Deep neural networks are increasingly exposed to attack threats,and at the same time,the need for privacy protection is growing.As a result,the challenge of developing neural networks that are both robust and capable ...Deep neural networks are increasingly exposed to attack threats,and at the same time,the need for privacy protection is growing.As a result,the challenge of developing neural networks that are both robust and capable of strong generalization while maintaining privacy becomes pressing.Training neural networks under privacy constraints is one way to minimize privacy leakage,and one way to do this is to add noise to the data or model.However,noise may cause gradient directions to deviate from the optimal trajectory during training,leading to unstable parameter updates,slow convergence,and reduced model generalization capability.To overcome these challenges,we propose an optimization algorithm based on double-integral coevolutionary neurodynamics(DICND),designed to accelerate convergence and improve generalization in noisy conditions.Theoretical analysis proves the global convergence of the DICND algorithm and demonstrates its ability to converge to near-global minima efficiently under noisy conditions.Numerical simulations and image classification experiments further confirm the DICND algorithm's significant advantages in enhancing generalization performance.展开更多
Heuristic optimization algorithms have been widely used in solving complex optimization problems in various fields such as engineering,economics,and computer science.These algorithms are designed to find high-quality ...Heuristic optimization algorithms have been widely used in solving complex optimization problems in various fields such as engineering,economics,and computer science.These algorithms are designed to find high-quality solutions efficiently by balancing exploration of the search space and exploitation of promising solutions.While heuristic optimization algorithms vary in their specific details,they often exhibit common patterns that are essential to their effectiveness.This paper aims to analyze and explore common patterns in heuristic optimization algorithms.Through a comprehensive review of the literature,we identify the patterns that are commonly observed in these algorithms,including initialization,local search,diversity maintenance,adaptation,and stochasticity.For each pattern,we describe the motivation behind it,its implementation,and its impact on the search process.To demonstrate the utility of our analysis,we identify these patterns in multiple heuristic optimization algorithms.For each case study,we analyze how the patterns are implemented in the algorithm and how they contribute to its performance.Through these case studies,we show how our analysis can be used to understand the behavior of heuristic optimization algorithms and guide the design of new algorithms.Our analysis reveals that patterns in heuristic optimization algorithms are essential to their effectiveness.By understanding and incorporating these patterns into the design of new algorithms,researchers can develop more efficient and effective optimization algorithms.展开更多
The optimization of reaction processes is crucial for the green, efficient, and sustainable development of the chemical industry. However, how to address the problems posed by multiple variables, nonlinearities, and u...The optimization of reaction processes is crucial for the green, efficient, and sustainable development of the chemical industry. However, how to address the problems posed by multiple variables, nonlinearities, and uncertainties during optimization remains a formidable challenge. In this study, a strategy combining interpretable machine learning with metaheuristic optimization algorithms is employed to optimize the reaction process. First, experimental data from a biodiesel production process are collected to establish a database. These data are then used to construct a predictive model based on artificial neural network (ANN) models. Subsequently, interpretable machine learning techniques are applied for quantitative analysis and verification of the model. Finally, four metaheuristic optimization algorithms are coupled with the ANN model to achieve the desired optimization. The research results show that the methanol: palm fatty acid distillate (PFAD) molar ratio contributes the most to the reaction outcome, accounting for 41%. The ANN-simulated annealing (SA) hybrid method is more suitable for this optimization, and the optimal process parameters are a catalyst concentration of 3.00% (mass), a methanol: PFAD molar ratio of 8.67, and a reaction time of 30 min. This study provides deeper insights into reaction process optimization, which will facilitate future applications in various reaction optimization processes.展开更多
High-dimensional and incomplete(HDI) matrices are commonly encountered in various big data-related applications for illustrating the complex interactions among numerous entities, like the user-item interactions in a c...High-dimensional and incomplete(HDI) matrices are commonly encountered in various big data-related applications for illustrating the complex interactions among numerous entities, like the user-item interactions in a commercial recommender system or the user-user interactions in a social network services system. The factorization of such an HDI matrix can embed the involved entities into the low-dimensional feature space for acquiring their principal representation, which is a vital task in various application scenes and is often established through the Latent Factor Analysis(LFA). Nevertheless, an HDI matrix can be huge when the corresponding application explodes to involve millions of users, items, or other interactive nodes. In this case, a parallel optimization algorithm is desired for raising the scalability and time efficiency of an LFA model. This paper provides a comprehensive review of the existing parallel optimization algorithms for the LFA model. Specifically, it performs: 1) discussion and summary of these algorithms based on computing architecture and mode, 2) empirical studies of representative models, and3) summary of the current challenges and future directions in this domain. This survey aims to offer an exhaustive review of Parallel Optimization Algorithms for High-Dimensional and Incomplete Matrix Factorization, thereby fostering further research in this field.展开更多
Storm identification and tracking based on weather radar data are essential to nowcasting and severe weather warning. A new two-dimensional storm identification method simultaneously seeking in two directions is propo...Storm identification and tracking based on weather radar data are essential to nowcasting and severe weather warning. A new two-dimensional storm identification method simultaneously seeking in two directions is proposed, and identification results are used to discuss storm tracking algorithms. Three modern optimization algorithms (simulated annealing algorithm, genetic algorithm and ant colony algorithm) are tested to match storms in successive time intervals. Preliminary results indicate that the simulated annealing algorithm and ant colony algorithm are effective and have intuitionally adjustable parameters, whereas the genetic algorithm is unsatisfaetorily constrained by the mode of genetic operations Experiments provide not only the feasibility and characteristics of storm tracking with modern optimization algorithms, but also references for studies and applications in relevant fields.展开更多
Real-world engineering design problems with complex objective functions under some constraints are relatively difficult problems to solve.Such design problems are widely experienced in many engineering fields,such as ...Real-world engineering design problems with complex objective functions under some constraints are relatively difficult problems to solve.Such design problems are widely experienced in many engineering fields,such as industry,automotive,construction,machinery,and interdisciplinary research.However,there are established optimization techniques that have shown effectiveness in addressing these types of issues.This research paper gives a comparative study of the implementation of seventeen new metaheuristic methods in order to optimize twelve distinct engineering design issues.The algorithms used in the study are listed as:transient search optimization(TSO),equilibrium optimizer(EO),grey wolf optimizer(GWO),moth-flame optimization(MFO),whale optimization algorithm(WOA),slimemould algorithm(SMA),harris hawks optimization(HHO),chimp optimization algorithm(COA),coot optimization algorithm(COOT),multi-verse optimization(MVO),arithmetic optimization algorithm(AOA),aquila optimizer(AO),sine cosine algorithm(SCA),smell agent optimization(SAO),and seagull optimization algorithm(SOA),pelican optimization algorithm(POA),and coati optimization algorithm(CA).As far as we know,there is no comparative analysis of recent and popular methods against the concrete conditions of real-world engineering problems.Hence,a remarkable research guideline is presented in the study for researchersworking in the fields of engineering and artificial intelligence,especiallywhen applying the optimization methods that have emerged recently.Future research can rely on this work for a literature search on comparisons of metaheuristic optimization methods in real-world problems under similar conditions.展开更多
To protect trains against strong cross-wind along Qinghai-Tibet railway, a strong wind speed monitoring and warning system was developed. And to obtain high-precision wind speed short-term forecasting values for the s...To protect trains against strong cross-wind along Qinghai-Tibet railway, a strong wind speed monitoring and warning system was developed. And to obtain high-precision wind speed short-term forecasting values for the system to make more accurate scheduling decision, two optimization algorithms were proposed. Using them to make calculative examples for actual wind speed time series from the 18th meteorological station, the results show that: the optimization algorithm based on wavelet analysis method and improved time series analysis method can attain high-precision multi-step forecasting values, the mean relative errors of one-step, three-step, five-step and ten-step forecasting are only 0.30%, 0.75%, 1.15% and 1.65%, respectively. The optimization algorithm based on wavelet analysis method and Kalman time series analysis method can obtain high-precision one-step forecasting values, the mean relative error of one-step forecasting is reduced by 61.67% to 0.115%. The two optimization algorithms both maintain the modeling simple character, and can attain prediction explicit equations after modeling calculation.展开更多
The vehicle routing problem(VRP)is a typical discrete combinatorial optimization problem,and many models and algorithms have been proposed to solve the VRP and its variants.Although existing approaches have contribute...The vehicle routing problem(VRP)is a typical discrete combinatorial optimization problem,and many models and algorithms have been proposed to solve the VRP and its variants.Although existing approaches have contributed significantly to the development of this field,these approaches either are limited in problem size or need manual intervention in choosing parameters.To solve these difficulties,many studies have considered learning-based optimization(LBO)algorithms to solve the VRP.This paper reviews recent advances in this field and divides relevant approaches into end-to-end approaches and step-by-step approaches.We performed a statistical analysis of the reviewed articles from various aspects and designed three experiments to evaluate the performance of four representative LBO algorithms.Finally,we conclude the applicable types of problems for different LBO algorithms and suggest directions in which researchers can improve LBO algorithms.展开更多
Traditional laboratory tests for measuring rock uniaxial compressive strength(UCS)are tedious and timeconsuming.There is a pressing need for more effective methods to determine rock UCS,especially in deep mining envir...Traditional laboratory tests for measuring rock uniaxial compressive strength(UCS)are tedious and timeconsuming.There is a pressing need for more effective methods to determine rock UCS,especially in deep mining environments under high in-situ stress.Thus,this study aims to develop an advanced model for predicting the UCS of rockmaterial in deepmining environments by combining three boosting-basedmachine learning methods with four optimization algorithms.For this purpose,the Lead-Zinc mine in Southwest China is considered as the case study.Rock density,P-wave velocity,and point load strength index are used as input variables,and UCS is regarded as the output.Subsequently,twelve hybrid predictive models are obtained.Root mean square error(RMSE),mean absolute error(MAE),coefficient of determination(R2),and the proportion of the mean absolute percentage error less than 20%(A-20)are selected as the evaluation metrics.Experimental results showed that the hybridmodel consisting of the extreme gradient boostingmethod and the artificial bee colony algorithm(XGBoost-ABC)achieved satisfactory results on the training dataset and exhibited the best generalization performance on the testing dataset.The values of R2,A-20,RMSE,and MAE on the training dataset are 0.98,1.0,3.11 MPa,and 2.23MPa,respectively.The highest values of R2 and A-20(0.93 and 0.96),and the smallest RMSE and MAE values of 4.78 MPa and 3.76MPa,are observed on the testing dataset.The proposed hybrid model can be considered a reliable and effective method for predicting rock UCS in deep mines.展开更多
Statistical distributions are used to model wind speed,and the twoparameters Weibull distribution has proven its effectiveness at characterizing wind speed.Accurate estimation of Weibull parameters,the scale(c)and sha...Statistical distributions are used to model wind speed,and the twoparameters Weibull distribution has proven its effectiveness at characterizing wind speed.Accurate estimation of Weibull parameters,the scale(c)and shape(k),is crucial in describing the actual wind speed data and evaluating the wind energy potential.Therefore,this study compares the most common conventional numerical(CN)estimation methods and the recent intelligent optimization algorithms(IOA)to show how precise estimation of c and k affects the wind energy resource assessments.In addition,this study conducts technical and economic feasibility studies for five sites in the northern part of Saudi Arabia,namely Aljouf,Rafha,Tabuk,Turaif,and Yanbo.Results exhibit that IOAs have better performance in attaining optimal Weibull parameters and provided an adequate description of the observed wind speed data.Also,with six wind turbine technologies rating between 1 and 3MW,the technical and economic assessment results reveal that the CN methods tend to overestimate the energy output and underestimate the cost of energy($/kWh)compared to the assessments by IOAs.The energy cost analyses show that Turaif is the windiest site,with an electricity cost of$0.016906/kWh.The highest wind energy output is obtained with the wind turbine having a rated power of 2.5 MW at all considered sites with electricity costs not exceeding$0.02739/kWh.Finally,the outcomes of this study exhibit the potential of wind energy in Saudi Arabia,and its environmental goals can be acquired by harvesting wind energy.展开更多
This paper systematically evaluates and compares three well-engineered and popular multi-objective optimization algorithms for the design of switched reluctance machines.The multi-physics and multi-objective nature of...This paper systematically evaluates and compares three well-engineered and popular multi-objective optimization algorithms for the design of switched reluctance machines.The multi-physics and multi-objective nature of electric machine design problems are discussed,followed by benchmark studies comparing generic algorithms(GA),differential evolution(DE)algorithms and particle swarm optimizations(PSO)on a 6/4 switched reluctance machine design with seven independent variables and a strong nonlinear multi-objective Pareto front.To better quantify the quality of the Pareto fronts,five primary quality indicators are employed to serve as the algorithm testing metrics.The results show that the three algorithms have similar performances when the optimization employs only a small number of candidate designs or ultimately,a significant amount of candidate designs.However,DE tends to perform better in terms of convergence speed and the quality of Pareto front when a relatively modest amount of candidates are considered.展开更多
A multi-strategy hybrid whale optimization algorithm(MSHWOA)for complex constrained optimization problems is proposed to overcome the drawbacks of easily trapping into local optimum,slow convergence speed and low opti...A multi-strategy hybrid whale optimization algorithm(MSHWOA)for complex constrained optimization problems is proposed to overcome the drawbacks of easily trapping into local optimum,slow convergence speed and low optimization precision.Firstly,the population is initialized by introducing the theory of good point set,which increases the randomness and diversity of the population and lays the foundation for the global optimization of the algorithm.Then,a novel linearly update equation of convergence factor is designed to coordinate the abilities of exploration and exploitation.At the same time,the global exploration and local exploitation capabilities are improved through the siege mechanism of Harris Hawks optimization algorithm.Finally,the simulation experiments are conducted on the 6 benchmark functions and Wilcoxon rank sum test to evaluate the optimization performance of the improved algorithm.The experimental results show that the proposed algorithm has more significant improvement in optimization accuracy,convergence speed and robustness than the comparison algorithm.展开更多
In this paper, we develop a new theoretical framework by means of the absorbing Markov process theory for analyzing some stochastic global optimization algorithms. Applying the framework to the pure random search, we ...In this paper, we develop a new theoretical framework by means of the absorbing Markov process theory for analyzing some stochastic global optimization algorithms. Applying the framework to the pure random search, we prove that the pure random search converges to the global minimum in probability and its time has geometry distribution. We also analyze the pure adaptive search by this framework and turn out that the pure adaptive search converges to the global minimum in probability and its time has Poisson distribution.展开更多
Optimization is the key to obtaining efficient utilization of resources in structural design.Due to the complex nature of truss systems,this study presents a method based on metaheuristic modelling that minimises stru...Optimization is the key to obtaining efficient utilization of resources in structural design.Due to the complex nature of truss systems,this study presents a method based on metaheuristic modelling that minimises structural weight under stress and frequency constraints.Two new algorithms,the Red Kite Optimization Algorithm(ROA)and Secretary Bird Optimization Algorithm(SBOA),are utilized on five benchmark trusses with 10,18,37,72,and 200-bar trusses.Both algorithms are evaluated against benchmarks in the literature.The results indicate that SBOA always reaches a lighter optimal.Designs with reducing structural weight ranging from 0.02%to 0.15%compared to ROA,and up to 6%–8%as compared to conventional algorithms.In addition,SBOA can achieve 15%–20%faster convergence speed and 10%–18%reduction in computational time with a smaller standard deviation over independent runs,which demonstrates its robustness and reliability.It is indicated that the adaptive exploration mechanism of SBOA,especially its Levy flight–based search strategy,can obviously improve optimization performance for low-and high-dimensional trusses.The research has implications in the context of promoting bio-inspired optimization techniques by demonstrating the viability of SBOA,a reliable model for large-scale structural design that provides significant enhancements in performance and convergence behavior.展开更多
The artificial immune algorithm is an intelligent optimization algorithm derived from the working mechanism of biological immune systems. It simulates immune response processes including biological antigen recognition...The artificial immune algorithm is an intelligent optimization algorithm derived from the working mechanism of biological immune systems. It simulates immune response processes including biological antigen recognition, antibody generation, clonal selection, immune memory, and immune suppression, and searches for optimal solutions through iterative population evolution. In recent years, artificial immune algorithms have been gradually applied in various fields such as industrial optimization, artificial intelligence, smart cities, and automatic control, showing favorable application value in scenarios including multi-objective constrained optimization, dynamic system scheduling, fault feature identification, and adaptive parameter tuning. However, with the continuous increase in the complexity of application scenarios, the inherent defects of classic artificial immune algorithms have become prominent. On this basis, based on the basic framework of artificial immune algorithms, this paper comprehensively analyzes the core key problems in algorithm operation and constructs a multi-dimensional and highly adaptive algorithm optimization system, aiming to provide comprehensive support for iterative optimization and scenario-based implementation of artificial immune algorithms.展开更多
A novel intelligent optimization algorithm inspired by nature,called sea otter optimization algorithm(SOOA),is proposed.The SOOA simulates the natural behaviors of sea otters,such as using tactile senses to search for...A novel intelligent optimization algorithm inspired by nature,called sea otter optimization algorithm(SOOA),is proposed.The SOOA simulates the natural behaviors of sea otters,such as using tactile senses to search for food in seawater,grooming their fur,feeding with the aid of stones,and escaping from danger.In the exploration stage,a wetness factor is introduced to control the behavior of sea otters in foraging and grooming;a danger factor is introduced to control the behavior of sea otters in feeding and avoiding dangers in the exploitation stage,and the behaviors of sea otters in responding to different dangers are mathematically modeled.The proposed algorithm is compared with 9 well-known intelligent optimization algorithms,and evaluated in 13 benchmark functions as well as wireless sensor network coverage optimization problems to verify the effectiveness of the proposed algorithm.The experimental results show that the node coverage after SOOA optimization reaches 91.2%in 2D environment and 90.47%in 3D environment.Compared with other algorithms,SOOA is superior and possesses the ability to solve complex optimization problems.展开更多
Dear Editor,With the rapid development of new-generation information and communication technology,the fusion of sensing,communication,computing,and control(S3C)is becoming increasingly significant for cyber-physical s...Dear Editor,With the rapid development of new-generation information and communication technology,the fusion of sensing,communication,computing,and control(S3C)is becoming increasingly significant for cyber-physical systems(CPS).However,due to the non-convexity,the curse of dimensionality,and the partial observability faced by CPS,traditional convex optimization algorithms are challenging to deal with S3C co-optimization.展开更多
Researchers continuously advance optimization algorithms,recognizing that no meta-heuristic can solve all problem types,as stated by the No Free Lunch theorem.This paper introduces the Propagation alongside Crossover(...Researchers continuously advance optimization algorithms,recognizing that no meta-heuristic can solve all problem types,as stated by the No Free Lunch theorem.This paper introduces the Propagation alongside Crossover(PAC)algorithm to address continuous optimization challenges.The primary goal of PAC is to structure the algorithmic phases in a manner that achieves a robust balance between exploration and exploitation through appropriately designed mechanisms at each stage.PAC simultaneously leverages the benefits of propagation,crossover,and mutation.Three independent operators are defined to generate new candidate solutions separately,and a novel selection strategy allows individuals produced by each operator,along with members of the current population,to independently enter the next generation.This design preserves population diversity,prevents all individuals from converging toward a single point,and enhances the algorithm’s ability to explore the solution space effectively.A key innovation of PAC is its three-mode propagation mechanism,which comprises local search,linear propagation toward the target point,and tear-drop shaped propagation toward the target point.Tear-drop propagation provides a precise and adaptive search around promising solutions,increasing diversity and preventing entrapment in local optima.The target point is typically set as the global optimum;however,when propagating the global optimum itself,a random point is used as the target to further enhance exploration and escape from local optima.The initial population is generated using chaotic mapping to ensure broad coverage of the search space.PAC was rigorously evaluated on 51 benchmark functions and three engineering problems,considering scalability,convergence,sensitivity,and computational efficiency.Comparative analyses with established optimization algorithms demonstrate PAC’s superior performance,as confirmed by Wilcoxon signed-rank and Friedman statistical tests.Furthermore,PAC was applied as a feature selection method on four diverse datasets,achieving substantial dimensionality reduction while outperforming comparative methods in classification accuracy.These results highlight PAC’s versatility,robustness,and practical effectiveness.展开更多
Background:Accurate segmentation of prostate tumors in magnetic resonance imaging(MRI)is critical for improving diagnostic accuracy and supporting clinical decision making.However,many existing approaches rely on supe...Background:Accurate segmentation of prostate tumors in magnetic resonance imaging(MRI)is critical for improving diagnostic accuracy and supporting clinical decision making.However,many existing approaches rely on supervised learning methods that require large annotated datasets and substantial computational resources,limiting their clinical applicability.This study aims to develop and evaluate a fully unsupervised framework for prostate tumor segmentation in multiparametric MRI using hybrid optimization and adaptive thresholding techniques.Methods:This study proposes an unsupervised prostate tumor segmentation framework based on hybrid optimization and adaptive thresholding.Two metaheuristic optimization algorithms,chaotic particle swarm optimization and forest optimization,were employed to optimize Otsu's variance-based thresholding and Kapur's entropy-based thresholding,resulting in four hybrid configurations.The framework was evaluated using multiparametric prostate MRI datasets,including apparent diffusion coefficient,T2-weighted,and diffusion-weighted imaging sequences.Segmentation performance was assessed using overlapbased and classification-based metrics.Statistical analysis included the computation of descriptive performance measures and confidence intervals to evaluate robustness and consistency across datasets.Results:The proposed framework demonstrated reliable and consistent segmentation performance across all MRI modalities.The Otsu-based hybrid configurations showed superior overlap and classification performance in diffusion-based imaging,whereas the entropy-based methods exhibited more conservative behavior on heterogeneous T2-weighted images.Overall,the optimization-based approaches achieved high segmentation accuracy and stability without the need for annotated training data.Conclusions:The proposed hybrid optimization and thresholding framework provides an effective,fully unsupervised solution for prostate tumor segmentation in multiparametric MRI.Its robustness,computational efficiency,and independence from training data highlight its potential for integration into clinical prostate cancer diagnostic workflows.展开更多
In this study,a collaborative optimization framework combining artificial fish swarm algorithm(AFSA)and Voronoi cell finite element method(VCFEM)is proposed to solve the problem of the influence of microstructure dist...In this study,a collaborative optimization framework combining artificial fish swarm algorithm(AFSA)and Voronoi cell finite element method(VCFEM)is proposed to solve the problem of the influence of microstructure distribution on the macroscopic mechanical properties of particle-reinforced composites.Compared with the traditional displacement-based finite element method,VCFEM significantly improves the computational efficiency of multi-inclusion problems by means of generalized stress function and element local adaptation technology,and accurately captures the stress field discontinuity and interface stress concentration phenomenon.At the same time,AFSA abandons the dependence of traditional optimization methods on simplified models,and directly searches for the global optimal solution through discrete topological variables(particle positions).Its natural selection mechanism and swarm intelligence characteristics effectively overcome the local optimal trap.The numerical simulation results show that the proposed method exhibits high accuracy in both single-and multi-inclusion models(the error with the commercial software MARC is less than 5%),and in the complex model with 100 inclusions,the maximum Mises stress is reduced by 32.6%after optimization.The synergistic effect of the two breaks through the trade-off between efficiency and accuracy in traditional optimization,and provides the ability of both computational efficiency and global optimization for multi-scale composite material design.展开更多
基金supported by the National Natural Science Foundation of China(62394340,62394345,62473383).This work was carried out in part using computing resources at the High Performance Computing Center of Central South University。
摘要Deep neural networks are increasingly exposed to attack threats,and at the same time,the need for privacy protection is growing.As a result,the challenge of developing neural networks that are both robust and capable of strong generalization while maintaining privacy becomes pressing.Training neural networks under privacy constraints is one way to minimize privacy leakage,and one way to do this is to add noise to the data or model.However,noise may cause gradient directions to deviate from the optimal trajectory during training,leading to unstable parameter updates,slow convergence,and reduced model generalization capability.To overcome these challenges,we propose an optimization algorithm based on double-integral coevolutionary neurodynamics(DICND),designed to accelerate convergence and improve generalization in noisy conditions.Theoretical analysis proves the global convergence of the DICND algorithm and demonstrates its ability to converge to near-global minima efficiently under noisy conditions.Numerical simulations and image classification experiments further confirm the DICND algorithm's significant advantages in enhancing generalization performance.
摘要Heuristic optimization algorithms have been widely used in solving complex optimization problems in various fields such as engineering,economics,and computer science.These algorithms are designed to find high-quality solutions efficiently by balancing exploration of the search space and exploitation of promising solutions.While heuristic optimization algorithms vary in their specific details,they often exhibit common patterns that are essential to their effectiveness.This paper aims to analyze and explore common patterns in heuristic optimization algorithms.Through a comprehensive review of the literature,we identify the patterns that are commonly observed in these algorithms,including initialization,local search,diversity maintenance,adaptation,and stochasticity.For each pattern,we describe the motivation behind it,its implementation,and its impact on the search process.To demonstrate the utility of our analysis,we identify these patterns in multiple heuristic optimization algorithms.For each case study,we analyze how the patterns are implemented in the algorithm and how they contribute to its performance.Through these case studies,we show how our analysis can be used to understand the behavior of heuristic optimization algorithms and guide the design of new algorithms.Our analysis reveals that patterns in heuristic optimization algorithms are essential to their effectiveness.By understanding and incorporating these patterns into the design of new algorithms,researchers can develop more efficient and effective optimization algorithms.
基金supported by the National Natural Science Foundation of China(22408227,22238005)the Postdoctoral Research Foundation of China(GZC20231576).
摘要The optimization of reaction processes is crucial for the green, efficient, and sustainable development of the chemical industry. However, how to address the problems posed by multiple variables, nonlinearities, and uncertainties during optimization remains a formidable challenge. In this study, a strategy combining interpretable machine learning with metaheuristic optimization algorithms is employed to optimize the reaction process. First, experimental data from a biodiesel production process are collected to establish a database. These data are then used to construct a predictive model based on artificial neural network (ANN) models. Subsequently, interpretable machine learning techniques are applied for quantitative analysis and verification of the model. Finally, four metaheuristic optimization algorithms are coupled with the ANN model to achieve the desired optimization. The research results show that the methanol: palm fatty acid distillate (PFAD) molar ratio contributes the most to the reaction outcome, accounting for 41%. The ANN-simulated annealing (SA) hybrid method is more suitable for this optimization, and the optimal process parameters are a catalyst concentration of 3.00% (mass), a methanol: PFAD molar ratio of 8.67, and a reaction time of 30 min. This study provides deeper insights into reaction process optimization, which will facilitate future applications in various reaction optimization processes.
基金supported in part by the National Key Research and Development Program of China(2024YFF0908200)the National Natural Science Foundation of China(62302402,62272078)+1 种基金the Chongqing Natural Science Foundation(CSTB2024TIAD-KPX0018,CSTB2023NSCO-LZX006)the Southwest University Graduate Research Innovation Project(SWUB24050)
摘要High-dimensional and incomplete(HDI) matrices are commonly encountered in various big data-related applications for illustrating the complex interactions among numerous entities, like the user-item interactions in a commercial recommender system or the user-user interactions in a social network services system. The factorization of such an HDI matrix can embed the involved entities into the low-dimensional feature space for acquiring their principal representation, which is a vital task in various application scenes and is often established through the Latent Factor Analysis(LFA). Nevertheless, an HDI matrix can be huge when the corresponding application explodes to involve millions of users, items, or other interactive nodes. In this case, a parallel optimization algorithm is desired for raising the scalability and time efficiency of an LFA model. This paper provides a comprehensive review of the existing parallel optimization algorithms for the LFA model. Specifically, it performs: 1) discussion and summary of these algorithms based on computing architecture and mode, 2) empirical studies of representative models, and3) summary of the current challenges and future directions in this domain. This survey aims to offer an exhaustive review of Parallel Optimization Algorithms for High-Dimensional and Incomplete Matrix Factorization, thereby fostering further research in this field.
基金National Natural Science Foundation of China (60674074)Natural Science Foundation of Jiangsu province (BK2009415)+5 种基金Research Fund for the Doctoral Program of Higher Education of China (20093228110002)College Graduate Student Research and Innovation Program of Jiangsu province (CX09B_227Z)Meteorology Industry Special Project of CMA (GYHY(QX)2007-6-2)National 863 Project (2007AA061901)Project of State Key Laboratory of Severe Weather of Chinese Academy of Meteorological Sciences (2008LASW-B11)Project 2009Y0006
摘要Storm identification and tracking based on weather radar data are essential to nowcasting and severe weather warning. A new two-dimensional storm identification method simultaneously seeking in two directions is proposed, and identification results are used to discuss storm tracking algorithms. Three modern optimization algorithms (simulated annealing algorithm, genetic algorithm and ant colony algorithm) are tested to match storms in successive time intervals. Preliminary results indicate that the simulated annealing algorithm and ant colony algorithm are effective and have intuitionally adjustable parameters, whereas the genetic algorithm is unsatisfaetorily constrained by the mode of genetic operations Experiments provide not only the feasibility and characteristics of storm tracking with modern optimization algorithms, but also references for studies and applications in relevant fields.
摘要Real-world engineering design problems with complex objective functions under some constraints are relatively difficult problems to solve.Such design problems are widely experienced in many engineering fields,such as industry,automotive,construction,machinery,and interdisciplinary research.However,there are established optimization techniques that have shown effectiveness in addressing these types of issues.This research paper gives a comparative study of the implementation of seventeen new metaheuristic methods in order to optimize twelve distinct engineering design issues.The algorithms used in the study are listed as:transient search optimization(TSO),equilibrium optimizer(EO),grey wolf optimizer(GWO),moth-flame optimization(MFO),whale optimization algorithm(WOA),slimemould algorithm(SMA),harris hawks optimization(HHO),chimp optimization algorithm(COA),coot optimization algorithm(COOT),multi-verse optimization(MVO),arithmetic optimization algorithm(AOA),aquila optimizer(AO),sine cosine algorithm(SCA),smell agent optimization(SAO),and seagull optimization algorithm(SOA),pelican optimization algorithm(POA),and coati optimization algorithm(CA).As far as we know,there is no comparative analysis of recent and popular methods against the concrete conditions of real-world engineering problems.Hence,a remarkable research guideline is presented in the study for researchersworking in the fields of engineering and artificial intelligence,especiallywhen applying the optimization methods that have emerged recently.Future research can rely on this work for a literature search on comparisons of metaheuristic optimization methods in real-world problems under similar conditions.
基金Project(2006BAC07B03) supported by the National Key Technology R & D Program of ChinaProject(2006G040-A) supported by the Foundation of the Science and Technology Section of Ministry of RailwayProject(2008yb044) supported by the Foundation of Excellent Doctoral Dissertation of Central South University
摘要To protect trains against strong cross-wind along Qinghai-Tibet railway, a strong wind speed monitoring and warning system was developed. And to obtain high-precision wind speed short-term forecasting values for the system to make more accurate scheduling decision, two optimization algorithms were proposed. Using them to make calculative examples for actual wind speed time series from the 18th meteorological station, the results show that: the optimization algorithm based on wavelet analysis method and improved time series analysis method can attain high-precision multi-step forecasting values, the mean relative errors of one-step, three-step, five-step and ten-step forecasting are only 0.30%, 0.75%, 1.15% and 1.65%, respectively. The optimization algorithm based on wavelet analysis method and Kalman time series analysis method can obtain high-precision one-step forecasting values, the mean relative error of one-step forecasting is reduced by 61.67% to 0.115%. The two optimization algorithms both maintain the modeling simple character, and can attain prediction explicit equations after modeling calculation.
摘要The vehicle routing problem(VRP)is a typical discrete combinatorial optimization problem,and many models and algorithms have been proposed to solve the VRP and its variants.Although existing approaches have contributed significantly to the development of this field,these approaches either are limited in problem size or need manual intervention in choosing parameters.To solve these difficulties,many studies have considered learning-based optimization(LBO)algorithms to solve the VRP.This paper reviews recent advances in this field and divides relevant approaches into end-to-end approaches and step-by-step approaches.We performed a statistical analysis of the reviewed articles from various aspects and designed three experiments to evaluate the performance of four representative LBO algorithms.Finally,we conclude the applicable types of problems for different LBO algorithms and suggest directions in which researchers can improve LBO algorithms.
基金supported by the National Natural Science Foundation of China(Grant No.52374153).
摘要Traditional laboratory tests for measuring rock uniaxial compressive strength(UCS)are tedious and timeconsuming.There is a pressing need for more effective methods to determine rock UCS,especially in deep mining environments under high in-situ stress.Thus,this study aims to develop an advanced model for predicting the UCS of rockmaterial in deepmining environments by combining three boosting-basedmachine learning methods with four optimization algorithms.For this purpose,the Lead-Zinc mine in Southwest China is considered as the case study.Rock density,P-wave velocity,and point load strength index are used as input variables,and UCS is regarded as the output.Subsequently,twelve hybrid predictive models are obtained.Root mean square error(RMSE),mean absolute error(MAE),coefficient of determination(R2),and the proportion of the mean absolute percentage error less than 20%(A-20)are selected as the evaluation metrics.Experimental results showed that the hybridmodel consisting of the extreme gradient boostingmethod and the artificial bee colony algorithm(XGBoost-ABC)achieved satisfactory results on the training dataset and exhibited the best generalization performance on the testing dataset.The values of R2,A-20,RMSE,and MAE on the training dataset are 0.98,1.0,3.11 MPa,and 2.23MPa,respectively.The highest values of R2 and A-20(0.93 and 0.96),and the smallest RMSE and MAE values of 4.78 MPa and 3.76MPa,are observed on the testing dataset.The proposed hybrid model can be considered a reliable and effective method for predicting rock UCS in deep mines.
基金The author extends his appreciation to theDeputyship forResearch&Innovation,Ministry of Education,Saudi Arabia for funding this research work through the Project Number(QUIF-4-3-3-33891)。
摘要Statistical distributions are used to model wind speed,and the twoparameters Weibull distribution has proven its effectiveness at characterizing wind speed.Accurate estimation of Weibull parameters,the scale(c)and shape(k),is crucial in describing the actual wind speed data and evaluating the wind energy potential.Therefore,this study compares the most common conventional numerical(CN)estimation methods and the recent intelligent optimization algorithms(IOA)to show how precise estimation of c and k affects the wind energy resource assessments.In addition,this study conducts technical and economic feasibility studies for five sites in the northern part of Saudi Arabia,namely Aljouf,Rafha,Tabuk,Turaif,and Yanbo.Results exhibit that IOAs have better performance in attaining optimal Weibull parameters and provided an adequate description of the observed wind speed data.Also,with six wind turbine technologies rating between 1 and 3MW,the technical and economic assessment results reveal that the CN methods tend to overestimate the energy output and underestimate the cost of energy($/kWh)compared to the assessments by IOAs.The energy cost analyses show that Turaif is the windiest site,with an electricity cost of$0.016906/kWh.The highest wind energy output is obtained with the wind turbine having a rated power of 2.5 MW at all considered sites with electricity costs not exceeding$0.02739/kWh.Finally,the outcomes of this study exhibit the potential of wind energy in Saudi Arabia,and its environmental goals can be acquired by harvesting wind energy.
摘要This paper systematically evaluates and compares three well-engineered and popular multi-objective optimization algorithms for the design of switched reluctance machines.The multi-physics and multi-objective nature of electric machine design problems are discussed,followed by benchmark studies comparing generic algorithms(GA),differential evolution(DE)algorithms and particle swarm optimizations(PSO)on a 6/4 switched reluctance machine design with seven independent variables and a strong nonlinear multi-objective Pareto front.To better quantify the quality of the Pareto fronts,five primary quality indicators are employed to serve as the algorithm testing metrics.The results show that the three algorithms have similar performances when the optimization employs only a small number of candidate designs or ultimately,a significant amount of candidate designs.However,DE tends to perform better in terms of convergence speed and the quality of Pareto front when a relatively modest amount of candidates are considered.
基金the National Natural Science Foundation of China(No.62176146)。
摘要A multi-strategy hybrid whale optimization algorithm(MSHWOA)for complex constrained optimization problems is proposed to overcome the drawbacks of easily trapping into local optimum,slow convergence speed and low optimization precision.Firstly,the population is initialized by introducing the theory of good point set,which increases the randomness and diversity of the population and lays the foundation for the global optimization of the algorithm.Then,a novel linearly update equation of convergence factor is designed to coordinate the abilities of exploration and exploitation.At the same time,the global exploration and local exploitation capabilities are improved through the siege mechanism of Harris Hawks optimization algorithm.Finally,the simulation experiments are conducted on the 6 benchmark functions and Wilcoxon rank sum test to evaluate the optimization performance of the improved algorithm.The experimental results show that the proposed algorithm has more significant improvement in optimization accuracy,convergence speed and robustness than the comparison algorithm.
摘要In this paper, we develop a new theoretical framework by means of the absorbing Markov process theory for analyzing some stochastic global optimization algorithms. Applying the framework to the pure random search, we prove that the pure random search converges to the global minimum in probability and its time has geometry distribution. We also analyze the pure adaptive search by this framework and turn out that the pure adaptive search converges to the global minimum in probability and its time has Poisson distribution.
摘要Optimization is the key to obtaining efficient utilization of resources in structural design.Due to the complex nature of truss systems,this study presents a method based on metaheuristic modelling that minimises structural weight under stress and frequency constraints.Two new algorithms,the Red Kite Optimization Algorithm(ROA)and Secretary Bird Optimization Algorithm(SBOA),are utilized on five benchmark trusses with 10,18,37,72,and 200-bar trusses.Both algorithms are evaluated against benchmarks in the literature.The results indicate that SBOA always reaches a lighter optimal.Designs with reducing structural weight ranging from 0.02%to 0.15%compared to ROA,and up to 6%–8%as compared to conventional algorithms.In addition,SBOA can achieve 15%–20%faster convergence speed and 10%–18%reduction in computational time with a smaller standard deviation over independent runs,which demonstrates its robustness and reliability.It is indicated that the adaptive exploration mechanism of SBOA,especially its Levy flight–based search strategy,can obviously improve optimization performance for low-and high-dimensional trusses.The research has implications in the context of promoting bio-inspired optimization techniques by demonstrating the viability of SBOA,a reliable model for large-scale structural design that provides significant enhancements in performance and convergence behavior.
基金Scientific Research Project of Hunan Provincial Department of Education(Project No.:22A0633)。
摘要The artificial immune algorithm is an intelligent optimization algorithm derived from the working mechanism of biological immune systems. It simulates immune response processes including biological antigen recognition, antibody generation, clonal selection, immune memory, and immune suppression, and searches for optimal solutions through iterative population evolution. In recent years, artificial immune algorithms have been gradually applied in various fields such as industrial optimization, artificial intelligence, smart cities, and automatic control, showing favorable application value in scenarios including multi-objective constrained optimization, dynamic system scheduling, fault feature identification, and adaptive parameter tuning. However, with the continuous increase in the complexity of application scenarios, the inherent defects of classic artificial immune algorithms have become prominent. On this basis, based on the basic framework of artificial immune algorithms, this paper comprehensively analyzes the core key problems in algorithm operation and constructs a multi-dimensional and highly adaptive algorithm optimization system, aiming to provide comprehensive support for iterative optimization and scenario-based implementation of artificial immune algorithms.
基金the Special Research Fund for the Na-tional Key Research and Development Program of China(No.2022ZD0119001)。
摘要A novel intelligent optimization algorithm inspired by nature,called sea otter optimization algorithm(SOOA),is proposed.The SOOA simulates the natural behaviors of sea otters,such as using tactile senses to search for food in seawater,grooming their fur,feeding with the aid of stones,and escaping from danger.In the exploration stage,a wetness factor is introduced to control the behavior of sea otters in foraging and grooming;a danger factor is introduced to control the behavior of sea otters in feeding and avoiding dangers in the exploitation stage,and the behaviors of sea otters in responding to different dangers are mathematically modeled.The proposed algorithm is compared with 9 well-known intelligent optimization algorithms,and evaluated in 13 benchmark functions as well as wireless sensor network coverage optimization problems to verify the effectiveness of the proposed algorithm.The experimental results show that the node coverage after SOOA optimization reaches 91.2%in 2D environment and 90.47%in 3D environment.Compared with other algorithms,SOOA is superior and possesses the ability to solve complex optimization problems.
基金supported by the National Natural Science Foundation of China(62522320,92267108,62173322)the Science and Technology Program of Liaoning Province(2026JH6/101100030)Liaoning Revitalization Talents Program(XLYC2403062)。
摘要Dear Editor,With the rapid development of new-generation information and communication technology,the fusion of sensing,communication,computing,and control(S3C)is becoming increasingly significant for cyber-physical systems(CPS).However,due to the non-convexity,the curse of dimensionality,and the partial observability faced by CPS,traditional convex optimization algorithms are challenging to deal with S3C co-optimization.
摘要Researchers continuously advance optimization algorithms,recognizing that no meta-heuristic can solve all problem types,as stated by the No Free Lunch theorem.This paper introduces the Propagation alongside Crossover(PAC)algorithm to address continuous optimization challenges.The primary goal of PAC is to structure the algorithmic phases in a manner that achieves a robust balance between exploration and exploitation through appropriately designed mechanisms at each stage.PAC simultaneously leverages the benefits of propagation,crossover,and mutation.Three independent operators are defined to generate new candidate solutions separately,and a novel selection strategy allows individuals produced by each operator,along with members of the current population,to independently enter the next generation.This design preserves population diversity,prevents all individuals from converging toward a single point,and enhances the algorithm’s ability to explore the solution space effectively.A key innovation of PAC is its three-mode propagation mechanism,which comprises local search,linear propagation toward the target point,and tear-drop shaped propagation toward the target point.Tear-drop propagation provides a precise and adaptive search around promising solutions,increasing diversity and preventing entrapment in local optima.The target point is typically set as the global optimum;however,when propagating the global optimum itself,a random point is used as the target to further enhance exploration and escape from local optima.The initial population is generated using chaotic mapping to ensure broad coverage of the search space.PAC was rigorously evaluated on 51 benchmark functions and three engineering problems,considering scalability,convergence,sensitivity,and computational efficiency.Comparative analyses with established optimization algorithms demonstrate PAC’s superior performance,as confirmed by Wilcoxon signed-rank and Friedman statistical tests.Furthermore,PAC was applied as a feature selection method on four diverse datasets,achieving substantial dimensionality reduction while outperforming comparative methods in classification accuracy.These results highlight PAC’s versatility,robustness,and practical effectiveness.
摘要Background:Accurate segmentation of prostate tumors in magnetic resonance imaging(MRI)is critical for improving diagnostic accuracy and supporting clinical decision making.However,many existing approaches rely on supervised learning methods that require large annotated datasets and substantial computational resources,limiting their clinical applicability.This study aims to develop and evaluate a fully unsupervised framework for prostate tumor segmentation in multiparametric MRI using hybrid optimization and adaptive thresholding techniques.Methods:This study proposes an unsupervised prostate tumor segmentation framework based on hybrid optimization and adaptive thresholding.Two metaheuristic optimization algorithms,chaotic particle swarm optimization and forest optimization,were employed to optimize Otsu's variance-based thresholding and Kapur's entropy-based thresholding,resulting in four hybrid configurations.The framework was evaluated using multiparametric prostate MRI datasets,including apparent diffusion coefficient,T2-weighted,and diffusion-weighted imaging sequences.Segmentation performance was assessed using overlapbased and classification-based metrics.Statistical analysis included the computation of descriptive performance measures and confidence intervals to evaluate robustness and consistency across datasets.Results:The proposed framework demonstrated reliable and consistent segmentation performance across all MRI modalities.The Otsu-based hybrid configurations showed superior overlap and classification performance in diffusion-based imaging,whereas the entropy-based methods exhibited more conservative behavior on heterogeneous T2-weighted images.Overall,the optimization-based approaches achieved high segmentation accuracy and stability without the need for annotated training data.Conclusions:The proposed hybrid optimization and thresholding framework provides an effective,fully unsupervised solution for prostate tumor segmentation in multiparametric MRI.Its robustness,computational efficiency,and independence from training data highlight its potential for integration into clinical prostate cancer diagnostic workflows.
基金funded by the National Natural Science Foundation of China(Grant No.12227801).
摘要In this study,a collaborative optimization framework combining artificial fish swarm algorithm(AFSA)and Voronoi cell finite element method(VCFEM)is proposed to solve the problem of the influence of microstructure distribution on the macroscopic mechanical properties of particle-reinforced composites.Compared with the traditional displacement-based finite element method,VCFEM significantly improves the computational efficiency of multi-inclusion problems by means of generalized stress function and element local adaptation technology,and accurately captures the stress field discontinuity and interface stress concentration phenomenon.At the same time,AFSA abandons the dependence of traditional optimization methods on simplified models,and directly searches for the global optimal solution through discrete topological variables(particle positions).Its natural selection mechanism and swarm intelligence characteristics effectively overcome the local optimal trap.The numerical simulation results show that the proposed method exhibits high accuracy in both single-and multi-inclusion models(the error with the commercial software MARC is less than 5%),and in the complex model with 100 inclusions,the maximum Mises stress is reduced by 32.6%after optimization.The synergistic effect of the two breaks through the trade-off between efficiency and accuracy in traditional optimization,and provides the ability of both computational efficiency and global optimization for multi-scale composite material design.