Conventional Particle Swarm Optimization Algorithm Research Articles

An exponential variation based PSO for analog circuit sizing in constrained environment

This work presents an Exponential Variation based Particle Swarm Optimization (EV-PSO) algorithm to improve the convergence rate and find an optimal solution to analog circuit optimization problems in a constrained-driven environment. Existing evolutionary algorithms have a lower convergence rate leading to higher design time. This work introduces two novel parameters, ζ1 and ζ2, into the velocity update equation. These parameters dynamically vary with the number of iterations. The algorithm was implemented on the Python platform. The results have shown that, in comparison to the considered existing methods, the exponential variation of the parameters ζ1 and ζ2 in the proposed algorithms have a larger rate of convergence. The proposed EV-PSO has a convergence rate of 27 iterations, which is 57.8%, 65.38%, and 59.1% better than the conventional PSO, differential evolution (DE) and genetic algorithm (GA) respectively. The typical design obtained from the optimal solution is verified through the simulation using 45-nm CMOS technology. The optimal solution presented in this work meets the desired input specifications within the specified constrained environment.

A Combined Marine Predators and Particle Swarm Optimization for Task Offloading in Vehicular Edge Computing Network

With the rapid advancement in technology, numerous advanced vehicular applications have emerged that generate large volumes of data that need to be processed on the fly. The vehicles' computing resources are limited and constrained in processing the huge amount of data generated by these applications. Cloud data centers, which are large and capable of processing the generated data, tend to be far away from the vehicles. The long distance between the cloud and the vehicles results in large transmission delays, making the cloud less suitable for executing such data. To address the long-standing issue of huge transmission delays in the cloud, edge computing, which deploys computing servers at the edge of the network, was introduced. The edge computing network shortens the communication distance between the vehicles and the processing resources and also provides more powerful computation compared to the vehicles' computing resources. The advantages offered by the vehicular edge network can only be fully realized with robust and efficient resource allocation. Poor allocation of these resources can lead to a worse situation than the cloud. In this paper, a hybrid Marine Predatory and Particle Swarm Optimization Algorithm (MPA–PSO) is proposed for optimal resource allocation. The MPA–PSO algorithm takes advantage of the effectiveness and reliability of the global and local search abilities of the Particle Swarm Optimization Algorithm (PSO) to improve the suboptimal global search ability of the MPA. This enhances the other steps in the MPA to ensure an optimal solution. The proposed MPA–PSO algorithm was implemented using MATLAB alongside the conventional PSO and MPA, and the proposed MPA–PSO recorded a significant improvement over the PSO and MPA.

Optimizing low-power task scheduling for multiple users and servers in mobile edge computing by the MUMS framework

In today's increasingly popular Internet of Things (IoT) technology, its energy consumption issue is also becoming increasingly prominent. Currently, the application of Mobile Edge Computing (MEC) in IoT is becoming increasingly important, and scheduling its tasks to save energy is imperative. To address the aforementioned issues, we propose a Multi-User Multi-Server (MUMS) scheduling framework aimed at reducing the energy consumption in MEC. The framework starts with a model definition phase, detailing multi-user multi-server systems through four fundamental models: communication, offloading, energy, and delay. Then, these models are integrated to construct an energy consumption optimization model for MUMS. The final step involves utilizing the proposed L1_PSO (an enhanced version of the standard particle swarm optimization algorithm) to solve the optimization problem. Experimental results demonstrate that, compared to typical scheduling algorithms, the MUMS framework is both reasonable and feasible. Notably, the L1_PSO algorithm reduces energy consumption by 4.6 % compared to Random Assignment and by 2.3 % compared to the conventional Particle Swarm Optimization algorithm.

Conflict Detection and Separation Configuration Method Based on Uncertain Flight Trajectory

Aiming at two aircraft conflict scenario in the pre-tactical stage, by converting the uncertain flight trajectory of the target aircraft into a spatio-temporal trajectory under its performance constraints, a conflict detection model based on truncated normal distribution was proposed,and influencing factors affecting the overall conflict probability were analysed by numerical simulation. For the conflict scenario, nonlinear particle swarm optimisation (NPSO) algorithm was applied to solve the optimal separation configuration strategy for the ownship. The simulation results show that, in comparison to conventional PSO algorithm, the improved NPSO algorithm improves the optimal value by 14.88% and decreases the maximum velocity change by 19.84%. The simulation also shows that the algorithm can maintain the minimum interval requirements under different initial parameters, demonstrating its strong adaptability.

Mobile robot path planning based on bi-population particle swarm optimization with random perturbation strategy

Path planning for mobile robots poses a challenging optimization problem, requiring the discovery of a near-optimal path within diverse constraints. Conventional particle swarm optimization (PSO) algorithms encounter limitations in solving constrained problems, vulnerability to local optima, and premature convergence. To address these challenges, this paper proposes a bi-population PSO algorithm with a random perturbation strategy (BPPSO), which divides particles into two subpopulations. The first subpopulation enhances global search capabilities by considering the quality of particles and the optimal solution of a randomly selected particle when updating velocities. The second subpopulation strengthens local search using a linear cognitive coefficient adjustment strategy. Moreover, a counter tracks iteration without improvement in the global best position. Upon reaching a predefined threshold, random perturbation is added to the positions of all particles in both subpopulations, increasing diversity and enhancing the ability to escape local optima. The performance of BPPSO was experimentally validated across three benchmark functions and four environment models. The results have demonstrated that the proposed BPPSO outperforms existing PSO algorithms and other established path planning algorithms in terms of path quality and running time, highlighting the feasibility of BPPSO in resolving the challenge of mobile robot path planning.

Multi-objective particle swarm optimization algorithm based on multi-strategy improvement for hybrid energy storage optimization configuration

In order to fully leverage the advantages of hybrid energy storage systems in mitigating voltage fluctuations, reducing curtailment rates of wind and solar power, minimizing active power losses, and enhancing power quality within distributed generation systems, while effectively balancing the economic and security aspects of the system, this paper establishes a multi-objective hybrid energy storage optimization configuration model that comprehensively considers the lifecycle economic costs, node voltage deviations, and system active power losses. To address the limitations of single-objective solution algorithms and the lack of diversity and premature convergence in multi-objective optimization processes, a multi-objective particle swarm optimization by multi-strategy improvements (CMOPSO-MSI) is proposed to solve the model. By introducing adaptive grid crowding distance and roulette wheel selection strategies to dynamically update the Pareto solution set, population uniformity and diversity are ensured. An improved dynamic nonlinear weighting strategy is introduced to enhance the algorithm's global search capability and convergence performance. A Gaussian mutation strategy is incorporated into the iteration process to enhance the uniformity of non-dominated solutions and particle search capabilities The aim is to achieve an optimal balance between the configuration cost and stability of hybrid energy storage systems. A simulation analysis under multiple cases is performed, taking an IEEE 33-node power distribution system as an example, with introducing photovoltaic and wind energy sources. The results demonstrate that the proposed algorithm achieves better Pareto frontiers and convergence performance compared to conventional multi-objective particle swarm optimization algorithms MOPSO, and classical multi-objective optimization algorithm NSGA-II, validating the effectiveness and accuracy of the proposed model and algorithm strategies in solving the hybrid energy storage optimization configuration problems. The approach concurrently considers system economics and grid stability while improving power quality.

An Effective Route Tracing Using Enhanced Ant Colony Optimization Techniques: Travelling Salesman Problem

The Travelling Salesman Problem (TSP) is a well-known optimization that determines the shortest route that visits a particular set of towns and returns to the start line. As an NP-hard, its complexity will increase considerably as the number of cities increases. Several heuristic algorithms, such as Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), and Genetic Algorithm (GA), have been developed to tackle this problem efficiently. This work establishes an approach that employs a multi-goal optimization algorithm that optimizes for minimizing the tour distances and maximizing the diversity of the towns visited. This paper aims to apply an enhanced ACO with conventional GA and PSO algorithms separately to leverage the strengths of both algorithms. The PSO and GA paths enhance the pheromone in global exploration, which speeds up the pheromone initialization of ACO. Thus, optimized routes by ant colony get integrated with pheromone reinforcement to obtain enhanced pheromone in the hybrid of GAACO and PSO-ACO. The ACO algorithm applies enhanced state transition to progress the search using the angle guidance function, and the best pheromone level improves convergence speed of the enhanced algorithms. This project has been designed as an intuitive and user-friendly interface for users to input TSP instances, select optimization algorithms, and visualize the solutions generated by each algorithm. Experiments are done to assess overall performance of ACO, GA-ACO, and PSO-ACO based on the best solution and convergence speed. Lastly, the effectiveness and performance of those algorithms in solving TSP across diverse scenarios and input parameters are compared.

Simultaneous Optimal Allocation of EVCSs and RESs Using an Improved Genetic Method

In the last decade, with the development of the electric vehicle industry and their acceptance in human societies, the participation plan of electric vehicles in supplying the load of the network has been taken into consideration. One of the requirements of this plan is the optimal location of the stations for these vehicles in the network so that they play an effective role in the operation of the network. In this regard, along with the construction of charging and discharging stations for electric vehicles, the construction of renewable sources in the network can play a complementary role for these stations. In this paper, the effect of using renewable resources as a supplement for smart charging stations and the placement of these stations to achieve technical and economic goals have been investigated. In order to manage the demand on the side of consumers and even out the load curve, the time of use mechanism as one of the demand response programs has been considered in this study. In this research, the improved nondominant sorting genetic algorithm is proposed to solve the problem, and the results of the proposed method are also compared with the conventional genetic and particle swarm optimization algorithms. All the simulations have been done in the MATLAB software and on the IEEE 33‐bus network. Based on the obtained results, after the implementation of the proposed plan in the distribution network, the objective functions of the loss, voltage drop, and the total cost have been reduced by 13.6%, 58.7%, and 54.4%, respectively, compared to the base conditions of the network.

Optimization of Location-Routing for Multi-Vehicle Combinations with Capacity Constraints Based on Binary Equilibrium Optimizers

The Location-Routing Problem (LRP) becomes a more intricate subject when the limits of capacities of vehicles and warehouses are considered, which is an NP-hard problem. Moreover, as the number of vehicles increases, the solution to LRP is exacerbated because of the complexity of transportation and the combination of routes. To solve the problem, this paper proposed a Discrete Assembly Combination-Delivery (DACA) strategy based on, the Binary Equilibrium Optimizer (BiEO) algorithm, in addition, this paper also proposes a mixed-integer linear programming model for the problem of this paper. Our primary objective is to address both the route optimization problem and the assembly group sum problem concurrently. Our BiEO algorithm was designed as discrete in decision space to meet the requirements of the LRP represented by the DACA strategy catering to the multi-vehicle LRP scenario. The efficacy of the BiEO algorithm with the DACA strategy is demonstrated. through empirical analysis utilizing authentic data from Changchun City, China, Remarkably, the experiments reveal that the BiEO algorithm outperforms conventional methods, specifically GA, PSO, and DE algorithms, resulting in reduced costs. Notably, the results show the DACA strategy enables the simultaneous optimization of the LRP and the vehicle routing problem (VRP), ultimately leading to cost reduction. This innovative algorithm proficiently tackles both the assembly group sum and route optimization problems intrinsic to multi-level LRP instances.

SCEHO-IPSO: A Nature-Inspired Meta Heuristic Optimization for Task-Scheduling Policy in Cloud Computing

Task scheduling is an emerging challenge in cloud platforms and is considered a critical application utilized by the cloud service providers and end users. The main challenge faced by the task scheduler is to identify the optimal resources for the input task. In this research, a Sine Cosine-based Elephant Herding Optimization (SCEHO) algorithm is incorporated with the Improved Particle Swarm Optimization (IPSO) algorithm for enhancing the task scheduling behavior by utilizing parameters like load balancing and resource allocation. The conventional EHO and PSO algorithms are improved utilizing a sine cosine-based clan-updating operator and human group optimizer that improve the algorithm’s exploration and exploitation abilities and avoid being trapped in the local optima problem. The efficacy of the SCEHO-IPSO algorithm is analyzed by using performance measures like cost, execution time, makespan, latency, and memory storage. The numerical investigation indicates that the SCEHO-IPSO algorithm has a minimum memory storage of 309 kb, a latency of 1510 ms, and an execution time of 612 ms on the Kafka platform, and the obtained results reveal that the SCEHO-IPSO algorithm outperformed other conventional optimization algorithms. The SCEHO-IPSO algorithm converges faster than the other algorithms in the large search spaces, and it is appropriate for large scheduling issues.

Layout optimization for underwater nozzle array of air-lifted artificial upwelling system based on discrete particle swarm algorithm

Artificial upwelling (AU) is widely recognized as a geoengineering tool to enhance oceanic fertility and stimulate the earth's capability of self-healing. Several air-lifted AU systems have been established to promote seaweed growth and facilitate carbon sequestration, for instance, in Norway and China. However, few researchers have addressed the critical issue of optimizing the layout of the underwater nozzle array (UNA), a key component of the air-lifted AU system. In this paper, we propose a novel method to optimize the layout of UNA by introducing and improving the discrete particle swarm optimization (DPSO) algorithm to guide the optimal nozzle positions. Furthermore, we develop the nutrient transport efficiency model to evaluate the performance of the AU system and apply it to investigate a typical AU system, namely the one in Aoshan Bay, China. Our results demonstrate that the proposed DPSO algorithm outperforms the conventional particle swarm optimization algorithm and the nutrient transport efficiency under the optimized UNA layouts was improved by an average of 14.5% to 35.0% compared to randomly generated layouts. These findings suggest that our optimization method could serve as a scientific reference for the engineering design of AU.

Cooperative Swarm Intelligence Algorithms for Adaptive Multilevel Thresholding Segmentation of COVID-19 CT-Scan Images

The Coronavirus Disease 2019 (COVID-19) is widespread throughout the world and poses a serious threat to public health and safety. A COVID-19 infection can be recognized using computed tomography (CT) scans. To enhance the categorization, some image segmentation techniques are presented to extract regions of interest from COVID-19 CT images. Multi-level thresholding (MLT) is one of the simplest and most effective image segmentation approaches, especially for grayscale images like CT scan images. Traditional image segmentation methods use histogram approaches; however, these approaches encounter some limitations. Now, swarm intelligence inspired meta-heuristic algorithms have been applied to resolve MLT, deemed an NP-hard optimization task. Despite the advantages of using meta-heuristics to solve global optimization tasks, each approach has its own drawbacks. However, the common flaw for most meta-heuristic algorithms is that they are unable to maintain the diversity of their population during the search, which means they might not always converge to the global optimum. This study proposes a cooperative swarm intelligence-based MLT image segmentation approach that hybridizes the advantages of parallel meta-heuristics and MLT for developing an efficient image segmentation method for COVID-19 CT images. An efficient cooperative model-based meta-heuristic called the CPGH is developed based on three practical algorithms: particle swarm optimization (PSO), grey wolf optimizer (GWO), and Harris hawks optimization (HHO). In the cooperative model, the applied algorithms are executed concurrently, and a number of potential solutions are moved across their populations through a procedure called migration after a set number of generations. The CPGH model can solve the image segmentation problem using MLT image segmentation. The proposed CPGH is evaluated using three objective functions, cross-entropy, Otsu’s, and Tsallis, over the COVID-19 CT images selected from open-sourced datasets. Various evaluation metrics covering peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and universal quality image index (UQI) were employed to quantify the segmentation quality. The overall ranking results of the segmentation quality metrics indicate that the performance of the proposed CPGH is better than conventional PSO, GWO, and HHO algorithms and other state-of-the-art methods for MLT image segmentation. On the tested COVID-19 CT images, the CPGH offered an average PSNR of 24.8062, SSIM of 0.8818, and UQI of 0.9097 using 20 thresholds.

Reactive Power Optimization Based on the Application of an Improved Particle Swarm Optimization Algorithm

Climate change, improved energy efficiency, and access to contemporary energy services are among the key topics investigated globally. The effect of these transitions has been amplified by increased digitization and digitalization, as well as the establishment of reliable information and communication infrastructures, resulting in the creation of smart grids (SGs). A crucial aspect in optimizing energy production and distribution is reactive power optimization, which involves the utilization of algorithms such as particle swarm optimization (PSO). However, PSO algorithms can suffer from premature convergence and being trapped in local optima. Therefore, in this research the design and development of an improved PSO algorithm for minimization of power loss in the context of SGs is the key contribution. For digital experimentation and benchmarking of the proposed framework, the IEEE 30-bus standardized model is utilized, which has indicated that an improvement of approximately 11% compared to conventional PSO algorithms can be achieved.

Optimizing TOC and IOC units of directional overcurrent relays in mutually coupled circuits using evolutionary PSO: Requirements and modeling

The efficient coordination of directional overcurrent relays is a challenging problem. Recent papers in the literature have focused on developing efficient algorithms to solve this issue. However, there is a lack of reporting practical procedures that affects the mathematical formulation to ensure accurate outputs by any optimization algorithm. In this paper, we show a comprehensive procedure that considers mutually coupled circuits via Graph Theory, the requirements of short-circuit current calculation, contingencies to be considered as well as the setting of Instantaneous Overcurrent (IOC) and Time Overcurrent (TOC) units, both for phase and ground protection. The simulation has been carried out by using a real electric network and C++ language programming. Computational simulation has shown the performance of the method, which provides high-quality solutions, with adequate coordination of the selected protective devices that increase the efficiency in setting this type of protection with safety. Evolutionary Particle Swarm Optimization (EPSO) outperformed conventional Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) as the best metaheuristic for optimally minimizing the proposed problem, achieving faster convergence times for the phase overcurrent protection scenario (16.36 s vs. 22.27 s and 17.03 s, respectively), and also for the ground overcurrent protection scenario (19.87 s vs. 20.44 s and 20.11 s, respectively).

An Improved Comprehensive Learning - Particle Swarm Optimization - Extended Kalman Filtering Method for the Online High-Precision State of Charge and Model Parameter Co-Estimation of Lithium-Ion Batteries

The precise assessment of the state of charge (SOC) of lithium-ion batteries (LIBs) is critical in battery management systems. This work offers a comprehensive learning particle swarm optimization (CLPSO) and extended Kalman filter (EKF) technique to forecast the SOC of LIBs in order to obtain an accurate SOC estimate for power batteries. Firstly, to address the challenge of identifying various parameters of the battery model, the bilinear transformation technique is employed to determine the parameters of the second-order RC equivalent circuit model. Secondly, to improve the fitness values for the conventional PSO algorithm, which is prone to entering local optimality, a learning strategy () is added to the particle velocity update method. The optimized PSO and EKF algorithms are integrated to perform online prediction of the SOC of LIBs. The experimental results demonstrate that under the conditions of the Beijing Bus Dynamic Stress Test (BBDST), Dynamic Stress Test (DST), and Hybrid Pulse Power Characterization Test (HPPC), the parameter identification inaccuracy of CLPSO is restricted to 1%. After multi-metric evaluation, the maximum error and mean absolute error of the CLPSO-EKF algorithm in SOC estimation are 0.32% and 0.0652%, respectively, demonstrating a higher robustness and accuracy advantage over other versions.

A Very Large-Scale Integration Global Routing Optimization Model for Hybrid Physarum Bionetworks

Interconnection of billion transistors in a single layer of a die with the advent of the nanometer regime imposes a great challenge to handle the increased complexity, particularly in the global routing of the Very Large-Scale Integration (VLSI) physical design phase which involves distinct optimization in the computation of overall interconnect wire-length. In classical graph theory, the VLSI global routing problem can be mapped as a Rectilinear Steiner Minimal Tree (RSMT) Problem, which in itself is an NP-complete problem. The use of metaheuristics in solving this problem plays a major role where Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO) proved to be efficient algorithms. Both algorithms face certain limitations and inconsistencies in determining maximum optimization. A new optimization algorithm with insight from the biological activity of microorganisms has been proposed in this paper which is based on the behavior of the unicellular organism Physarum Polycephalum aiming at minimizing the wire length of VLSI interconnects. The paper further explores a new hybridization technique employing the use of Physarum BioNetwork and Particle Swarm Optimization together where PSO generate better possible Steiner’s in the initial stage for the final process using Physarum BioNetwork to ensure better convergence. Complexity analysis of the proposed algorithm has been performed and the simulation results achieved greater efficiency when compared with the conventional PSO algorithm and available industry benchmark over-optimizing Global Routing problem in VLSI design.

Dedicated Adaptive Particle Swarm Optimization Algorithm for Digital Twin Based Control Optimization of the Plug-In Hybrid Vehicle

The digital twin (DT) is a promising technology that will provide a cyber-physical platform to enable rapid product development boosted by artificial intelligence and big data. This paper focuses on DT-based optimization of the energy management strategy (EMS) for a plug-in hybrid vehicle (PHEV). A dedicated adaptive particle swarm optimization (DAPSO) algorithm is developed to enhance the optimality and trustworthiness of the DT-based EMS optimization in a variety of driving conditions. By using the chassis dynamometer data, the DAPSO is developed by incorporating the widely-used PSO algorithm with an adaptive swarm control strategy that coordinates the exploration and exploitation of the individual swarming particles following the global information extracted from the swarm. With the cross-validation testing under three worldwide driving conditions, this study determines the unified settings of the DAPSO algorithm for the PHEV application. Experimental evaluations are conducted by monitoring the PHEV’s performance using different EMSs with control thresholds optimized by the DAPSO and conventional PSO algorithms (baseline). The results show that by introducing DAPSO for DT-based EMS optimization, up to 24% improvement in cost function value (weighted sum of the fuel consumption and SoC sustaining error) and more than 49.1% reduction in computing time can be achieved compared to the baseline methods.

Adaptive particle swarm optimization based hybrid small-signal modeling of GaN HEMT

Based on the GaN HEMT 20-element small-signal model, an improved particle swarm algorithm is proposed in this paper for the optimization of the intrinsic parameters. The conventional Particle Swarm Optimization (PSO) algorithm is prone to fall into local optimum solutions when parameter optimization is performed, in turn to affect the accuracy of experimental results. To solve the above problem, dynamic evolutionary estimation, elite learning strategies and adaptive strategies are added to the traditional PSO algorithm, in turn to yield Adaptive Particle Swarm Optimization (APSO) algorithm in this paper. The experimental results show that the situation of falling into a local optimum for the traditional PSO algorithm is greatly improved by the APSO algorithm, and that the model parameters of the GaN HEMT small-signal model can be extracted more accurately and faster in the frequency range of 0.5–20 GHz using the APSO algorithm.

A hybrid dipper throated optimization algorithm and particle swarm optimization (DTPSO) model for hepatocellular carcinoma (HCC) prediction

Hepatocellular carcinoma (HCC) is a form of liver cancer that is widespread in Europe, Africa, and Asia. The early identification of HCC is critical in improving the likelihood of survival, and as such, it is necessary to identify its distinct characteristics. Several algorithms have been developed to predict HCC early, and machine learning algorithms are essential in solving various classification and regression problems in different applications. In this paper, a hybrid machine learning model is presented for HCC prediction that merges the Naive Bayes (NB), Random Forest (RF), Logistic Regression (LR), Linear Discriminant Analysis (LDA) models with a Deep Neural Network (DNN) as a meta-model. The paper proposes a new algorithm for HCC prediction, the hybrid Dipper Throated Optimization and Particle Swarm Optimization (DTPSO), which combines the advantages of both DTO and PSO algorithms to obtain the best solution. The dataset employed in this research comprises 165 cases and 50 features, including 49 predictors and one target feature. Data cleaning, random oversampling, and data normalization were performed to prepare the data for additional processing. The effectiveness of the proposed DTPSO-based model is evaluated using evaluation metrics such as accuracy, Matthew's correlation coefficient (MCC), F1 score, sensitivity, specificity, and area under the receiver operating characteristic curve (AUC). The outcomes showed that the DTPSO-based model outperformed both the blending-based ensemble machine learning model and the conventional DTO and PSO algorithms. In the experiments, the accuracy of the blending-based model was 96.00%, whereas the accuracy of the DTPSO-based model was 98.52%. The accuracy rates for the DTO, whale optimization algorithm (WOA), grey wolf optimizer (GWO), and PSO algorithms are 96.25%, 94.81%, 95.77%, and 97.44%, respectively.

Inversion of TEM measurement data via a quantum particle swarm optimization algorithm with the elite opposition-based learning strategy

The fine interpretation and inversion of transient electromagnetic method measurement data have the problems of nonlinearity, multi-solution, and ill condition. However, the conventional particle swarm optimization (PSO) nonlinear inversion methods suffer from prematurity, slow convergence, and low calculation accuracy. To solve these problems, a quantum PSO (QPSO) algorithm based on the elite opposition-based learning (EOL) strategy is proposed. Firstly, three performances tests of the EOL-QPSO algorithm are carried out with Peaks, Schaffer and Rastrigin functions. The results show that the EOL-QPSO algorithm has excellent solution accuracy, efficient calculation speed and balanced exploitation and exploration capability. Secondly, the conventional PSO algorithm and the EOL-QPSO algorithm are used to compare the inversion of the theoretical model and the synthetic data with noise, and combined with Bayesian method, the posterior model probability statistics of the synthetic data are carried out. The research shows that the EOL-QPSO inversion algorithm is improved in terms of calculation accuracy, calculation efficiency, anti-noise performance and exploitation and exploration capability, and it can accurately obtain the posterior estimates of the real model. Finally, the inversion of field-measured data demonstrates that the EOL-PSO inversion method accurately reflects the position of the water-accumulated goaf.