of scheduling process leads to the reduction of execution time, cost, etc. So, this paper presents an enhanced recent ant-lion optimization (ALO) algorithm hybridized with popular particle swarm optimization (PSO) algorithm to optimize a workflow scheduling specifically for cloud. A security approach called Data Encryption Standard (DES) is used for encoding the cloud information while scheduling is carried out. The research aims to contribute an enhanced workflow scheduling more safely than the existing frameworks. Enhancement procedures are evaluated in terms of cost, load, and makespan. The simulation procedures are done by utilizing the CloudSim tool. The proposed hybrid optimization results contrasted with well-known existing approaches. The existing round-robin (RR), ALO and PSO methods are selected to compare and identify the potency of the proposed system. The outcomes indicated that the proposed technique minimizes the cost by 9.8% of GA-PSO, 10% of PSO, 20% of ALO, 30% of RR and 12% of GA. Load balancing and makespan of the proposed method reduces by 8% than GA-PSO, 10% than ALO, 20% than PSO, 35% than RR and 45% than GA. The energy consumption and reliability performance are also reasonably well.

A Novel Sigmoid-Function-Based Adaptive Weighted Particle Swarm Optimizer.

In this paper, a novel particle swarm optimization (PSO) algorithm is put forward where a sigmoid-function-based weighting strategy is developed to adaptively adjust the acceleration coefficients. The newly proposed adaptive weighting strategy takes into account both the distances from the particle to the global best position and from the particle to its personal best position, thereby having the distinguishing feature of enhancing the convergence rate. Inspired by the activation function of neural networks, the new strategy is employed to update the acceleration coefficients by using the sigmoid function. The search capability of the developed adaptive weighting PSO (AWPSO) algorithm is comprehensively evaluated via eight well-known benchmark functions including both the unimodal and multimodal cases. The experimental results demonstrate that the designed AWPSO algorithm substantially improves the convergence rate of the particle swarm optimizer and also outperforms some currently popular PSO algorithms.

An improved particle swarm optimization algorithm and its application in solving forward kinematics of a 3-DoF parallel manipulator

This paper proposes an improved particle swarm optimization to study the forward kinematic of a solar tracking device which has two rotational and one translational degree of freedom. The forward kinematics of the parallel manipulator is transformed into an optimization problem by solving the inverse kinematics equations. The proposed method combines inertial weight with the iterations number and the distance between current swarm particles and the optimum to improve convergence ability and speed. The novel cognitive and social parameters are adjusted by the inertia weight to enhance unity and intelligence of the algorithm. A stochastic mutation is used to diversify swarm for faster convergence via local optima evasion in high dimensional complex optimization problems. The performance of the proposed method is demonstrated by applying it to four benchmark functions and comparing convergence with three popular particle swarm optimization methods to verify the feasibility of the improved method. The behaviors of the proposed method using variable cognitive and social parameters and fixed value are also tested to verify fast convergence speed of variable parameters method. And further, an application example uses the method to determine the forward kinematics of a three-degree-of-freedom parallel manipulator. Finally, the mechanism simulations model of the parallel manipulator are carefully built and analyzed to verify the correctness of the proposed algorithm in PTC Creo Parametric software. In all cases tested, the proposed algorithm achieved much faster convergence and either improved or proximal fitness values.

Design and implementation of sharp edge FIR filters using hybrid differential evolution particle swarm optimization

The filter is an important building block of modern communication and electronic systems. Based on well-defined bandwidth, it extracts the desired portion of the spectrum when the raw input signal is applied. Efficacy of filtering depends on the preciseness of bandwidth to avoid co-channel interference and signal loss. In addition, it must provide higher stopband attenuation and passband attenuation very close to unity with a tolerable quantity of pass/stop band ripple. Design/implementation of sharp edge modern FIR filter is structured as a multi-objective, constrained, complex, and highly nonlinear (hence multimodal) error minimization challenge. Hence, this work proposes a novel objective (normalized error fitness) function and a robust hybrid algorithm for the effective searching of the optimal filter coefficients for providing excellent sharp edge frequency response during the filtering action. Most popular particle swarm optimization (PSO) and differential evolution (DE) algorithm are effectively combined together to frame the proposed hybrid DE-PSO algorithm for enhancing the exploration and exploitation abilities of it. The proposed hybrid algorithm is validated using twelve different benchmark functions. Through simulations, the qualitative performance of the proposed approach is compared with the conventional PSO, DE, real-coded genetic algorithm and the Parks–McClellan method.

Joint power allocation and user association in non-orthogonal multiple access networks: An evolutionary approach

In this paper, the problem of joint power allocation and user association is studied for non-orthogonal multiple access (NOMA) downlink networks with multiple base stations (BSs). We consider that users are grouped into orthogonal clusters to allocate into different physical resource blocks (PRBs). The problem is formulated using two different utility functions. The first is the maximization of the weighted sum rate and the other is the maximization of the minimum achievable user rate. We apply two different evolutionary algorithms in order to solve this problem. Namely, the recently introduced Salp Swarm Algorithm (SSA) and the popular Particle Swarm Optimization (PSO). The simulation results show that the above-described problem can be effectively solved by both algorithms. SSA is more efficient in average than PSO. The effect of increasing the number of user is also studied. In this case the problem becomes more difficult to solve, which indicates that more network resources are required.

An expanded particle swarm optimization based on multi-exemplar and forgetting ability

There are two phenomena in human society and biological systems. One is that people prefer to extract knowledge from multiple exemplars to obtain better learning ability. The other one is the forgetting ability that helps the encoding and consolidation of new information by removing unused or unwanted memories. Inspired by these phenomena, this paper transplants the multi-exemplar and forgetting ability to particle swarm optimization (PSO), and proposes an eXpanded PSO, called XPSO. Firstly, XPSO expands the “social-learning” part of each particle from one exemplar to two exemplars, learning from both the locally and the globally best exemplars. Secondly, XPSO assigns different forgetting abilities to different particles, simulating the forgetting phenomenon in the human society. Under the multi-exemplar learning model with forgetting ability, XPSO further adopts an adaptive scheme to update the acceleration coefficients and selects a reselection mechanism to update the population topology. The effectiveness of these additional proposed strategies is verified by extensive experiments. Moreover, comparison results among XPSO and other 9 popular PSO as well as 3 non-PSO algorithms on CEC’13 test suite suggest that XPSO attains a very promising performance for solving different types of functions, contributing to both higher solution accuracy and faster convergence speed.

A Novel Particle Swarm Optimization Approach for Patient Clustering From Emergency Departments

In this paper, a novel particle swarm optimization (PSO) algorithm is proposed in order to improve the accuracy of traditional clustering approaches with applications in analyzing real-time patient attendance data from an accident & emergency (A&E) department in a local U.K. hospital. In the proposed randomly occurring distributedly delayed PSO (RODDPSO) algorithm, the evolutionary state is determined by evaluating the evolutionary factor in each iteration, based on whether the velocity updating model switches from one mode to another. With the purpose of reducing the possibility of getting trapped in the local optima and also expanding the search space, randomly occurring time-delays that reflect the history of previous personal best and global best particles are introduced in the velocity updating model in a distributed manner. Eight well-known benchmark functions are employed to evaluate the proposed RODDPSO algorithm which is shown via extensive comparisons to outperform some currently popular PSO algorithms. To further illustrate the application potential, the RODDPSO algorithm is successfully exploited in the patient clustering problem for data analysis with respect to a local A&E department in West London. Experiment results demonstrate that the RODDPSO-based clustering method is superior over two other well-known clustering algorithms.

A novel optimized SVM algorithm based on PSO with saturation and mixed time-delays for classification of oil pipeline leak detection

ABSTRACTIn this paper, a novel particle swarm optimization (PSO) algorithm is proposed in order to improve the accuracy of the traditional support vector machine (SVM) approaches with applications in analyzing data of oil pipeline leak detection. In the proposed saturated and mix-delayed particle swarm optimization (SMDPSO) algorithm, the evolutionary state is determined by evaluating the evolutionary factor in each iteration, based on which the velocity updating model switches from one to another. With the purpose of reducing the possibility of getting trapped in the local optima and also expanding the search space, time-varying time-delays and distributed time-delays are introduced in the velocity updating model to respectively reflect the history of previous personal and global optimum particles. The introduction of saturation constraint ensures that the particles will convergence in case that the velocity of the particles is too large. Eight well-known benchmark functions are employed to evaluate the proposed SMDPSO algorithm which is shown via extensive comparisons to outperform some currently popular PSO algorithms. To further illustrate the application potential, the developed framework SMDPSO-based SVM algorithm is exploited in the problem of oil pipeline leak detection. Experiment results demonstrate that the SMDPSO-based SVM method is superior over other well-known classification algorithms.