Particle Swarm Research Articles

Optimal design and numerical studies of negative stiffness device–TMD controlled systems using PSO algorithm

In recent years, research on negative stiffness devices (NSDs) for vibration control has increased. This study examines the combination of NSDs with tuned mass dampers (TMDs) and explores the NSD-TMD as a nonlinear energy sink (NES). The particle swarm optimization (PSO) algorithm was employed to determine the optimal parameters for the TMD, NSD-TMD, and NES systems. The optimization procedure proves that the PSO algorithm is suitable for solving the optimization problem of the complex systems with strong nonlinearity. The overall procedure is effective and demonstrates strong convergence. The force transmissibility curves of the optimized systems were compared, revealing that the NSD-TMD achieved the best vibration performance, while the NES system demonstrated the target energy transfer (TET) property. Another interesting characteristic of the NSD-TMD system is that it does not necessarily require a large additional mass or damping factor to achieve optimal performance. An actual vertical vibration control scenario for a pedestrian bridge was analyzed using various control strategies. Human-induced force excitations were simulated using a code-defined method. The acceleration responses of an uncontrolled pedestrian bridge and the three optimized control systems were compared in both time and frequency domains. Results further verified the force transmissibility curves. The NSD-TMD system outperformed the other two systems, particularly in reducing the first-order response. Conversely, the NES system proved less effective for controlling human-induced vibration with harmonic force excitations.

Analysis and Prediction of Nonlinear Hysteretic Behaviors of Graphite Magnetorheological Grease at Different Temperatures.

Magnetorheological grease (MRG) is considered a promising alternative to magnetorheological fluids as a smart material because of its higher stability and less leakage. To enhance yield stresses in various applications, graphite is incorporated as an additive, resulting in graphite magnetorheological grease (GMRG). However, the nonlinear hysteresis properties of this new material and its prediction methods have not been investigated. Therefore, in this work, the nonlinear hysteretic properties of GMRG at different temperatures, magnetic fields, and frequencies are systematically investigated and compared with those of MRG. The results of rheological experiments show that graphite enhances the shear stress of GMRG in the hysteresis curve through its reinforcing effect on the magnetic chains. The strain hardening, elasticity, and viscosity of GMRG are enhanced, but an increase in temperature decreases this efficacy. A prediction model based on the particle swarm optimization neural network algorithm (PSO-BP) is also proposed to efficiently and accurately control the nonlinear behavior of GMRG in engineering. The hysteresis curves of GMRG under different external excitations are characterized and predicted by the particle swarm optimization neural network approach. The statistical results show that the PSO-BP-based hysteresis characteristic estimates have satisfactory accuracy. In the test data, the PSO-BP model demonstrates improvements in RMSE, MAE, and SMAPE by 19.5%, 20.6%, and 21.0%, respectively, compared to the conventional BP network, which maintains an R2 value exceeding 0.95. This method provides an efficient solution for researchers to carry out reliable performance prediction in work such as genetic engineering of materials and related engineering applications.

Multi-objective optimization of solar air heater having centerline perforated sine wave baffles using experimental and machine learning based approaches

ABSTRACT The efficiency of smooth surface solar air heaters (SAHs) is often limited by viscous boundary layer formation and aerodynamic constraints, resulting in suboptimal thermal performance. This study introduces a novel enhancement technique using centerline perforated sine wave baffles as turbulators on the SAH surface to improve heat transfer and reduce flow resistance. The current work deals with experimental analysis of solar air heater performance using centerline perforated sine wave baffles placed as turbulators over the surface of solar air heater. Experimental analyses are conducted by varying Reynolds number, relative baffle pitch, relative baffle height, angle of attack, and relative perforation diameter, ranging from 3000 to 18,000, 8 to 14, 0.4 to 0.55, 10° to 45°, and 0.1 to 0.2 respectively. Collected experimental data are utilized to develop predictive machine learning models for Nusselt number, friction factor, and thermo-hydraulic analysis. Several models including Linear Regression, Random Forest, K-Nearest Neighbors, Adaptive Boosting, and Extreme Gradient Boosting are employed, with their performance evaluated using Mean Absolute Error, Mean Squared Error, Root Mean Squared Error, and R2. Extreme Gradient Boosting emerges as the most effective predictive model with an R2 value of 98.2%, alongside Mean Absolute Error and Root Mean Squared Error values of 8.025 and 11.3 respectively. Multi-objective optimization techniques such as Particle Swarm Optimization, Simulated Annealing, Genetic Algorithm, and Hybrid Genetic Algorithm are employed for this purpose. The optimized parameters obtained from Genetic Algorithm include Reynolds number, and values of 17,447, 8.37, 0.48, 25.045, and 0.11 respectively, aiming at maximizing and while minimizing. The results of genetic algorithms are being taken as optimal parameters which resulted in Reynolds number, relative baffle pitch, relative baffle height, angle of attack, and relative perforation diameter as 17,447, 8.37, 0.48, 25.045 and 0.11.

Compressive strength of bentonite concrete using state-of-the-art optimised XGBoost models

ABSTRACT This study proposes an advanced soft-computing approach for predicting the compressive strength (CS) of bentonite concrete using an optimised XGBoost model. Bentonite is valued as a partial cement replacement for its environmental benefits and improved concrete properties, but predicting CS remains challenging due to complex constituent interactions. The study’s motivation is the increasing interest in sustainable materials like bentonite as a partial cement replacement, which presents unique challenges due to its high plasticity and swelling properties. While hybrid XGBoost models are effective in civil engineering, their application for CS prediction in concrete is limited. This research simulates hybrid XGBoost models using particle swarm optimisation (PSO), genetic algorithm (GA), and dragonfly optimisation (DO), supported by a comprehensive dataset with varied mix proportions and multicollinearity analysis. Hyperparameter tuning and feature selection techniques were applied to optimise the model’s performance. The results demonstrate that the PSO-XGBoost is the best performing model (R2 = 0.974, RMSE = 0.038), followed by DO-XGBoost and GA-XGBoost. All the hybrid XGBoost models perform better than conventional XGBoost model. The developed robust soft-computing based prediction methodology can serve as a reliable alternative tool for predicting the CS of bentonite concrete, thereby facilitating the design and development of sustainable concrete mixtures with enhanced performance characteristics.

A Case Study on the Application of Evolutionary Algorithms for Solving Non-linear Programming Problems in Water Resource Management

Evolutionary algorithms have been proposed and used in this case study for the solution to non-linear programming problems related to water resources. Heuristic, a type of optimization algorithm characterized by population-based search as well as using the genetic algorithms, are used to model and determine the optimal distribution and utilization of aquatic resources based on environmental and demand factors. These materials include examples based on water distribution networks, managing a reservoir, and forecasting demands of customers, demonstrating the effectiveness of the aforementioned algorithms in solving non-linear constraint problems and in dealing with multiple objectives. The comparative analysis is based on a number of simulation experiments to examine the efficiency of such microevolutionary algorithms as Genetic Algorithm, Particle Swarm Optimization, and Differential Evolution in contrast to the traditional optimization algorithms. These results show that there is significant value in using evolutionary algorithms as a basis for managing and modelling water resources as it offers a pragmatic approach and has the potential to meet the demands of the water industry in terms of sustainability, cost and resource requirements. There seems to be considerable scope for extension of these algorithms to a wide range of natural resources management and administration.

Optimal sizing and placement of STATCOM, TCSC and UPFC using a novel hybrid genetic algorithm-improved particle swarm optimization

The increase in global power demand has caused most of today's power networks to become overloaded especially in Sub-Saharan Africa. The increased load demand can be met through expansion of existing generation and transmission system. However, construction of new power infrastructure is limited by financing and technical constraints. Thus, power networks have been left to operate at overload conditions with high power losses and many power quality (PQ) problems. Flexible AC Transmission System (FACTS) devices can improve the power transfer capability of the existing transmission networks without the need of constructing new power infrastructure. In this paper, a multi-objective function comprising of minimization of power loss (PL), voltage deviation (VD) and operational cost (OC) was formulated and solved using a novel algorithm. A novel Genetic Algorithm-Improved Particle Swarm Optimization (GA-IPSO) technique is proposed in this paper for optimization of size and location of FACTS devices. Static Synchronous Compensator (STATCOM), Thyristor Controlled Series Capacitor (TCSC) and Unified Power Flow Controller (UPFC) are the three FACTS devices considered. The proposed technique was validated using IEEE-33 Bus Test System, which is a popular benchmark Radial Distribution System (RDS). The three FACTS devices were optimized separately and also in a combined manner. Under the separate optimization, the size and location of individual FACTS devices were optimized. For combined optimization, the sizes and locations of more than one device were optimized in the same test system. For separate optimization, UPFC produced the best results by reducing the active power losses by 38.44 % and OC from $1.59×105 to $ 1.15×105. Under the combined optimization, combination of TCSC, STATCOM and UPFC gave better results by achieving active power loss reduction of 56.09 % and reducing OC from $1.59×105 to $ 1.03×105. Comparison of GA-IPSO technique with other algorithms such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Improved Grey Wolf Optimization (IGWO) and Differential Evolution Algorithm (DEA) showed that the proposed hybrid technique was superior and more efficient in solving the FACTS optimization problem.

A colorimetric sensor array combined with a hybrid feature selection approach for discrimination of citrus infested by Bactrocera dorsalis (Hendel)

Changes in citrus volatile organic compounds (VOCs) induced by Bactrocera dorsalis (Hendel) infestation can serve as characteristic identifiers for non-destructive detection of infested citrus. This study proposed an innovative method combining colorimetric sensor array (CSA) technology with machine learning algorithms for the discrimination of B. dorsalis infestation in citrus. Gas chromatography-mass spectrometry (GC-MS) analysis identified key VOCs, including d-limonene, linalool, and decanal, as infestation markers. Subsequently, various porphyrin and metalloporphyrin dyes exhibiting sensitivity to these VOCs were selected to construct the CSA. To enhance detection accuracy, a hybrid feature selection method integrating ReliefF and Particle Swarm Optimization (PSO) was implemented. Subsequently, the optimized features subsets were utilized to develop classification models. Specifically, a binary classification model employing the K Nearest Neighbor (KNN) algorithm achieved a high accuracy of 93.89 % in distinguishing between healthy and infected citrus. Furthermore, a multi-class classification model using KNN was developed to differentiate among invasive, incubation, and infestation stages, attaining a remarkable accuracy of 97.78 %. This approach presents a promising solution for early detection of B. dorsalis infestation in citrus.

VIS/NIR Spectroscopy as a Non-Destructive Method for Evaluation of Quality Parameters of Three Bell Pepper Varieties Based on Soft Computing Methods

Spectroscopic analysis was employed to evaluate the quality of three bell pepper varieties within the 350–1150 nm wavelength range. Quality parameters such as firmness, pH, soluble solids content, titratable acids, vitamin C, total phenols, and anthocyanins were measured. To enhance data reliability, principal component analysis (PCA) was used to identify and remove outliers. Raw spectral data were initially modeled using partial least squares regression (PLSR). To optimize wavelength selection, support vector machines (SVMs) were combined with genetic algorithms (GAs), particle swarm optimization (PSO), ant colony optimization (ACO), and imperial competitive algorithm (ICA). The most effective wavelength selection method was subsequently used for further analysis. Three modeling techniques—PLSR, multiple linear regression (MLR), and artificial neural networks (ANNs)—were applied to the selected wavelengths. PLSR analysis of raw data yielded a maximum R2 value of 0.98 for red pepper pH, while the lowest R2 (0.58) was observed for total phenols in yellow peppers. SVM-PSO was determined to be the optimal wavelength selection algorithm based on ratio of performance to deviation (RPD), root mean square error (RMSE), and correlation values. An average of 15 effective wavelengths were identified using this combined approach. Model performance was evaluated using root mean square error of cross-validation and coefficient of determination (R2). ANN consistently outperformed MLR and PLSR in predicting firmness, pH, soluble solids content, titratable acids, vitamin C, total phenols, and anthocyanins for all three varieties. R2 values for the ANN model ranged from 0.94 to 1.00, demonstrating its superior predictive capability. Based on these results, ANN is recommended as the most suitable method for evaluating the quality parameters of bell peppers using spectroscopic data.

Evolutionary game and LGPSO for attack-defense confrontation analysis in WSN from macro perspective

Wireless sensor network node security requires effective security mechanisms to protect the security and reliability, so as to ensure that sensor nodes can operate normally and provide reliable data in various environments. The security state change of wireless sensor network nodes is an important research content in the field of wireless sensor security. In this paper, an evolutionary game model is proposed to analyze the security state changes of sensor network nodes from a macro perspective. The existing methods define the parameters subjectively, which leads to the lack of rationality. In this paper, a Levy Flight Global Learning Particle Swarm Optimization (LGPSO) is proposed to calculate the Nash equilibrium of the game and quantify the parameters of the evolutionary game. The method proposed in this paper determines the parameters of the evolutionary game by solving the Nash equilibrium, which makes the model more realistic. The LGPSO has better optimization performance than other algorithms in solving Nash equilibrium problems. The CEC2013 dataset is used to test the performance of LGPSO. The experimental results show that LGPSO is superior to all other algorithms on 68% of the problems. This paper also discusses the influence of the game difficulty coefficient on the evolution process, and experiments show that a larger coefficient is more beneficial to the defender. The macro analysis in this paper provides the method of active defense for the attack-defense confrontation in wireless sensor networks.

Enhanced power system stabilizer tuning using marine predator algorithm with comparative analysis and real time validation

This study concentrates on the implementation of Marine Predator Algorithm (MPA) scheme for tuning of a power system stabilizer’s (PSS’s) parameters to damp the low-frequency oscillations in a power system. To this, the single machine infinite bus system (SMIB), the Western System Coordinating Council (WSCC) and the New England 10 machine 39-bus power system are utilized for testing and comparing different metaheuristic algorithms using different fitness functions. Optimal PSS parameters of SMIB test system are validated using CU-SLRT Std, a real-time digital simulator. The comparative studies demonstrate that the MPA optimized PSS yields improvements of up to 98.62% in the Particle Swarm Optimization (PSO) at 69.42%, Whale Optimization Algorithm (WOA) at 71.79%, Flower Pollination Algorithm (FPA) at 72.39%, African vulture optimization algorithm (AVOA) at 78.04%, Wild Horse Optimization (WHO) algorithm at 68.57% under various operating scenarios. The superiority of the MPA optimized PSS has been validated using Hardware-in-the-loop implementation for the SMIB test system.

AGWO-PSO-VMD-TEFCG-AlexNet bearing fault diagnosis method under strong noise

To solve the difficult problem of early bearing fault diagnosis under strong- background-noise, an AGWO-PSO-VMD-TEFCG-Alexnet bearing fault diagnosis method based on Augmented Grey Wolf Optimizer (AGWO), Particle Swarm Optimization (PSO), Variational Mode Decomposition (VMD) and TEFCG-AlexNet convolutional neural network deep learning algorithm is proposed. The comprehensive evaluation index of VMD is designed by using the envelope entropy (EE), and the optimal modulus and penalty factor of VMD are found adaptively by using the AGWO-PSO. Using the feature index and time–frequency characteristics of screened IMF, the time–frequency enhancement feature map is established. The bearing fault diagnosis method is constructed by TEFCG-AlexNet. The early bearing fault data set with strong-background-noise is tested and the decomposition effect is compared with the same type VMD algorithm,the results show that the proposed method has the best diagnosis effect. It’s proved that this method has better characteristics of fault feature recognition and diagnosis.

Parametric sensitivity analysis of the friction coefficient of coated textured surface in the rotary vane actuator end seal

This paper utilizes the extended Fourier amplitude sensitivity test (EFAST) method to analyze the effects of varying speeds on the friction coefficient of the coated textured end seal surface in rotary vane actuators. The analysis focuses on the first-order, total, and coupled sensitivities of root mean square (RMS) roughness, texture depth, and texture area ratio. The accuracy and validity of the numerical simulations are experimentally verified. At low speeds (20 rpm), RMS roughness shows the highest first-order sensitivity, 1.247 and 2.181 times greater than texture depth and texture area ratio. Using Support Vector Regression and Particle Swarm Optimization, the optimal parameters were determined: an RMS roughness ofs 0.1012 μm, a texture area ratio of 77.99%, and a texture depth of 2.9601 μm. The model can also predict the friction coefficient for various parameter combinations at different speeds.

Dynamics and Chaos Intensity Analysis of Under-Actuated Mechanism by Uniformity and Particle Swarm Optimization

Dynamics and Chaos Intensity Analysis of Under-Actuated Mechanism by Uniformity and Particle Swarm Optimization

Assessment of water electrolysis projects for green hydrogen production with a novel hybrid Q-learning algorithm and molecular fuzzy-based modelling

Determining the most important criteria for increasing the efficiency of water electrolysis investments provides businesses with a competitive advantage. Although there are many studies in the literature on this importance, there are very few studies determining the most important of these performance indicators. To satisfy this gap, the purpose of this study is to make assessment of water electrolysis projects for green hydrogen production via a novel model. First, the balanced expert evaluation matrices are obtained by q-learning algorithm. Secondly, the criteria for water electrolysis investments are prioritized using molecular fuzzy Bayesian network (BANEW). Thirdly, green hydrogen strategies for water electrolysis investments are ranked with molecular fuzzy multi-objective particle swarm optimization (MOPSO). The most important contribution of this study to the literature is the determination of the criteria that should be applied primarily for the performance increase of water electrolysis investments by creating a new model. The use of molecular fuzzy numbers is a very important contribution of the model to the literature. In this process, the use of three-dimensional geometric figures allows the reduction of uncertainties in decision-making processes. The findings indicate that lifespan of electrolysers and production capacity are the most essential criteria. Additionally, proton exchange membrane electrolysers and alkaline water electrolysis are found as the most critical green hydrogen strategies. Extending the life of electrolysers is crucial to increase sustainability in hydrogen production and reduce long-term costs. In this context, research incentives should be provided for the development of materials and technologies to increase the durability of electrolysers. Similarly, establishing quality standards to extend the life of electrolysers also contributes to achieving this goal.

The multi-depot pickup and delivery vehicle routing problem with time windows and dynamic demands

The rapid development of the urban logistics recycling industry, combined with the complexity of the pickup and delivery networks, has created a surge in dynamic customer demands and exacerbated the difficulty of logistics resource sharing. Accordingly, this work focuses on a multi-depot pickup and delivery vehicle routing problem with time windows and dynamic demands, which incorporates resource sharing. A bi-objective mathematical model is formulated to minimize the total operating cost and number of vehicles. A three-dimensional affinity propagation clustering and an adaptive nondominated sorting genetic algorithm-II are combined to find Pareto optimal solutions. A dynamic demand insertion strategy is proposed to determine the vehicle service sequences for dynamic situations. Combined with an elite iteration mechanism to prevent the proposed algorithm from falling into search stagnation and improve the convergence performance. The superiority of the proposed algorithm is verified by comparing with CPLEX solver (i.e., ILOG CPLEX Optimization Studio 12.10), multi-objective ant colony optimization, multi-objective particle swarm optimization, multi-objective evolutionary algorithm, multi-objective genetic algorithm, and decomposition-based multi-objective evolutionary algorithm with tabu search. Besides, the proposed model and algorithm are tested by a real-world case study in Chongqing city, China, and the further analysis indicates that significant improvement can be achieved. Furthermore, by incorporating the recognition and prediction techniques of artificial intelligence on dynamic demand data, the proposed approach can realize the self-optimization of multi-depot vehicle routes and the precise allocation of logistics resources in dynamic environments. This study is conducive to the construction of a digitally-intelligent urban logistics system.

Fitting method of spinning projectile tri-orthogonal geomagnetic output based on improved particle swarm optimization algorithm

Fitting method of spinning projectile tri-orthogonal geomagnetic output based on improved particle swarm optimization algorithm

Dynamic scheduling strategy and algorithm for mixed batch scheduling in vacuum freeze-dried fruit processes

Abstract Vacuum freeze-dried fruit processes consisting of heating and holding are modelled as a mixed batch scheduling with the objective of minimizing the makespan. The jobs differ from each other in job family, size, weight and ready time. The batch processing time is determined by the longest job and the total weight of the jobs in the batch. A mixed-integer linear programming model is developed and tested with small-scale examples. Typical batch scheduling strategies are analysed and a machine-based dynamic programming strategy is proposed. The machine-based dynamic scheduling strategy is applied to design improved genetic and particle swarm optimization algorithms, which demonstrate the effectiveness of this strategy. The worst-case ratio of the algorithms using machine dynamic programming strategy are proved. Numerical experiments show that the heuristic algorithm, genetic algorithm, and particle swarm optimization algorithm based on machine dynamic scheduling strategy outperform related algorithms using greedy and job-based dynamic scheduling strategies.

Cooperative metaheuristic algorithm for global optimization and engineering problems inspired by heterosis theory

Swarm Intelligence-based metaheuristic algorithms are widely applied to global optimization and engineering design problems. However, these algorithms often suffer from two main drawbacks: susceptibility to the local optima in large search space and slow convergence rate. To address these issues, this paper develops a novel cooperative metaheuristic algorithm (CMA), which is inspired by heterosis theory. Firstly, simulating hybrid rice optimization algorithm (HRO) constucted based on heterosis theory, the population is sorted by fitness and divided into three subpopulations, corresponding to the maintainer, restorer, and sterile line in HRO, respectively, which engage in cooperative evolution. Subsequently, in each subpopulation, a novel three-phase local optima avoidance technique-Search-Escape-Synchronize (SES) is introduced. In the search phase, the well-established Particle Swarm Optimization algorithm (PSO) is used for global exploration. During the escape phase, escape energy is dynamically calculated for each agent. If it exceeds a threshold, a large-scale Lévy flight jump is performed; otherwise, PSO continues to conduct the local search. In the synchronize phase, the best solutions from subpopulations are shared through an elite-based strategy, while the classical Ant Colony Optimization algorithm is employed to perform fine-tuned local optimization near the shared optimal solutions. This process accelerates convergence, maintains population diversity, and ensures a balanced transition between global exploration and local exploitation. To validate the effectiveness of CMA, this study evaluates the algorithm using 26 well-known benchmark functions and 5 real-world engineering problems. Experimental results demonstrate that CMA outperforms the 10 state-of-the-art algorithms evaluated in the study, which is a very promising for engineering optimization problem solving.

Thermal energy analysis using artificial neural network and particle swarm optimization approach in partially ionized hyperbolic tangent material with ternary hybrid nanomaterials

This investigation holds significant pragmatic implications for endeavors aimed at curbing energy losses stemming from diverse factors. A neural network propelled by artificial intelligence, employing the Levenberg-Marquardt technique (ANN-LMM) has been devised for integrating ternary hybrid nanoparticles into a partially ionized hyperbolic tangent liquid flowing over an extended melting surface (PIHTL-SMS). The substance motion equivalence is delineated, considering the rotational outcome. The heat energy is formulated by amalgamating viscous intemperance and Joule heat contributions. To streamline complexity, the resulting PDEs are transmuted into a series of ordinary differential equations (ODEs) through resemblance transformations. A reference dataset for ANN-LMM is produced encompassing diverse significant model permutations and pretending situations utilizing the Lobatto III-A statistical technique. This reference data undergoes verification, evaluation and training procedures to refine the estimated explanation towards achieving anticipated outcomes. The precision, constancy, capability and resilience of ANN-LMM are substantiated concluded mean squared error (MSE)-based fitness curves, error histograms, regression plots and absolute error evaluations. A relative examination elucidates the correctness of the suggested solver, exhibiting entire errors within the array of 10-10 to 10-06 for all significant constraints. Resulting differential equations are also solved using particle swarm optimization (PSO) approach. In PSO several parameters are optimized to enhance the performance of the algorithm. Optimizing these parameters help to improve the effectiveness and efficiency of the PSO algorithm for given problem. PSO converges quickly to optimal or near-optimal solutions, making it efficient for problems with large domain. Several pivotal graphs are constructed to illustrate the impact of emergent constraints on fluid temperature and velocity profiles. The outcomes underscore the numerical technique as a potent instrument for tackling the intricate conjoined ODEs system prevalent in fluid mechanism and allied intemperance presentations in technology. Additionally, improvements in the Forchheimer constraint and the Weissenberg number are deemed imperative for regulating fluid velocity. Unlike prior research that mostly concentrated on single or binary nanofluids, this work presents the integration of ternary hybrid nanoparticles into a partly ionized hyperbolic tangent liquid, a unique technique. Improved accuracy and processing efficiency are also provided by using an ANN-LMM neural network to solve the complicated transformed ODEs. Comparison of ANN, PSO results and existing results are done which shows validity of the current analysis. This work is unique in that it offers a deeper understanding of fluid behavior at advanced thermal settings by including emergent restrictions, viscous dissipation, and Joule heating.

A Multi-Strategy Co-Evolutionary Particle Swarm Optimization Algorithm with Its Convergence Analysis

Compared to the single-strategy particle swarm optimization (PSO) algorithm, the multi-strategy PSO shows potential advantages in solving complex optimization problems. In this study, a novel framework of the multi-strategy co-evolutionary PSO (M-PSO) is first proposed in which a matrix parameter pool scheme is introduced. In the scheme, multiple strategies are taken into account in the matrix parameter pool and new hybrid strategies can be generated. Then, the convergence analysis is made and the convergence conditions are provided for the co-evolutionary PSO framework when some operators are specified. Subsequently, based on the PSO framework, a novel multi-strategy co-evolutionary PSO is developed using [Formula: see text]-learning which is a classical reinforcement learning technique. In the proposed M-PSO, both the parameter optimization by the orthogonal method and the convergence conditions are embedded to improve the performance of the algorithm. Finally, the experiments are conducted on two test suites, CEC2017 and CEC2019, and the results indicate that M-PSO outperforms several meta-heuristic algorithms on most of the test problems.