Comprehensive Learning Particle Swarm Optimization Research Articles

Predicting anti-trypanosome effect of carbazole-derived compounds by powerful SVM with novel kernel function and comprehensive learning PSO.

In order to predict the anti-trypanosome effect of carbazole-derived compounds by quantitative structure-activity relationship, five models were established by the linear method, random forest, radial basis kernel function support vector machine, linear combination mix-kernel function support vector machine, and nonlinear combination mix-kernel function support vector machine (NLMIX-SVM). The heuristic method and optimized CatBoost were used to select two different key descriptor sets for building linear and nonlinear models, respectively. Hyperparameters in all nonlinear models were optimized by comprehensive learning particle swarm optimization with low complexity and fast convergence. Furthermore, the models' robustness and reliability underwent rigorous assessment using fivefold and leave-one-out cross-validation, y-randomization, and statistics including concordance correlation coefficient (CCC), [Formula: see text] , [Formula: see text] , and [Formula: see text] . Among all the models, the NLMIX-SVM model, which was established by support vector regression using a nonlinear combination of radial basis kernel function, sigmoid kernel function, and linear kernel function as a new kernel function, demonstrated excellent learning and generalization abilities as well as robustness: [Formula: see text] = 0.9581, mean square error (MSE) = 0.0199 for the training set and [Formula: see text] = 0.9528, MSE = 0.0174 for the test set. [Formula: see text] , [Formula: see text] , CCC, [Formula: see text] , [Formula: see text], and [Formula: see text] are 0.9539, 0.8908, 0.9752, 0.9529, 0.9528, and 0.9633, respectively. The NLMIX-SVM method proved to be a promising way in quantitative structure-activity relationship research. In addition, molecular docking experiments were conducted to analyze the properties of new derivatives, and a new potential candidate drug molecule was ultimately found. In summary, this study will provide help for the design and screening of novel anti-trypanosome drugs.

Comprehensive Learning Particle Swarm Optimization Based on Optimal Particle Recombination

Particle swarm optimization (PSO) algorithm has been widely used in large-scale complex problems such as resource allocation in recent years because of its simple implementation and easy operation. However, the slow convergence speed and low solution accuracy of the algorithm also restrict its further application. To solve the above problems, this paper introduces the chromosome crossing characteristics of genetic algorithm (GA), and proposes a comprehensive learning particle swarm optimization based on optimal particle recombination. With the help of the ability of comprehensive learning strategy to efficiently explore the solution space, this method organically combines the excellent information explored by each particle through the optimal particle recombination, so as to obtain a better individual, speed up the convergence speed of the algorithm, and improve the solution accuracy of the problem. The experimental results of benchmark function show that the proposed algorithm has faster convergence speed and optimization accuracy than the original algorithm, and the results of Friedman test and Wilcoxon signed-rank test prove the feasibility of the optimal particle recombination operation in particle swarm optimization.

Fractional-order modified heterogeneous comprehensive learning particle swarm optimizer for intelligent disease detection in IoMT environment

This paper presents an alternative early disease detection technique based on the Internet of Medical Things (IoMT) to improve the healthcare system. Since it is necessary to address different aspects to help healthcare organizations to improve their efficiency. Early disease detection using a fast and efficient test, such as chest X-ray images, is one of the most important issues. In this paper, we develop an efficient model to allocate abnormalities in medical chest X-ray images. The developed model consists of a set of stages; the first stage is to segment the images using a multilevel thresholding technique to determine the lung inside the image, then extracting the features from the segmented objects using different extractor methods. Then, we proposed a Fractional-order modified Heterogeneous comprehensive learning particle swarm optimizer (FMHCLPSO) as a feature selection method to determine the relevant features used to improve the detection process. To evaluate the performance of the developed IoMT model, a set of three medical datasets is used, called Covid-19 & Pneumonia, X-raycovid, and Radiography. The results illustrate the high efficiency of the developed model to detect diseases based on performance measures. Furthermore, We compared the proposed method to several existing methods, and it showed significant performance.

A neighborhood comprehensive learning particle swarm optimization for the vehicle routing problem with time windows

Vehicle routing problem with time windows (VRPTW), which is a typical NP-hard combinatorial optimization problem, plays an important role in modern logistics and transportation systems. Recent years, heuristic and meta-heuristic algorithms have attracted many researchers’ attentions to solve the VRPTW problems. As an outstanding meta-heuristic algorithm, particle swarm optimization (PSO) algorithm exhibits very promising performance on continuous problems. However, how to adapt PSO to efficiently deal with VRPTW is still challenging work. In this paper, we propose a neighborhood comprehensive learning particle swarm optimization (N-CLPSO) to solve VRPTW. To improve the exploitation capability of N-CLPSO, we introduce a new remove-reinsert neighborhood search mechanism, which consists of the removed operator and the reinsert operator. When performing the removed operator, the probability of adjacency between two customers is calculated by an information matrix (IM), which is constructed based on the customers’ time-space information and elite individuals’ local information. When executing the reinsert operator, the IM and a cost matrix (CM), which is introduced to record the cost of customer insertion, are used to find an optimal insert position. Moreover, to enhance the exploration of N-CLPSO, a semi-random disturbance strategy is proposed, in which elites’ longest common sequences (LCS) are saved, aiming to prevent population degradation. The N-CLPSO algorithm is tested on 56 Solomon benchmark instances, and it attains the optimal solutions on 29 instances. The simulation results and comparison results illustrate that the proposed algorithm outperforms or can compete with the majority of other 3 PSO variants as well as other 12 state-of-the-art algorithms.

Recuperation based multi-objective generation expansion planning for a real-world power system

This paper proposed a multi-objective-based Generation Expansion Planning (GEP) for the real-word power generation system of Tamil Nadu, an Indian state. GEP aims to solve numerous conflicting problems for constructing new power plants. The proposed approaches are Multi-Objective Comprehensive Learning Particle Swarm Optimization (MOCLPSO) and Circle Search algorithm. The key objectives of the proposed method is to reduce budget, to maximize reliability and to minimize the pollutant discharge. Therefore, the apt formulations are modeled and solved to establish the conflicting facets of GEP problem. This paper implements MOCLPSO algorithm to solve Multi-Objective GEP (MOGEP) problem for 7-year and 14-year planning horizon. By then, the proposed model is implemented at MATLAB/Simulink platform and the implementation is calculated. The proposed method shows better results in all approaches like Seagull Optimization Algorithm (SOA), Particle Swarm Optimization (PSO) and Cuckoo Search algorithm. The outcomes establish the competence of MOCLPSO and Circle Search Algorithm to offer good-ranged Pareto optimal non-dominated solutions.

A Novel Black Widow Optimized Controller Approach for Automatic Generation Control in Modern Hybrid Power Systems

This research paper demonstrates an application of the Black Widow Optimization (BWO) approach to address the issue of load-frequency control (LFC) in networked power systems. BWO is an innovative metaheuristic method that quickly suggests technique is initially evaluated on a non-reheat thermal-thermal (NRTT) power system spanning two areas of interconnection, and then it is applied to two different actual power systems: (a) a two-area thermal-thermal considering Generation Rate Constraint (GRC); and (b) a two-area having thermal, hydro, wind, solar, and gas systems. The BWO method uses two fitness functions based on integral time multiplied absolute error (ITAE) and integral square error (ISE) to optimize controller gains. The suggested BWO algorithm's performance has been compared to that of existing meta-heuristic optimization methods, such as grey wolf optimization (GWO), comprehensive learning particle swarm optimization (CLPSO), and an ensemble of parameters in differential evolution (EPSDE). The simulation results show that BWO's tuning skills are better than other population-based planning methods like CLPSO, EPSDE, and GWO. The ITAE value is enhanced by 33.28% (GWO), 40.28% (EPSDE), and 43.27% (CLPSO) when the BWO algorithm is used in conjunction with the PID Controller for thermal system.

Chaotic heterogeneous comprehensive learning PSO method for size and shape optimization of structures

This paper proposes a novel chaotic heterogeneous comprehensive learning particle swarm optimization (CLPSO) method for the simultaneous size and shape design of structures. The heterogeneous CLPSO divides the particles into two explorative and exploitative subpopulations. The exploration performs the global searches for the set of best particles experienced solely within its own subpopulation, whilst the exploitation refines the deep searches learnt from the global best particle over an entire population. In essence, the proposed method maintains a good balance between the global explorative and local exploitative optimization schemes. The global searches within the explorative subpopulation are independent to the exploitative simulations even if the latter scheme prematurely converges to the local swarm position. For both subpopulations, the comprehensive learning approach constructs the particles through a cross-positioning process on the individual variable space and avoids the local optimal pitfall. Moreover, the chaotic logistic map within the exploitative optimization tests the global best particle through the set of diversely generated samples and hence enhances the local search ability. Various enriching techniques, including automatic adaptive (inertial weight and acceleration) parameters with dynamic space reduction, are incorporated to improve the likelihood of finding the optimal solution of practical-scale problems at modest computing efforts. The accuracy and robustness of the proposed method are illustrated through a number of planar and spatial truss design benchmarks subjected to the challenging nonconvex and/or nonsmooth programs.

Binary Comprehensive Learning Particle Swarm Optimization Approach for Optimal Design of Nonlinear Steel Structures with Standard Sizes

This paper proposes the binary comprehensive learning particle swarm optimization (BCLPSO) method to determine the optimal design for nonlinear steel structures, adopting standard member sizes. The design complies with the AISC-LRFD standard specifications. Moreover, the sizes and layouts of cross-brace members, appended to the steel frames, are simultaneously optimized. Processing this design is as challenging as directly solving the nonlinear integer programming problem, where any solution approaches are often trapped into local optimal pitfalls or even do not converge within finite times. Herein, the BCLPSO method incorporates not only a comprehensive learning technique but also adopts a decoding process for discrete binary variables. The former ascertains the cross-positions among the sets of best swarm particles at each dimensional space. The latter converts design variables into binary bit-strings. This practice ensures that local optimal searches and premature termination during optimization can be overcome. The influence of an inertial weight parameter on the BCLPSO approach is investigated, where the value of 0.98 is recommended. The accuracy and robustness of the proposed method are illustrated through several benchmarks and practical structural designs. These indicate that the lowest minimum total design weight (some 3% reduction as compared to the benchmark) can be achieved of about 40% lower than the total number of analyses involved.

Rumors Suppression in Healthcare System: Opinion-Based Comprehensive Learning Particle Swarm Optimization

The rumors in the healthcare system have the attributes of fast spread and severe social influence. Even worse, it may cause the collapse of medical services and the death of many patients. To prevent its serious impact on society, the target of rumor suppression for the healthcare system is to restrain the spread of rumors (negative opinions) and maximize the spread of antirumors (positive opinions). Therefore, in this article, for the first time, we propose comprehensive learning-based particle swarm optimization with opinion maximization (OM) to address the rumors suppression problem in the healthcare system. We define the rumor suppression problem in the healthcare system based on OM and devise two opinion propagation models. Then, we propose a directed acyclic graph-based objective function to evaluate the opinion propagation and solve this problem using comprehensive learning particle swarm optimization. Experimental results show that our proposed scheme achieves better results for positive opinion propagation in the scenario of rumor suppression in the healthcare system than the baseline algorithms.

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.

Harris Hawks Optimization-Based Clustering Algorithm for Vehicular Ad-Hoc Networks

Vehicular ad-hoc network (VANET) is highly dynamic due to the high speed and sparse distribution of vehicles on the road. This creates major challenges (e.g., network fragmentation, packet routing) for the researchers to enable robust, reliable, and scalable communication, especially in a highly dense network. Clustering in VANET is one of the remedies to address the scalability issue. However, it is observed in the literature, that existing clustering techniques produce a high number of clusters for the vehicular environment. Consequently, it increases the consumption of scarce resources in a wireless network. Furthermore, it also increases the communication overhead as well as the number of hops for data routing. As a result communication latency also increases and the reliability of communication protocol decreases. So it is highly desirable to find out the optimal clusters for a given vehicular environment. As finding optimal clusters is a multi-objective combinatorial optimization problem, therefore by employing nature-inspired meta-heuristic algorithms we can optimize the multi-objective problem. To this end, we proposed a novel clustering algorithm based on the Harris Hawks Optimization (HHO) algorithm for VANET (HHOCNET). HHO algorithm is a nature-inspired meta-heuristic algorithm inspired by the foraging maneuver of hawks called surprise pounce. The proposed framework imitates the cooperative foraging maneuver of hawks (i.e., surprise pounce for creating optimized vehicular clusters). The stochastic operators of the HHO algorithm and proper maintenance of the equilibrium state between the operations of exploration and exploitation enable the proposed algorithm to escape from the local optima and provide a globally optimal solution (i.e., the optimal number of vehicular clusters). Simulations are performed in MATLAB and the results are compared with the state-of-art schemes (i.e., Gray Wolf optimization-based clustering algorithm (GWOCNET), Multi-objective Particle Swarm Optimization (MO, PSO), and Comprehensive Learning Particle Swarm Optimization (CLPSO)) using different performance metrics. The results demonstrate that the proposed approach is an effective approach for clustering in VANET and outer performs the other benchmark algorithms in terms of optimizing the multi-objective clustering problem. HHOCNET algorithm selects 36.04% of nodes as cluster heads while the existing state-of-the-art schemes are providing 50.42%, 56.7%, and 60.89% for GWOCNET, CLPSO, and Multi-objective Particle Swarm Optimization (MOPSO). The proposed HHOCNET algorithm enhances the performance of the vehicular network by up to 15%. Consequently, it increases network efficiency by reducing the consumption of the required wireless resources. It also reduces the number of hops for packet routing. Hence it achieves a minimum end-to-end communication latency.

Multi-Objective Based Generation Expansion Planning for Utility Power System of Tamil Nadu State Considering Recuperation of Older Power Plants

Generation Expansion Planning (GEP) is a problem that comprises multiple contradictory features while planning to construct new generating units. It must be solved by considering cost, reliability and environmental emission. Hence the mathematical representations have been developed to be accurate, and to improve the understanding of the multifaceted and contradictory aspects of the GEP problem. In this study, the Multi-Objective Comprehensive Learning Particle Swarm Optimization (MOCLPSO) algorithm is implemented for solving Multi-Objective GEP (MOGEP) problem. The objectives such as minimization of overall cost, decrement of the pollutant emission and enhancement of reliability have been considered by considering the constraints. The real-world MOGEP problem has been solved for seven-year (from the year 2020 to 2027) and fourteen-year (from the year 2020 to 2034) planning span for the utility power system of Tamil Nadu state, India. The problem is solved for four different cases with the consideration of retirement and recuperation of the older generating units. coal, gas, oil, nuclear, hydel, wind, Solar-photovoltaic (SPV) and biomass power plants were considered in this planning study. The results establish the competence of MOCLPSO to produce well-spread Pareto optimal non-dominated solutions of the MOGEP problem.

Identification of heat transfer coefficients in continuous casting by a GPU-based improved comprehensive learning particle swarm optimization algorithm

The heat transfer coefficients (HTCs) of the secondary cooling zone (SCZ) are a critical boundary condition for numerical modeling of solidification heat transfer in the continuous casting process. However, it is difficult to identify accurately these HTCs. Due to the high computational complexity, the computation time in the identification process is not negligible, especially during the process of optimization and heat transfer model solution. To solve those problems, we first developed an improved comprehensive learning particle swarm optimization algorithm (ICL-PSO) to identify more accurate HTCs in the SCZ of continuous casting. Secondly, a two-layer parallel algorithm that implements ICL-PSO on a graphics processing unit (GPU) was then designed and tested to reduce the computation time of identifying these HTCs. Finally, the experimental results show that the accuracy of the proposed algorithm for HTC identification and the efficiency of GPU-accelerated computation have been improved.

Sequential most probable point update combining Gaussian process and comprehensive learning PSO for structural reliability-based design optimization

This paper proposes an efficient reliability-based design optimization (RBDO) method that advantageously decouples comprehensive learning particle swarm optimization (CLPSO) algorithm with Gaussian process regression (GPR) model, termed as GPR-CLPSO. The method iteratively performs the CLPSO with deterministic parameters based on the most probable point (MPP) underpinning limit-state functions (LSFs) iteratively updated by the active learning reliability evaluation process. The GPR model approximates, from the design data given by CLPSO, the spectrum of LSFs under random parameters, and hence enables a significant computational reduction of Monte-Carlo simulations (MCSs) for failure probability approximation. The expected feasibility function is maximized using the CLPSO code to systematically refine the GPR model by adaptively adding new (intelligent) learning points in the region with high-reliability sensitivity leading to the more accurate prediction of failure probability. A novel inverse MCS constraint boundary method is developed to redefine the MPP assigned for the CLPSO algorithm in determining the new optimal design. The method efficiently leverages the decoupling approach, whilst significantly alleviating computing efforts, to quickly and accurately capture the optimal RBDO design. The resulting failure probability well satisfies the allowable limit. Four RBDO examples are provided to illustrate applications and robustness of the proposed decoupling GPR-CLPSO approach.

Cooperative path planning optimization for multiple UAVs with communication constraints

Path planning is a complicated optimization problem that is crucial for the safe flight of unmanned aerial vehicles (UAVs). Especially in the scenarios involving multiple UAVs, this problem is highly challenging due to the constraints of complex environments, various tasks and inherent UAV maneuverability. In this paper, a cooperative path planning model for multiple UAVs is presented. In addition to common limitations such as the path length minimization, UAV maneuverability limitation and collision avoidance, the communication requirements between UAVs and the impact of obstacles in the flight environment on the quality of communication are also taken into account in the presented path planning model. On this basis, the corresponding objective function is designed. Then, an improved particle swarm optimization (PSO) algorithm is proposed to solve the above path planning problem. Utilizing the ideas of the dynamic multi-swarm PSO (DMSPSO) algorithm and the comprehensive learning PSO (CLPSO) algorithm, the proposed algorithm, denoted as CL-DMSPSO, further improves the performance of both algorithms. The effectiveness and superiority of the novel CL-DMSPSO algorithm is verified on benchmark functions, especially for complex multimodal functions. Finally, we present an effective path planning method using CL-DMSPSO to generate optimized flyable paths for multiple UAVs. And simulation and comparison results on the designed scenario indicate the proposed UAV path planning method can efficiently plan high-quality paths for UAVs and demonstrate the advantages of the proposed CL-DMSPSO algorithm compared with other PSO algorithms in UAV path planning.

Combined Gaussian Local Search and Enhanced Comprehensive Learning PSO Algorithm for Size and Shape Optimization of Truss Structures

This paper proposes the use of enhanced comprehensive learning particle swarm optimization (ECLPSO), combined with a Gaussian local search (GLS) technique, for the simultaneous optimal size and shape design of truss structures under applied forces and design constraints. The ECLPSO approach presents two novel enhancing techniques, namely perturbation-based exploitation and adaptive learning probability, in addition to its distinctive diversity of particles. This prevents the premature convergence of local optimal solutions. In essence, the perturbation enables the robust exploitation in the updating velocity of particles, whilst the learning probabilities are dynamically adjusted by ranking information on the personal best particles. Based on the results given by ECLPSO, the GLS technique takes data from the global best particle and personal best particles in the last iteration to generate samples from a Gaussian distribution to improve convergence precision. A combination of these techniques results in the fast convergence and likelihood to obtain the optimal solution. Applications of the combined GLS-ECLPSO method are illustrated through several successfully solved truss examples in two- and three-dimensional spaces. The robustness and accuracy of the proposed scheme are illustrated through comparisons with available benchmarks processed by other meta-heuristic algorithms. All examples show simultaneous optimal size and shape distributions of truss structures complying with limit state design specifications.

Intelligent algorithms for six degrees of freedom robot trajectory planning considering vibration suppression

The residual vibration of the flexible joint manipulator during and after the movement will seriously affects the positioning accuracy of the manipulator. This paper discusses the trajectory planning method for suppressing the joint vibration. A trajectory optimal model which contains the minimization of both time and jerk was proposed. An optimization method based on comprehensive learning particle swarm optimization (CLPSO) algorithm was utilized for solving the optimal problem. Compared with other optimal solution method, CLPLO has the advantages of avoiding premature convergence. A numerical simulation case shows that the optimal trajectory obtained in this paper generated less joint vibration. The effectiveness of the proposed method was verified to some extent.

Design of fractional comprehensive learning PSO strategy for optimal power flow problems

Optimal reactive power dispatch (ORPD) is one of the paramount issue for the researchers during the investigation of power system performance in dynamic load scenarios. In this paper, a new nature inspired computing paradigm based on fractional order comprehensive learning particle swarm optimization (FO-CLPSO) is designed and implemented for solving the reactive power dispatch problems. The objective of the study is to improve the power system efficiency by reducing line losses, enhancing bus voltage profiles and reducing the operating cost of the system for different load factors. The decision variables for the fitness evaluation are the tap changer settings, generator bus voltages, fixed capacitors and flexible AC transmission systems (FACTS). The operation, validity and scalability of the FO-CLPSO are tested on standard IEEE 30 bus and IEEE-57 bus systems. The exploitation and exploration for FO-CLPSO are further extended using different fractional orders for minimization problems in ORPD to critically analyze the performance by comparing with several state of art counterpart methodologies. The stability, consistency, robustness and reliability of FO-CLPSO for the solution of ORPD problems is also substantiated through detailed statistical analyses including the development of empirical cumulative distribution functions, probability plots, box plot illustrations and histograms both for precision and complexity metrics.

Optimized Machine Learning-Based Intrusion Detection System for Fog and Edge Computing Environment

As a new paradigm, fog computing (FC) has several characteristics that set it apart from the cloud computing (CC) environment. Fog nodes and edge computing (EC) hosts have limited resources, exposing them to cyberattacks while processing large streams and sending them directly to the cloud. Intrusion detection systems (IDS) can be used to protect against cyberattacks in FC and EC environments, while the large-dimensional features in networking data make processing the massive amount of data difficult, causing lower intrusion detection efficiency. Feature selection is typically used to alleviate the curse of dimensionality and has no discernible effect on classification outcomes. This is the first study to present an Effective Seeker Optimization model in conjunction with a Machine Learning-Enabled Intrusion Detection System (ESOML-IDS) model for the FC and EC environments. The ESOML-IDS model primarily designs a new ESO-based feature selection (FS) approach to choose an optimal subset of features to identify the occurrence of intrusions in the FC and EC environment. We also applied a comprehensive learning particle swarm optimization (CLPSO) with Denoising Autoencoder (DAE) for the detection of intrusions. The development of the ESO algorithm for feature subset selection and the DAE algorithm for parameter optimization results in improved detection efficiency and effectiveness. The experimental results demonstrated the improved outcomes of the ESOML-IDS model over recent approaches.

A multi-body dynamical evolution model for generating the point set with best uniformity

Generating the low-discrepancy point sets in high-dimensional space is an optimization problem which involves two issues: how to define the objective function of optimization, and how to optimize this optimization problem with tens of thousands of variables. Inspired by natural phenomena, we make two assumptions: the first is that the static solution to the multi-body problem is a low-discrepancy point set, and the second is that the discrepancy of bodies is the lowest when the potential energy is the smallest. Under these assumptions, the objective function is defined as the potential energy of the point set. A dynamical evolutionary model (DEM) based on the minimum potential energy principle is established to construct low-discrepancy point sets. The central difference algorithm is adopted to solve the DEM and the selection of coefficients to ensure the convergence is discussed in detail. Numerical examples confirm the assumption that there is a significant positive correlation between the potential energy and the discrepancy. We also combine the DEM with the restarting technique to generate a series of low-discrepancy point sets. These point sets are unbiased and perform better than other low-discrepancy point sets in terms of the discrepancy, the potential energy, integrating eight test functions and computing the statistical moments for two practical stochastic problems. Numerical examples also show that the DEM can generate uniformly distributed point sets in non-cubes. More interestingly, it is observed that the DEM point sets can greatly improve the convergence speed of the heterogeneous comprehensive learning particle swarm optimization.