Improved Particle Swarm Optimization Research Articles

Modeling and diagnosis of water quality parameters in wastewater treatment process based on improved particle swarm optimization and self-organizing neural network

The study designs a strategy to predict water quality parameters and identify faults in the activated sludge process. The proposed method combines the improved beetle antennae search (IBAS) with the dynamic particle swarm multi-objective optimization algorithm based on crowding distance (DMOPSO-CD), named DMOPSO-CD-IBAS. The fault diagnosis prediction interval of chemical oxygen demand (COD), biochemical oxygen demand (BOD5) and total suspended substance (TSS) was conducted by self-organizing fuzzy neural network with an efficient scheme for parsimonious (SOFNN-ESP). DMOPSO-CD enhances the efficiency of the beetle antenna search by adjusting inertia weights and acceleration factors, reaching the optimal state with a fitness value of 0.0961. Furthermore, the crowding distance sorting preserve the external elite set and update the global optimal values, upgrading the individual search mechanism of beetle antenna search to a group search mechanism to enhance population diversity. The proposed fault diagnosis method's effectiveness is validated through three specific faults (sensor fault of COD and BOD5, and the index of sludge expansion) during the sewage treatment process. The results of the prediction mean square error, root mean square error, and average absolute error of the proposed model were kept at about 0.011, 0.15 and 0.524, respectively, having better tracking performance and stronger robustness than SOFNN-ESP and backpropagation.

Optimizing inset-fed rectangular micro strip patch antenna by improved particle swarm optimization and simulated annealing

ABSTRACT The recent wireless communication systems require high gain, lightweight, low profile, and simple antenna structures to ensure high efficiency and reliability. The existing microstrip patch antenna (MPA) design approaches attain low gain and high return loss. To solve this issue, the geometric dimensions of the antenna should be optimized. The improved Particle Swarm Optimization (PSO) algorithm which is the combination of PSO and simulated annealing (SA) approach (PSO-SA) is employed in this paper to optimize the width and length of the inset-fed rectangular microstrip patch antennas for Ku-band and C-band applications. The inputs to the proposed algorithm such as substrate height, dielectric constant, and resonant frequency and outputs are optimized for width and height. The return loss and gain of the antenna are considered for the fitness function. To calculate the fitness value, the Feedforward Neural Network (FNN) is employed in the PSO-SA approach. The design and optimization of the proposed MPA are implemented in MATLAB software. The performance of the optimally designed antenna with the proposed approach is evaluated in terms of the radiation pattern, return loss, Voltage Standing Wave Ratio (VSWR), gain, computation time, directivity, and convergence speed.

Efficient particulate matter source localization in dynamic indoor environments: An experimental study by a multi-robot system

This study tackles the urgent issue of indoor particulate matter (PM) pollutants, highlighting the critical need for efficient source localization due to its significant health risks. Moving beyond traditional constant-rate gas emission research, we explore real-world PM releases using a multi-robot system, enabling effective PM source localization in dynamically ventilated environments. Initial data collection on airflow and PM concentrations helps optimize our system for mechanical ventilation challenges. Through 90 experiments across six scenarios, we evaluate the improved whale optimization algorithm (IWOA) and improved particle swarm optimization (IPSO) methods, assessing their ability to identify both constant and variable PM sources and their adaptability to different pollutants. The results show a success rate of 73.3 % for both methods in locating constant PM sources, with IPSO offering a slight edge in efficiency. Moreover, in tasks involving ethanol vapor, the methods exhibited higher success rates, indicating uniform performance across a variety of pollutants. This consistency, alongside the noted variations in success rates, is primarily attributed to the complexities of PM dispersion. Importantly, our study highlights the methods' adaptability to periodic PM sources with variable release rates, maintaining high success without extra localization steps. This research advances indoor air quality management and emphasizes the importance of flexible, effective pollutant control strategies for public health protection.

Development of metaheuristic algorithms for efficient path planning of autonomous mobile robots in indoor environments

The application of efficient path planning algorithms for two-wheeled Autonomous Mobile Robots (AMRs) in static environments with obstacles is a significant challenge in robotics research. Existing methods, such as the A star (A*) algorithm utilized in Robot Operating System 2 (ROS2), can provide optimal paths but may have high computational complexity in intricate environments. This study explores the potential of three metaheuristic algorithms - Improved Particle Swarm Optimization (IPSO), Improved Grey Wolf Optimizer (IGWO), and Artificial Bee Colony (ABC) - for planning efficient and smooth paths in static environments. These algorithms are selected due to their ability to efficiently find near-optimal solutions and avoid local minima. In this study, the researchers designed and built a two-wheeled AMR using a Raspberry Pi 4 microcontroller as the main processing unit, working in conjunction with an Arduino Mega for controlling the DC motor drive through an MDD10A motor driver circuit. The robot is equipped with an RPLiDAR A1 sensor to read 360-degree distance values for mapping and obstacle avoidance. The experimental results clearly indicate that the metaheuristic algorithms, especially ABC, can calculate paths up to 7% shorter than A* while requiring only one-tenth of the time. Moreover, ABC demonstrates superior motion smoothness when applied to the actual two-wheeled robot in static environments. This work represents a significant step in developing algorithms for two-wheeled robots that are ready to support real-world operations in industries, logistics, healthcare, or various service sectors, which can help increase efficiency and reduce operating costs in the future.

A new IPCA-CPSO-BP Model for Predicting Gas Emission in Underground Coal Mines

Gas has become the primary factor restricting the safe and efficient production of coal mines. Gas emission prediction model is very important for mine gas emission prediction and gas disaster prevention. The improved principal component analysis (IPCA) was used to reduce the dimension of 13 influencing factors of gas emission, and the CPSO-BP neural network prediction model was built with MATLAB software to predict the absolute gas emission of Zhongtai Mining.The results show that the cumulative contribution rate of principal components is not less than 95%, and the number of principal components after improvement is reduced from the original 6 to 3, which effectively solves the problem of excessive principal components and data redundancy caused by the correlation difference between various influencing factors and gas emission amount. At the same time, the optimized particle swarm optimization algorithm alleviates the trouble that the particle swarm optimization algorithm is prone to fall into the local optimal solution. By coupling the improved particle swarm optimization algorithm with BP neural network, the problem of BP neural network's over-dependence on the initial value of weights and thresholds is solved, and the optimal initial weights and thresholds are provided for BP neural network, improving the accuracy of model prediction results. The average relative error of the original BP neural network is 1.6638%, the normalized mean square error is 0.3155, and the regression correlation index is 0.8157. The IPCA-CPSO-BP prediction model decreased to 0.5749%, 0.1143 and 0.9758, respectively. IPCA improves the data dimensionality reduction ability of principal component analysis, IPCA-CPSO-BP enhances the stability of particle swarm optimization algorithm, and significantly improves the prediction accuracy of BP model. The prediction trend is highly consistent with the actual value, which verifies the reliability of the model and provides strong data support for mine gas prevention and control.

A novel coupled rainfall prediction model based on stepwise decomposition technique

The traditional decomposed ensemble prediction model decomposes the entire rainfall sequence into several sub-sequences, dividing them into training and testing periods for modeling. During sample construction, future information is erroneously mixed into the training data, making it challenging to apply in practical rainfall forecasting. This paper proposes a novel stepwise decomposed ensemble coupling model, realized through variational mode decomposition (VMD) and bidirectional long short-term memory neural network (BiLSTM) models. Model parameters are optimized using an improved particle swarm optimization (IPSO). The performance of the model was evaluated using rainfall data from the Southern Four Lakes basin. The results indicate that: (1) Compared to the PSO algorithm, the IPSO algorithm-coupled model shows a minimum decrease of 2.70% in MAE and at least 2.62% in RMSE across the four cities in the Southern Four Lakes basin; the IPSO algorithm results in a minimum decrease of 25.58% in MAE and at least 28.19% in RMSE for the VMD-BiLSTM model. (2) When compared to IPSO-BiLSTM, the VMD-IPSO-BiLSTM based on the stepwise decomposition technique exhibits a minimum decrease of 26.54% in MAE and at least 34.16% in RMSE. (3) The NSE for the testing period of the VMD-IPSO-BiLSTM model in each city surpasses 0.88, indicating higher prediction accuracy and providing new insights for optimizing rainfall forecasting.

A carbon price ensemble prediction model based on secondary decomposition strategies and bidirectional long short‐term memory neural network by an improved particle swarm optimization

AbstractTo further enhance the precision of carbon trading price forecasting, this research proposes a combined forecasting model, CEEMDAN–VMD–IPSO–BiLSTM, considering the unsatisfactory high‐frequency sequence decomposition and the reliance on unidirectional neural networks in current carbon price‐prediction models. First of all, the original sequence of carbon prices is decomposed into multiple independent subsequences through the completely ensemble empirical mode decomposition with adaptive noise (CEEMDAN) technique. The sample entropy values of each subsequence are calculated to reconstruct them as high‐frequency, low‐frequency, and trend sequences. Second, we employ the variational mode decomposition (VMD) approach to decompose the high‐frequency series. The obtained subsequences, along with the low‐frequency and trend sequences, are separately input into an improved particle swarm optimization (IPSO) optimized bidirectional long short‐term memory neural network (BiLSTM) model for forecasting. Finally, an IPSO–BiLSTM model is used to integrate the forecasting outcomes from the previous step, yielding the ultimate results for predicting carbon prices. The case studies reveal that compared with the benchmark model, this model exhibits superior predictive precision and universality. It offers theoretical support for optimizing carbon market operations and fostering low‐carbon economic growth, holding practical importance.

Maximum span determination and optimal sizing of cable for improved performance of droop-controlled DC microgrid

DC microgrids are seen as smart solutions to interface DC loads and distributed energy resources (DERs). However, in DC microgrids, the placement of sources and loads as well as the size of cable impact the system’s span, regulation of voltage, and losses. This paper proposes novel algorithms to determine the maximum span and optimal size of cable for the improved performance of a droop-controlled DC microgrid. The proposed algorithms utilize an improved power flow analysis (IPFA) method based on Newton-Raphson technique to determine the maximum span and the optimal size of cable, enhancing the voltage regulation and reducing the cost. Additionally, the impacts of power rating, droop constants, and size of cable on the DC microgrid’s maximum span are investigated and reported. Owing to the intricate nature of the problem concerning the ideal size of cable for the droop-controlled DC microgrid, a heuristic optimization approach is employed. Further to enhance the rate of convergence and computational performance, an improved particle swarm optimization (IPSO) is also proposed. The constraint of keeping the bus voltage variations below the allowable voltage regulation limits is applied to the objective function of the optimization problem. In the case of a droop-controlled, DC microgrid having a specified configuration, the suggested algorithm can determine the ideal size of cable, guaranteeing both the least cost and enhanced voltage regulation. Comprehensive numerical and modelling results have been presented for a droop-controlled DC microgrid with different loads and DERs to verify the effectiveness of the proposed methods. Furthermore, the analysis reveals that configuration III of the DC microgrid with an optimal cable size of 19 mm2 lowers the absolute voltage regulation to as low as 1.06 V. The results of the detailed analysis validate the enhanced performance of the proposed algorithms and are highly useful to both system designers and consumers of the DC microgrids, eventually paving the way for the widespread use of DC microgrids in the future.

Deep Reinforcement Learning-Driven UAV Data Collection Path Planning: A Study on Minimizing AoI

As a highly efficient and flexible data collection device, Unmanned Aerial Vehicles (UAVs) have gained widespread application because of the continuous proliferation of Internet of Things (IoT). Addressing the high demands for timeliness in practical communication scenarios, this paper investigates multi-UAV collaborative path planning, focusing on the minimization of weighted average Age of Information (AoI) for IoT devices. To address this challenge, the multi-agent twin delayed deep deterministic policy gradient with dual experience pools and particle swarm optimization (DP-MATD3) algorithm is presented. The objective is to train multiple UAVs to autonomously search for optimal paths, minimizing the AoI. Firstly, considering the relatively slow learning speed and susceptibility to local minima of neural network algorithms, an improved particle swarm optimization (PSO) algorithm is utilized for parameter optimization of the multi-agent twin delayed deep deterministic policy gradient (MATD3) neural network. Secondly, with the introduction of the dual experience pools mechanism, the efficiency of network training is significantly improved. Experimental results show DP-MATD3 outperforms MATD3 in average weighted AoI. The weighted average AoI is reduced by 33.3% and 27.5% for UAV flight speeds of v = 5 m/s and v = 10 m/s, respectively.

Trajectory Planning for Autonomous Formation of Wheeled Mobile Robots via Modified Artificial Potential Field and Improved PSO Algorithm

This paper addresses two substantial aspects in the field of robotics: trajectory planning and trajectory tracking for multi-robot systems. The collective movement of the multi-wheeled mobile robots is based on a formation control with a leader–follower strategy. To ensure safe navigation toward the destination within a workspace containing multiple obstacles, we skillfully combine the Modified Artificial Potential Field (MAPF) method and the Improved Particle Swarm Optimization (IPSO) algorithm for a group of nonholonomic mobile robots. A global planner based on IPSO algorithm is assigned to the leader robot, to find the optimal collision-free path. Compared to recent nature-inspired methodologies, the improvement suggested enhance the search capabilities of the algorithm, resulting in a 2% reduction in path length and a 29% decrease in computation time. Simultaneously, the follower robot has the ability to employ either a formation policy or a local planner using MAPF. The proposed modifications address the primary limitations of the conventional method, notably the susceptibility to local minima and the challenge of reaching goals near obstacles. Furthermore, this local planner is adept at evading both static and dynamic obstacles. Extensive real hardware experiments are conducted within multiple scenarios using the mobile robot Qbot-2e to corroborate the obtained simulation results and validate the effectiveness of the proposed approaches both in tracking the desired trajectories, finding the optimal feasible collision-free path and avoiding static and dynamic obstacles for multi-robot systems.

Emergency control of firefighting vehicles based on distributed integer programming

Fire-related emergency vehicle scheduling has always been an important part of autonomous vehicle emergency management. To maintain the fire safety of buildings and reduce the transportation loss of emergency resources, this paper constructs a multi-objective integer planning model for fire emergency resource scheduling, which minimizes the time spent in the transportation of fire materials and considers the transportation needs of potential fire vehicles. The fixed-point iterative algorithm is realized and optimized, and distributed computing is adopted to improve the solving speed. In this paper, the comparison and simulation experiments with Branch and Bound, improved particle swarm optimization and other algorithms are carried out. The results show that the model and the algorithm can effectively deal with the fire emergency vehicle scheduling problem under different simulated fires and multiple fires occurring at the same time, and have certain advantages in numerical stability and convergence speed.

3D position deployment and performance optimization of mmWave UAV-assisted HetIoT under jamming condition

Heterogeneous Internet of Things (HetIoT) has received widespread attention due to its provision of various convenient services in fields such as smart cities, intelligent transportation, environmental monitoring and security systems. Due to HetIoT inherently demands high data rates, bandwidth, and low latency, the application of millimeter-wave (mmWave) unmanned aerial vehicle (UAV) as emergency aerial base station (ABS) providing services to HetIoT users has become a low-cost and efficient means. However, due to the sensitivity of mmWave to obstacles and jamming, guaranteeing network performance has become a pressing issue. This paper considers a mmWave UAV-assisted HetIoT under jamming conditions, where auxiliary ABSs serve multiple ground users (GUs) who generate a large amount of sensor data. We establish a coverage maximization problem under the constraints of signal-to-interference ratio (SIR) threshold, maximum power of ABSs and maximum number of GUs that the base station can serve, and propose a novel ABS hovering deployment algorithm M-HiAPSO that combines the artificial potential field (APF) method and the improved particle swarm optimization (PSO) algorithm in a hierarchical manner. Specifically, the multi-element APF method is used to characterize the horizontal force between nodes, combined with the improved hierarchical adaptive PSO algorithm to adjust the horizontal position of the ABS to obtain the optimal UAV hovering position and power allocation strategy. Numerical results show that the coverage rate reached 96.2% when the number of iterations was 283, and it can reach up to 99.6%.

A novel thermal turbulence reconstruction method using proper orthogonal decomposition and compressed sensing coupled based on improved particle swarm optimization for sensor arrangement

With the development of offshore wind turbine single power toward levels beyond 10 MW, the increase in heat loss of components in the nacelle leads to a high local temperature in the nacelle, which seriously affects the performance of the components. Accurate reconstruction and control of thermal turbulence in the nacelle can alleviate this problem. However, the physical environment of thermal turbulence in the nacelle is very complex. Due to the intermittent and fluctuating nature of turbulence, the turbulent thermal environment is highly nonlinear when coupled with the temperature field. This leads to large reconstruction errors in existing reconstruction methods. Therefore, we improve the sparse reconstruction method for compressed sensing (CS) based on the concept of virtual time using proper orthogonal decomposition (POD). The POD-CS method links the turbulent thermal environment reconstruction with matrix decomposition to ensure computational accuracy and computational efficiency. The improved particle swarm optimization (PSO) is used to optimize the sensor arrangement to ensure stability of the reconstruction and to save sensor resources. We apply this novel and improved PSO-POD-CS coupled reconstruction method to the thermal turbulence reconstruction in the nacelle. The effects of different basis vector dimensions and different sensor location arrangements (boundary and interior) on the reconstruction errors are also evaluated separately, and finally, the desired reconstruction accuracy is obtained. The method is of research value for the reconstruction of conjugate heat transfer problems with high turbulence intensity.

Reentry trajectory optimization of hypersonic glide vehicle based on improved particle swarm algorithm

The reentry process of hypersonic glide vehicle presents a host of intricate constraint issues. A method for optimizing the reentry trajectory of hypersonic glide vehicle is presented to achieve the shortest possible reentry time. The approach utilizes the improved particle swarm optimization (IPSO) algorithm. Firstly, population initialization is performed using the quasi-oppositional differential evolution (QODE) strategy to promote diversity within the population. Then an adaptive adjustment algorithm is designed for the inertia weight coefficient and learning factor to achieve a balance between global and local search capabilities. Finally, utilizing the IPSO algorithm for optimizing the flight parameters of the reentry trajectory, the reentry time is reduced from 338 seconds to 335 seconds. The simulations results indicate that the IPSO algorithm outperforms both the standard PSO algorithm and genetic algorithm (GA) in terms of optimization performance index.

Low-carbon economic operation strategy for multi-agent integrated energy system considering uncertainty of renewable energy power generation

The uncertainty of renewable energy output threatens the operation safety of multi-agent integrated energy system (MAIES), which makes it difficult to balance the low-carbon economic operation demands of various stakeholders. However, the existing research solely focuses on the operational strategy of multi-agent game involving integrated energy suppliers and users in deterministic scenarios, overlooking the complementary supporting role and game interaction of shared energy storage and wind farm as independent entities of interest under the instability of renewable energy power generation. Hence, this paper first establishes the optimal operation models for integrated energy system operator (IESO), user aggregator (UA), shared energy storage operator (SESO), and wind farm operator (WFO) considering the stepped carbon trading. Second, in the face of the actual situation of uncertainty of photovoltaic and wind power output, fuzzy chance-constrained programming is adopted for processing. Then, a bi-layer game equilibrium model with IESO as a leader and UA, SESO, and WFO as followers is proposed, and the existence and uniqueness of Stackelberg equilibrium solution are proved. Finally, simulation calculation is carried out based on the YALMIP toolbox in the Matlab R2023a software, and the improved particle swarm optimization algorithm and CPLEX solver are used to solve the model. The results demonstrate that the participation of SESO and WFO as independent stakeholders in the game interaction can improve the economic and environmental benefits of MAIES. The iterative optimization of demand response subsidy prices can effectively motivate users to participate in demand response, improve the ability of MAIES to cope with the uncertain risks of renewable energy generation and load, and reduce the power grid dispatch pressure.

Study on agricultural drought disaster risk assessment in Heilongjiang reclamation area based on SSAPSO optimization projection pursuit model.

Heilongjiang reclamation area serves as a crucial hub for commodity grain production and strategic reserves in China, playing a vital role in maintaining national food security. Investigating the assessment of agricultural drought risk in this region can yield valuable insights into spatial and temporal variations in drought risk. Such insights can aid in formulating effective strategies for disaster prevention and mitigation, thereby minimizing food losses caused by drought disasters. This study employs a comprehensive indicator system comprising 17 indicators categorized into hazard, exposure, vulnerability, and resistance capacity. The projection pursuit model is applied to evaluate regional drought risk, while the PSO algorithm, optimized by the SSA algorithm, addresses the limitations of low local search ability and search accuracy during the large-scale search process of the PSO optimization algorithm. This study examines and compares the optimization and convergence capabilities of three algorithms: real number encoding-based genetic algorithm (RAGA), particle swarm optimization algorithm (PSO), and sparrow algorithm-based improved particle swarm optimization algorithm (SSAPSO). The analysis demonstrates that SSAPSO exhibits superior optimization performance and convergence properties, establishing it as a highly effective algorithm for optimization tasks. The findings reveal the following trends: over time, agricultural drought risk in Heilongjiang reclamation area has generally declined, with fluctuations observed in hazard and vulnerability, an increase in exposure, and a continuous enhancement of resistance capacity. Spatially, the western region exhibits significantly higher agricultural drought risk compared to the eastern region, primarily due to elevated hazard and vulnerability, coupled with lower resistance capacity. As the agricultural economy grows and agricultural expertise accumulates, the risk of agricultural drought decreases. However, variations in economic growth among different regions lead to diverse spatial distributions of risk.

Intelligent Low-Consumption Optimization Strategies: Economic Operation of Hydropower Stations Based on Improved LSTM and Random Forest Machine Learning Algorithm

The economic operation of hydropower stations has the potential to increase water use efficiency. However, there are some challenges, such as the fixed and unchangeable flow characteristic curve of the hydraulic turbines, and the large number of variables in optimal load distribution, which limit the progress of research. In this paper, we propose a new optimal method of the economic operation of hydropower stations based on improved Long Short-Term Memory neural network (I-LSTM) and Random Forest (RF) algorithm. Firstly, in order to accurately estimate the water consumption, the LSTM model’s hyperparameters are optimized using improved particle swarm optimization, and the I-LSTM method is proposed to fit the flow characteristic curve of the hydraulic turbines. Secondly, the Random Forest machine learning algorithm is introduced to establish a load-distribution model with its powerful feature extraction and learning ability. To improve the accuracy of the load-distribution model, we use the K-means algorithm to cluster the historical data and optimize the parameters of the Random Forest model. A Hydropower Station in China is selected for a case study. It is shown that (1) the I-LSTM method fits the operating characteristics under various working conditions and actual operating characteristics of hydraulic turbines, ensuring that they are closest to the actual operating state; (2) the I-LSTM method is compared with Support Vector Machine (SVM), Extreme Learning Machine (ELM) and Long Short-Term Memory neural network (LSTM). The prediction results of SVM have a large error, but compared with ELM and LSTM, MSE is reduced by about 46% and 38% respectively. MAE is reduced by about 25% and 21%, respectively. RMSE is reduced by about 27% and 24%, respectively; (3) the RF algorithm performs better than the traditional dynamic programming algorithm in load distribution. With the passage of time and the increase in training samples, the prediction accuracy of the Random Forest model has steadily improved, which helps to achieve optimal operation of the units, reducing their average total water consumption by 1.24%. This study provides strong support for the application of intelligent low-consumption optimization strategies in hydropower fields, which can bring higher economic benefits and resource savings to renewable energy production.

Adaptive Reactive Power Optimization in Offshore Wind Farms Based on an Improved Particle Swarm Algorithm

To address the reactive power optimization control problem in offshore wind farms (OWFs), this paper proposes an adaptive reactive power optimization control strategy based on an improved Particle Swarm Optimization (PSO) algorithm. Firstly, an OWF multi-objective optimization control model is established, with the total sum of voltage deviations at wind turbine (WT) terminals, active power network losses, and reactive power margin of WTs as comprehensive optimization objectives. Innovatively, adaptive weighting coefficients are introduced for the three sub-objectives, enabling the weights of each optimization objective to be adaptively adjusted based on real-time operating conditions, thus enhancing the adaptability of the reactive power optimization model to changes in operating conditions. Secondly, a Uniform Adaptive Particle Swarm Optimization (UAPSO) algorithm is proposed. On one hand, the algorithm initializes the particle swarm using a uniform initialization method; on the other hand, it improves the particle velocity update formula, allowing the inertia coefficient to adaptively adjust based on the number of iterations and the fitness ranking of particles. Simulation results demonstrate the following: (1) Under various operating conditions, the proposed adaptive multi-objective reactive power optimization strategy can ensure the stability of node voltages in offshore wind farms, reduce active power losses, and simultaneously improve reactive power margins. (2) Compared with the traditional PSO algorithm, UAPSO exhibits an approximately 10% improvement in solution speed and enhanced solution accuracy.

Application of improved particle swarm optimization algorithm in the proportional integral differential-controlled semi-active suspension system

To enhance the control performance of semi-active suspension systems, this research proposes a particle swarm optimization algorithm (PSO) with adaptive nonlinear correction of inertia weights, which is then integrated with a proportional integral differential (PID) algorithm. To this end, this research establishes quarter semi-active and passive suspension models of automobiles by utilizing the Matlab/Simulink simulation platform. In this foundation, this research further compares the advantages and disadvantages regarding performance indexes of semi-active suspension controlled by the adaptive inertia weighted particle swarm optimization (APSO) algorithm and the PID algorithm, as well as the PID-controlled semi-active suspension and passive suspension through simulation. Simulation results indicate that performance indicator values for different suspension types increase with higher pavement grades. Compared with passive suspension, the semi-active suspension controlled by APSO and PID algorithms presents significantly improved performance indexes, with reductions of at least 31.61% in root mean square (RMS) concerning body vertical acceleration, 1.78% in suspension dynamic deflection, and 22.13% in tire dynamic loads. Moreover, analysis of suspension system frequency response characteristics demonstrates a significant decrease in droop acceleration transmission rate for the semi-active suspension with APSO and PID algorithms across the whole frequency range compared with that of the PID-controlled suspension and passive suspension. On the same note, despite the higher values of suspension dynamic deflection and tire dynamic load transfer rate in certain frequency bands, they are generally within acceptable suspension limits. Simply put, the findings confirm the feasibility of applying the APSO algorithm in PID-controlled semi-active suspension systems, which effectively improves both vehicle ride comfort and handling stability.

Multi-Strategy Improved Particle Swarm Optimization Algorithm and Gazelle Optimization Algorithm and Application

In addressing the challenges associated with low convergence accuracy and unstable optimization results in the original gazelle optimization algorithm (GOA), this paper proposes a novel approach incorporating chaos mapping termed multi-strategy particle swarm optimization with gazelle optimization algorithm (MPSOGOA). In the population initialization stage, segmented mapping is integrated to generate a uniformly distributed high-quality population which enhances diversity, and global perturbation of the population is added to improve the convergence speed in the early iteration and the convergence accuracy in the late iteration. By combining particle swarm optimization (PSO) and GOA, the algorithm leverages individual experiences of gazelles, which improves convergence accuracy and stability. Tested on 35 benchmark functions, MPSOGOA demonstrates superior performance in convergence accuracy and stability through Friedman tests and Wilcoxon signed-rank tests, surpassing other metaheuristic algorithms. Applied to engineering optimization problems, including constrained implementations, MPSOGOA exhibits excellent optimization performance.