Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when ta...Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.展开更多
It is well-known that appropriately determining the solution space and initializations is crucial for obtaining high-quality optimal solutions for optimization problems,considering both gradient-based and gradient-fre...It is well-known that appropriately determining the solution space and initializations is crucial for obtaining high-quality optimal solutions for optimization problems,considering both gradient-based and gradient-free techniques.However,the general framework for adaptively dealing with a particular optimization problem is commonly overlooked and thus still hidden in the literature.To overcome this limitation,a new approach assisted by the neural network(NN)is proposed for solving high-dimensional optimization issues.By restructuring the search space to optimize the objective function via a nonlinear mapping constructed by an autoencoder(AE),the surrogate solution space is constructed by a network training process and dynamically oriented to the optimal solution of the optimization issue.To enhance the optimization efficiency and address non-smooth problems,the classical metaheuristic grey wolf optimizer(GWO)and the adaptive moment estimation(Adam)are sequentially employed to complement the disadvantages of the constituted models.The effectiveness of the proposed approach is validated by solving a set of mathematical functions with 1000-dimensional and three large-scale truss design optimization problems.Several numerical experiments show that the solution space is reduced in terms of both size and complexity based on the restructuring procedure,in which the global optimal solution is still conserved,leading to better optimization efficiency when solving optimization problems with complex search domains with large dimensions.In addition,the hybrid optimizer has also been proven to be more effective when combined with the restructuring technique owing to the use of the Adam algorithm in the second phase.展开更多
Designing appropriate loss functions is critical to the success of supervised learning models.However,most conventional losses are fixed and manually designed,making them suboptimal for diverse and dynamic learning sc...Designing appropriate loss functions is critical to the success of supervised learning models.However,most conventional losses are fixed and manually designed,making them suboptimal for diverse and dynamic learning scenarios.In this work,we propose an Adaptive Meta-Loss Network(Adaptive-MLN)that learns to generate taskagnostic loss functions tailored to evolving classification problems.Unlike traditional methods that rely on static objectives,Adaptive-MLN treats the loss function itself as a trainable component,parameterized by a shallow neural network.To enable flexible,gradient-free optimization,we introduce a hybrid evolutionary approach that combines GeneticAlgorithms(GA)for global exploration and Evolution Strategies(ES)for local refinement.This co-evolutionary process dynamically adjusts the loss landscape,improvingmodel generalization without relying on analytic gradients or handcrafted heuristics.Experimental evaluations on synthetic tasks and the CIFAR-10 andMNIST datasets demonstrate that our approach consistently outperforms standard losses such as Cross-Entropy and Mean Squared Error in terms of accuracy,convergence,and adaptability.展开更多
Correlation function of acceleration responses-based damage identificationmethods has been developed and employed,while they still face the difficulty in identifying local orminor structural damages.To deal with this ...Correlation function of acceleration responses-based damage identificationmethods has been developed and employed,while they still face the difficulty in identifying local orminor structural damages.To deal with this issue,a robust structural damage identification method is developed,integrating a modified holistic swarm optimization(MHSO)algorithm with a hybrid objective function.The MHSO is developed by combining Hammersley sequencebased population initialization,chaotic search around the worst solution,and Hooke-Jeeves pattern search around the best solution,thereby improving both global exploration and local exploitation capabilities.A hybrid objective function is constructed by merging acceleration correlation function-based and strain correlation function-based objective functions,effectively leveraging the complementary sensitivities of global and local responses.To further suppress spurious solutions and promote sparsity in parameter estimation,an additional L0.5 regularization term is introduced.The effectiveness of the proposed method is validated through numerical simulations on a simply supported beam and a steel girder benchmark structure.Comparative studies with sequential quadratic programming,genetic algorithm,andHSO demonstrate that theMHSOachieves superior accuracy and convergence efficiency,even with limited sensors and 20%noise-contaminated measurements.Results highlight that the hybrid objective function significantly enhances the detection of both major and minor damages,while the inclusion of sparse regularization improves robustness against noise and model uncertainties.The findings indicate that the proposed framework provides a reliable and computationally efficient solution for simultaneous localization and quantification of structural damages,offering promising applicability to real-world structural health monitoring scenarios.展开更多
The penalty function method is a significant method for solving nonlinear constrained optimization problems(COP).In this paper,a new quadratic continuous differentiable smooth penalty function is proposed for the l_(1...The penalty function method is a significant method for solving nonlinear constrained optimization problems(COP).In this paper,a new quadratic continuous differentiable smooth penalty function is proposed for the l1exact penalty function.The error estimations between the objective function values of the smooth penalty problem,the penalty problem and the original problem are also studied.Furthermore,based on the smoothed penalty function,an algorithm for solving COP is proposed,and the convergence of the algorithm is proved.Finally,several numerical examples are given to illustrate the effectiveness of the proposed algorithm.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
This paper investigates input–output constraints adaptive fuzzy control strategy with cooperative optimization approach of the gain and time-varying nonlinear disturbance observer for manipulator systems.First,the st...This paper investigates input–output constraints adaptive fuzzy control strategy with cooperative optimization approach of the gain and time-varying nonlinear disturbance observer for manipulator systems.First,the static control gain strategies cannot simultaneously optimize system performances during both dynamic and steady-state stages.To address this problem,a novel cooperative optimization approach of the gain(COG)based on tracking error is proposed to replace the traditional static gain strategies.Second,a time-varying nonlinear disturbance observer(NDO)is proposed to accurately estimate variable disturbances and mitigate harmful observation peak at the initial stage of manipulator tracking.Furthermore,an auxiliary system and an asymmetric time-varying barrier Lyapunov function are used to ensure that the inputs and outputs of the system remain within predefined constraints.Notably,the traditional backstepping control relies on precise model information.To minimize the impact of model uncertainties on tracking performance,an adaptive fuzzy control is employed to design the controller,eliminating the need for precise model information.Finally,the effectiveness of the proposed input–output constraints adaptive fuzzy control strategy with COG and time-varying NDO is verified and analyzed through comparative experiments on a two-joint manipulator platform.展开更多
This paper presents a new approach to tuning the cost function weights of a nonlinear model predictive controller(NMPC)using offline Bayesian optimization(BO).We propose a recursive weight selection method that integr...This paper presents a new approach to tuning the cost function weights of a nonlinear model predictive controller(NMPC)using offline Bayesian optimization(BO).We propose a recursive weight selection method that integrates BO directly into the NMPC simulation loop and targets an economic cost function.This approach identifies weights that optimize an economic cost function,ensuring that controller performance is aligned with the operational economics of the process.A case study involving an interconnected tank system with nonlinear level and temperature dynamics illustrates the method.Two operating conditions are tested:an undisturbed scenario and a disturbed one,incorporating sensor noise and model–plant mismatch.In both scenarios,the BO-tuned NMPC outperforms Traditional and Satisficing-based weight strategies,yielding smoother control actions.In the disturbed case,cost reductions of up to 4.5%are achieved.The results confirm that offline BO-based tuning offers a viable and robust alternative to manual or online adaptive strategies,especially in systems where online retraining is impractical.Sensitivity tests further highlight the importance of informed search interval selection to ensure convergence and performance.展开更多
Objective Humans are exposed to complex mixtures of environmental chemicals and other factors that can affect their health.Analysis of these mixture exposures presents several key challenges for environmental epidemio...Objective Humans are exposed to complex mixtures of environmental chemicals and other factors that can affect their health.Analysis of these mixture exposures presents several key challenges for environmental epidemiology and risk assessment,including high dimensionality,correlated exposure,and subtle individual effects.Methods We proposed a novel statistical approach,the generalized functional linear model(GFLM),to analyze the health effects of exposure mixtures.GFLM treats the effect of mixture exposures as a smooth function by reordering exposures based on specific mechanisms and capturing internal correlations to provide a meaningful estimation and interpretation.The robustness and efficiency was evaluated under various scenarios through extensive simulation studies.Results We applied the GFLM to two datasets from the National Health and Nutrition Examination Survey(NHANES).In the first application,we examined the effects of 37 nutrients on BMI(2011–2016 cycles).The GFLM identified a significant mixture effect,with fiber and fat emerging as the nutrients with the greatest negative and positive effects on BMI,respectively.For the second application,we investigated the association between four pre-and perfluoroalkyl substances(PFAS)and gout risk(2007–2018 cycles).Unlike traditional methods,the GFLM indicated no significant association,demonstrating its robustness to multicollinearity.Conclusion GFLM framework is a powerful tool for mixture exposure analysis,offering improved handling of correlated exposures and interpretable results.It demonstrates robust performance across various scenarios and real-world applications,advancing our understanding of complex environmental exposures and their health impacts on environmental epidemiology and toxicology.展开更多
For the optimization of fundamental eigenfrequency in vibrating structures,it has been proven that multi-scale structures have advantages over single scale structures.This study introduces a two-scale topology optimiz...For the optimization of fundamental eigenfrequency in vibrating structures,it has been proven that multi-scale structures have advantages over single scale structures.This study introduces a two-scale topology optimization method using a data-driven microstructure model based on a multiple variable cutting(M-VCUT)level set approach.This method aims to maximize the fundamental eigenfrequency of two-scale structures.The method consists of two parts:offline database construction and online topology optimization.In the process of offline database construction,many microstructures are obtained by varying the value of geometric parameters according to the M-VCUT level set approach;then,a mapping relationship between the geometric parameters and the homogenized mechanical properties of microstructures is established by compactly supported radial basis function interpolation,which gives the data-driven microstructure model.In the process of online optimization,the homogenized mechanical properties corresponding to arbitrary design variables are obtained by using the data-driven microstructure model,whose computational costs are much less than those of the homogenization.Topology optimization is carried out with this data-driven model to enhance computational efficiency.In order to adapt the method of moving asymptotes(MMA),the eigenfrequency maximization problem is converted to its reciprocal minimization problem for sensitivity calculation.The method’s effectiveness is proved through several numerical examples.展开更多
Purpose-With the continuous expansion of railway hubs,increasing functional complexity and growing capacity constraints,the coordinated and efficient utilization of transportation resources-such as stations,lines and ...Purpose-With the continuous expansion of railway hubs,increasing functional complexity and growing capacity constraints,the coordinated and efficient utilization of transportation resources-such as stations,lines and maintenance facilities-has become a critical issue for improving hub operational efficiency.This study focuses on the division of functions within railway hubs that incorporate shared stations operating under mixed high-speed and conventional train services.Design/methodology/approach-An optimization model for hub functional allocation is developed to achieve efficient resource utilization in hubs containing mixed-operation stations.A node-arc network representation combined with an improved multi-commodity flow model is employed,taking train dwell and operation time within the hub as the optimization objective.A case study is conducted to derive optimized solutions,followed by both qualitative and quantitative analyses.Findings-The results indicate that optimizing train operation routes and station assignments within the hub can effectively reduce the total occupation time of train flows and significantly improve resource utilization efficiency.Originality/value-The proposed model demonstrates both scientific rigor and practical effectiveness.In realworld operations,it can provide operators with preliminary and proactive functional allocation schemes,help identify key constraints limiting hub capacity utilization and offer decision support for transport plan adjustments or infrastructure and facility upgrades.展开更多
In this paper, a bionic optimization algorithm based dimension reduction method named Ant Colony Optimization -Selection (ACO-S) is proposed for high-dimensional datasets. Because microarray datasets comprise tens o...In this paper, a bionic optimization algorithm based dimension reduction method named Ant Colony Optimization -Selection (ACO-S) is proposed for high-dimensional datasets. Because microarray datasets comprise tens of thousands of features (genes), they are usually used to test the dimension reduction techniques. ACO-S consists of two stages in which two well-known ACO algorithms, namely ant system and ant colony system, are utilized to seek for genes, respectively. In the first stage, a modified ant system is used to filter the nonsignificant genes from high-dimensional space, and a number of promising genes are reserved in the next step. In the second stage, an improved ant colony system is applied to gene selection. In order to enhance the search ability of ACOs, we propose a method for calculating priori available heuristic information and design a fuzzy logic controller to dynamically adjust the number of ants in ant colony system. Furthermore, we devise another fuzzy logic controller to tune the parameter (q0) in ant colony system. We evaluate the performance of ACO-S on five microarray datasets, which have dimensions varying from 7129 to 12000. We also compare the performance of ACO-S with the results obtained from four existing well-known bionic optimization algorithms. The comparison results show that ACO-S has a notable ability to" generate a gene subset with the smallest size and salient features while yielding high classification accuracy. The comparative results generated by ACO-S adopting different classifiers are also given. The proposed method is shown to be a promising and effective tool for mining high-dimension data and mobile robot navigation.展开更多
In normed linear spaces,by applying the Minkowski difference,the concepts of efficient solutions,weakly efficient solutions,proper efficient solutions and Henig efficient solutions are introduced for set optimization ...In normed linear spaces,by applying the Minkowski difference,the concepts of efficient solutions,weakly efficient solutions,proper efficient solutions and Henig efficient solutions are introduced for set optimization with respect to co-radiant sets,and the relationships among them is discussed.Optimality conditions for minimal solutions and strictly minimal solutions of scalar set optimization are established by using the generalized oriented distance functions,respectively.The relationship between the solutions of set optimization problem and the solutions of scalar problem is studied.Several examples are given to explain our result.Properties of Gerstewitz’s functions with respect to co-radiant sets are discussed,which are used to establish sufficient conditions for weakly efficient solutions of set optimization.展开更多
Structural Reliability-Based Topology Optimization(RBTO),as an efficient design methodology,serves as a crucial means to ensure the development ofmodern engineering structures towards high performance,long service lif...Structural Reliability-Based Topology Optimization(RBTO),as an efficient design methodology,serves as a crucial means to ensure the development ofmodern engineering structures towards high performance,long service life,and high reliability.However,in practical design processes,topology optimization must not only account for the static performance of structures but also consider the impacts of various responses and uncertainties under complex dynamic conditions,which traditional methods often struggle accommodate.Therefore,this study proposes an RBTO framework based on a Kriging-assisted level set function and a novel Dynamic Hybrid Particle Swarm Optimization(DHPSO)algorithm.By leveraging the Kriging model as a surrogate,the high cost associated with repeatedly running finite element analysis processes is reduced,addressing the issue of minimizing structural compliance.Meanwhile,the DHPSO algorithm enables a better balance between the population’s developmental and exploratory capabilities,significantly accelerating convergence speed and enhancing global convergence performance.Finally,the proposed method is validated through three different structural examples,demonstrating its superior performance.Observed that the computational that,compared to the traditional Solid Isotropic Material with Penalization(SIMP)method,the proposed approach reduces the upper bound of structural compliance by approximately 30%.Additionally,the optimized results exhibit clear material interfaces without grayscale elements,and the stress concentration factor is reduced by approximately 42%.Consequently,the computational results fromdifferent examples verify the effectiveness and superiority of this study across various fields,achieving the goal of providing more precise optimization results within a shorter timeframe.展开更多
This psychobiography aimed to uncover the characteristics of optimal personality functioning(OPF)across the lifespan of Chabani Manganyi(1940–2024),the first Black South African clinical psychologist.The methodology ...This psychobiography aimed to uncover the characteristics of optimal personality functioning(OPF)across the lifespan of Chabani Manganyi(1940–2024),the first Black South African clinical psychologist.The methodology used in this study encompassed an existential Franklian scholarly psychobiography.Sources of data on Manganyi included only publicly available primary and secondary data.Primary sources included Manganyi’s own writings,such as his autobiography,as well as his academic publications,including the biographies he wrote on creative individuals such as Gordimer,Sekoto and Mphahlele.Secondary sources included scholarly publications by academics and colleagues who knew him,as well as tributes,historical accounts,and archival records related to South African psychology scholarship during apartheid and the country’s transition to democracy.The study’s data sources were captured using online research platforms and search engines that included EBSCOhost,ResearchGate,Google Scholar,the University of the Free State’s Kovsie Catalogue and ProQuest.Alexander’s(1988,1990)biographical approach,which lists nine indicators of thematic salience(i.e.,uniqueness,negation,emphasis,primacy,frequency,error or distortion,isolation,incompletion,and omission)were utilized for the identification,extraction and compilation of salient data for analysis,alongside Frankl’s proposed nine characteristics of optimal personality functioning.Findings revealed that Manganyi personified characteristics of self-determining action,which were consistently evident in his pursuit of education,his intellectual independence,and his scholarly innovations in the field of South African psychology.Manganyi also personified a sense of self-transcendence,primarily expressed through his scholarship,mentorship,and social advocacy.He consistently positioned his dedication to work in his search for broader societal comprehension and transformation,beyond his personal advancement.Manganyi also exhibited qualities of future-directedness,work as vocation,and the search for meaning in resilient living,serving as a role model in managing challenging life and historical circumstances in transformative ways.The findings align with Frankl’s existential characteristics of optimal personality functioning as applied within this scholarly psychobiographical approach,highlighting its cross-cultural transportability in studying historical figures.展开更多
Dear Editor,This letter addresses distributed optimization for resource allocation problems with time-varying objective functions and time-varying constraints.Inspired by the distributed average tracking(DAT)approach,...Dear Editor,This letter addresses distributed optimization for resource allocation problems with time-varying objective functions and time-varying constraints.Inspired by the distributed average tracking(DAT)approach,a distributed control protocol is proposed for optimal resource allocation.The convergence to a time-varying optimal solution within a predefined time is proved.Two numerical examples are given to illustrate the effectiveness of the proposed approach.展开更多
The Dynamical Density Functional Theory(DDFT)algorithm,derived by associating classical Density Functional Theory(DFT)with the fundamental Smoluchowski dynamical equation,describes the evolution of inhomo-geneous flui...The Dynamical Density Functional Theory(DDFT)algorithm,derived by associating classical Density Functional Theory(DFT)with the fundamental Smoluchowski dynamical equation,describes the evolution of inhomo-geneous fluid density distributions over time.It plays a significant role in studying the evolution of density distributions over time in inhomogeneous systems.The Sunway Bluelight II supercomputer,as a new generation of China’s developed supercomputer,possesses powerful computational capabilities.Porting and optimizing industrial software on this platform holds significant importance.For the optimization of the DDFT algorithm,based on the Sunway Bluelight II supercomputer and the unique hardware architecture of the SW39000 processor,this work proposes three acceleration strategies to enhance computational efficiency and performance,including direct parallel optimization,local-memory constrained optimization for CPEs,and multi-core groups collaboration and communication optimization.This method combines the characteristics of the program’s algorithm with the unique hardware architecture of the Sunway Bluelight II supercomputer,optimizing the storage and transmission structures to achieve a closer integration of software and hardware.For the first time,this paper presents Sunway-Dynamical Density Functional Theory(SW-DDFT).Experimental results show that SW-DDFT achieves a speedup of 6.67 times within a single-core group compared to the original DDFT implementation,with six core groups(a total of 384 CPEs),the maximum speedup can reach 28.64 times,and parallel efficiency can reach 71%,demonstrating excellent acceleration performance.展开更多
Corosolic acid,a naturally occurring pentacyclic triterpenic acid,is widely recognized for its broad spectrum of biological activities,particularly its antidiabetic properties,making it a popular ingredient in dietary...Corosolic acid,a naturally occurring pentacyclic triterpenic acid,is widely recognized for its broad spectrum of biological activities,particularly its antidiabetic properties,making it a popular ingredient in dietary supplements for regulating blood sugar levels.Beyond its anti-diabetic effects,recent studies have revealed its therapeutic potential in areas such as anti-cancer,anti-inflammatory,and antibacterial activities.However,its clinical application is hindered by poor water solubility and low bioavailability due to its molecular structure.This review systematically examines the pharmacological activities of corosolic acid,emphasizing its mechanisms of action in disease intervention.Emerging strategies to overcome its inherent limitations,including chemical modifications,microbial transformations,and advanced delivery systems,are also discussed.Notably,some chemical derivatives exhibitα-glucosidase inhibition with IC50 values half that of corosolic acid.Microbial transformations have been shown to enhance its bioavailability while reducing cancer cell toxicity.Additionally,corosolic acid-based delivery systems have demonstrated significant improvements in solubility,stability,and biological activity.By consolidating current insights into its functional properties and biological activity enhancement methods,this review aims to emphasize the practical application values in food and medicine and the future development of corosolic acid as a versatile bioactive compound.展开更多
The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the effi...The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.展开更多
The multi-objective optimization of backfill effect based on response surface methodology and desirability function(RSM-DF)was conducted.Firstly,the test results show that the uniaxial compressive strength(UCS)increas...The multi-objective optimization of backfill effect based on response surface methodology and desirability function(RSM-DF)was conducted.Firstly,the test results show that the uniaxial compressive strength(UCS)increases with cement sand ratio(CSR),slurry concentration(SC),and curing age(CA),while flow resistance(FR)increases with SC and backfill flow rate(BFR),and decreases with CSR.Then the regression models of UCS and FR as response values were established through RSM.Multi-factor interaction found that CSR-CA impacted UCS most,while SC-BFR impacted FR most.By introducing the desirability function,the optimal backfill parameters were obtained based on RSM-DF(CSR is 1:6.25,SC is 69%,CA is 11.5 d,and BFR is 90 m3/h),showing close results of Design Expert and high reliability for optimization.For a copper mine in China,RSM-DF optimization will reduce cement consumption by 4758 t per year,increase tailings consumption by about 6700 t,and reduce CO2emission by about 4758 t.Thus,RSM-DF provides a new approach for backfill parameters optimization,which has important theoretical and practical values.展开更多
基金funded by National Natural Science Foundation of China(Nos.12402142,11832013 and 11572134)Natural Science Foundation of Hubei Province(No.2024AFB235)+1 种基金Hubei Provincial Department of Education Science and Technology Research Project(No.Q20221714)the Opening Foundation of Hubei Key Laboratory of Digital Textile Equipment(Nos.DTL2023019 and DTL2022012).
摘要Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.
基金Project supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF),funded by the Ministry of Science and ICT(No.RS-2024-00337001)。
摘要It is well-known that appropriately determining the solution space and initializations is crucial for obtaining high-quality optimal solutions for optimization problems,considering both gradient-based and gradient-free techniques.However,the general framework for adaptively dealing with a particular optimization problem is commonly overlooked and thus still hidden in the literature.To overcome this limitation,a new approach assisted by the neural network(NN)is proposed for solving high-dimensional optimization issues.By restructuring the search space to optimize the objective function via a nonlinear mapping constructed by an autoencoder(AE),the surrogate solution space is constructed by a network training process and dynamically oriented to the optimal solution of the optimization issue.To enhance the optimization efficiency and address non-smooth problems,the classical metaheuristic grey wolf optimizer(GWO)and the adaptive moment estimation(Adam)are sequentially employed to complement the disadvantages of the constituted models.The effectiveness of the proposed approach is validated by solving a set of mathematical functions with 1000-dimensional and three large-scale truss design optimization problems.Several numerical experiments show that the solution space is reduced in terms of both size and complexity based on the restructuring procedure,in which the global optimal solution is still conserved,leading to better optimization efficiency when solving optimization problems with complex search domains with large dimensions.In addition,the hybrid optimizer has also been proven to be more effective when combined with the restructuring technique owing to the use of the Adam algorithm in the second phase.
基金supported by the National Natural Science Foundation of China(NSFC)under Grant number:82171965.
摘要Designing appropriate loss functions is critical to the success of supervised learning models.However,most conventional losses are fixed and manually designed,making them suboptimal for diverse and dynamic learning scenarios.In this work,we propose an Adaptive Meta-Loss Network(Adaptive-MLN)that learns to generate taskagnostic loss functions tailored to evolving classification problems.Unlike traditional methods that rely on static objectives,Adaptive-MLN treats the loss function itself as a trainable component,parameterized by a shallow neural network.To enable flexible,gradient-free optimization,we introduce a hybrid evolutionary approach that combines GeneticAlgorithms(GA)for global exploration and Evolution Strategies(ES)for local refinement.This co-evolutionary process dynamically adjusts the loss landscape,improvingmodel generalization without relying on analytic gradients or handcrafted heuristics.Experimental evaluations on synthetic tasks and the CIFAR-10 andMNIST datasets demonstrate that our approach consistently outperforms standard losses such as Cross-Entropy and Mean Squared Error in terms of accuracy,convergence,and adaptability.
摘要Correlation function of acceleration responses-based damage identificationmethods has been developed and employed,while they still face the difficulty in identifying local orminor structural damages.To deal with this issue,a robust structural damage identification method is developed,integrating a modified holistic swarm optimization(MHSO)algorithm with a hybrid objective function.The MHSO is developed by combining Hammersley sequencebased population initialization,chaotic search around the worst solution,and Hooke-Jeeves pattern search around the best solution,thereby improving both global exploration and local exploitation capabilities.A hybrid objective function is constructed by merging acceleration correlation function-based and strain correlation function-based objective functions,effectively leveraging the complementary sensitivities of global and local responses.To further suppress spurious solutions and promote sparsity in parameter estimation,an additional L0.5 regularization term is introduced.The effectiveness of the proposed method is validated through numerical simulations on a simply supported beam and a steel girder benchmark structure.Comparative studies with sequential quadratic programming,genetic algorithm,andHSO demonstrate that theMHSOachieves superior accuracy and convergence efficiency,even with limited sensors and 20%noise-contaminated measurements.Results highlight that the hybrid objective function significantly enhances the detection of both major and minor damages,while the inclusion of sparse regularization improves robustness against noise and model uncertainties.The findings indicate that the proposed framework provides a reliable and computationally efficient solution for simultaneous localization and quantification of structural damages,offering promising applicability to real-world structural health monitoring scenarios.
基金supported by the National Natural Science Foundation of China(Nos.11471102 and 12071112)Basic Research Projects for Key Scientific Research Projects of Henan Projects of China(No.20ZX001).
摘要The penalty function method is a significant method for solving nonlinear constrained optimization problems(COP).In this paper,a new quadratic continuous differentiable smooth penalty function is proposed for the l1exact penalty function.The error estimations between the objective function values of the smooth penalty problem,the penalty problem and the original problem are also studied.Furthermore,based on the smoothed penalty function,an algorithm for solving COP is proposed,and the convergence of the algorithm is proved.Finally,several numerical examples are given to illustrate the effectiveness of the proposed algorithm.
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supported by the National Natural Science Foundation of China(Grant No.62273189)the Natural Science Foundation of Shandong Province(Grant No.ZR2021MF005)the Systems Science Plus Joint Research Program of Qingdao University(Grant No.XT2024201).
摘要This paper investigates input–output constraints adaptive fuzzy control strategy with cooperative optimization approach of the gain and time-varying nonlinear disturbance observer for manipulator systems.First,the static control gain strategies cannot simultaneously optimize system performances during both dynamic and steady-state stages.To address this problem,a novel cooperative optimization approach of the gain(COG)based on tracking error is proposed to replace the traditional static gain strategies.Second,a time-varying nonlinear disturbance observer(NDO)is proposed to accurately estimate variable disturbances and mitigate harmful observation peak at the initial stage of manipulator tracking.Furthermore,an auxiliary system and an asymmetric time-varying barrier Lyapunov function are used to ensure that the inputs and outputs of the system remain within predefined constraints.Notably,the traditional backstepping control relies on precise model information.To minimize the impact of model uncertainties on tracking performance,an adaptive fuzzy control is employed to design the controller,eliminating the need for precise model information.Finally,the effectiveness of the proposed input–output constraints adaptive fuzzy control strategy with COG and time-varying NDO is verified and analyzed through comparative experiments on a two-joint manipulator platform.
基金supported by the National Council for Scientific and Technological Development(CNPq,Brazil,Project Nos.406477/2022-1,402377/2022-2,and 406703/2023-0)the Fundação de AmparoàPesquisa e Inovação do Estado de Santa Catarina(Project Nos.00001993/2024 and 2023TR001506).
摘要This paper presents a new approach to tuning the cost function weights of a nonlinear model predictive controller(NMPC)using offline Bayesian optimization(BO).We propose a recursive weight selection method that integrates BO directly into the NMPC simulation loop and targets an economic cost function.This approach identifies weights that optimize an economic cost function,ensuring that controller performance is aligned with the operational economics of the process.A case study involving an interconnected tank system with nonlinear level and temperature dynamics illustrates the method.Two operating conditions are tested:an undisturbed scenario and a disturbed one,incorporating sensor noise and model–plant mismatch.In both scenarios,the BO-tuned NMPC outperforms Traditional and Satisficing-based weight strategies,yielding smoother control actions.In the disturbed case,cost reductions of up to 4.5%are achieved.The results confirm that offline BO-based tuning offers a viable and robust alternative to manual or online adaptive strategies,especially in systems where online retraining is impractical.Sensitivity tests further highlight the importance of informed search interval selection to ensure convergence and performance.
基金supported in part by the Young Scientists Fund of the National Natural Science Foundation of China(Grant Nos.82304253)(and 82273709)the Foundation for Young Talents in Higher Education of Guangdong Province(Grant No.2022KQNCX021)the PhD Starting Project of Guangdong Medical University(Grant No.GDMUB2022054).
摘要Objective Humans are exposed to complex mixtures of environmental chemicals and other factors that can affect their health.Analysis of these mixture exposures presents several key challenges for environmental epidemiology and risk assessment,including high dimensionality,correlated exposure,and subtle individual effects.Methods We proposed a novel statistical approach,the generalized functional linear model(GFLM),to analyze the health effects of exposure mixtures.GFLM treats the effect of mixture exposures as a smooth function by reordering exposures based on specific mechanisms and capturing internal correlations to provide a meaningful estimation and interpretation.The robustness and efficiency was evaluated under various scenarios through extensive simulation studies.Results We applied the GFLM to two datasets from the National Health and Nutrition Examination Survey(NHANES).In the first application,we examined the effects of 37 nutrients on BMI(2011–2016 cycles).The GFLM identified a significant mixture effect,with fiber and fat emerging as the nutrients with the greatest negative and positive effects on BMI,respectively.For the second application,we investigated the association between four pre-and perfluoroalkyl substances(PFAS)and gout risk(2007–2018 cycles).Unlike traditional methods,the GFLM indicated no significant association,demonstrating its robustness to multicollinearity.Conclusion GFLM framework is a powerful tool for mixture exposure analysis,offering improved handling of correlated exposures and interpretable results.It demonstrates robust performance across various scenarios and real-world applications,advancing our understanding of complex environmental exposures and their health impacts on environmental epidemiology and toxicology.
基金supported by the National Natural Science Foundation of China(Grant No.12272144).
摘要For the optimization of fundamental eigenfrequency in vibrating structures,it has been proven that multi-scale structures have advantages over single scale structures.This study introduces a two-scale topology optimization method using a data-driven microstructure model based on a multiple variable cutting(M-VCUT)level set approach.This method aims to maximize the fundamental eigenfrequency of two-scale structures.The method consists of two parts:offline database construction and online topology optimization.In the process of offline database construction,many microstructures are obtained by varying the value of geometric parameters according to the M-VCUT level set approach;then,a mapping relationship between the geometric parameters and the homogenized mechanical properties of microstructures is established by compactly supported radial basis function interpolation,which gives the data-driven microstructure model.In the process of online optimization,the homogenized mechanical properties corresponding to arbitrary design variables are obtained by using the data-driven microstructure model,whose computational costs are much less than those of the homogenization.Topology optimization is carried out with this data-driven model to enhance computational efficiency.In order to adapt the method of moving asymptotes(MMA),the eigenfrequency maximization problem is converted to its reciprocal minimization problem for sensitivity calculation.The method’s effectiveness is proved through several numerical examples.
基金China Academy of Railway Sciences Research Fund(award number:2024YJ50).
摘要Purpose-With the continuous expansion of railway hubs,increasing functional complexity and growing capacity constraints,the coordinated and efficient utilization of transportation resources-such as stations,lines and maintenance facilities-has become a critical issue for improving hub operational efficiency.This study focuses on the division of functions within railway hubs that incorporate shared stations operating under mixed high-speed and conventional train services.Design/methodology/approach-An optimization model for hub functional allocation is developed to achieve efficient resource utilization in hubs containing mixed-operation stations.A node-arc network representation combined with an improved multi-commodity flow model is employed,taking train dwell and operation time within the hub as the optimization objective.A case study is conducted to derive optimized solutions,followed by both qualitative and quantitative analyses.Findings-The results indicate that optimizing train operation routes and station assignments within the hub can effectively reduce the total occupation time of train flows and significantly improve resource utilization efficiency.Originality/value-The proposed model demonstrates both scientific rigor and practical effectiveness.In realworld operations,it can provide operators with preliminary and proactive functional allocation schemes,help identify key constraints limiting hub capacity utilization and offer decision support for transport plan adjustments or infrastructure and facility upgrades.
摘要In this paper, a bionic optimization algorithm based dimension reduction method named Ant Colony Optimization -Selection (ACO-S) is proposed for high-dimensional datasets. Because microarray datasets comprise tens of thousands of features (genes), they are usually used to test the dimension reduction techniques. ACO-S consists of two stages in which two well-known ACO algorithms, namely ant system and ant colony system, are utilized to seek for genes, respectively. In the first stage, a modified ant system is used to filter the nonsignificant genes from high-dimensional space, and a number of promising genes are reserved in the next step. In the second stage, an improved ant colony system is applied to gene selection. In order to enhance the search ability of ACOs, we propose a method for calculating priori available heuristic information and design a fuzzy logic controller to dynamically adjust the number of ants in ant colony system. Furthermore, we devise another fuzzy logic controller to tune the parameter (q0) in ant colony system. We evaluate the performance of ACO-S on five microarray datasets, which have dimensions varying from 7129 to 12000. We also compare the performance of ACO-S with the results obtained from four existing well-known bionic optimization algorithms. The comparison results show that ACO-S has a notable ability to" generate a gene subset with the smallest size and salient features while yielding high classification accuracy. The comparative results generated by ACO-S adopting different classifiers are also given. The proposed method is shown to be a promising and effective tool for mining high-dimension data and mobile robot navigation.
基金Supported by the National Natural Science Foundation of China Grant(11961047).
摘要In normed linear spaces,by applying the Minkowski difference,the concepts of efficient solutions,weakly efficient solutions,proper efficient solutions and Henig efficient solutions are introduced for set optimization with respect to co-radiant sets,and the relationships among them is discussed.Optimality conditions for minimal solutions and strictly minimal solutions of scalar set optimization are established by using the generalized oriented distance functions,respectively.The relationship between the solutions of set optimization problem and the solutions of scalar problem is studied.Several examples are given to explain our result.Properties of Gerstewitz’s functions with respect to co-radiant sets are discussed,which are used to establish sufficient conditions for weakly efficient solutions of set optimization.
基金fundings supported by Sichuan Science and Technology Program(2025YFHZ0065).
摘要Structural Reliability-Based Topology Optimization(RBTO),as an efficient design methodology,serves as a crucial means to ensure the development ofmodern engineering structures towards high performance,long service life,and high reliability.However,in practical design processes,topology optimization must not only account for the static performance of structures but also consider the impacts of various responses and uncertainties under complex dynamic conditions,which traditional methods often struggle accommodate.Therefore,this study proposes an RBTO framework based on a Kriging-assisted level set function and a novel Dynamic Hybrid Particle Swarm Optimization(DHPSO)algorithm.By leveraging the Kriging model as a surrogate,the high cost associated with repeatedly running finite element analysis processes is reduced,addressing the issue of minimizing structural compliance.Meanwhile,the DHPSO algorithm enables a better balance between the population’s developmental and exploratory capabilities,significantly accelerating convergence speed and enhancing global convergence performance.Finally,the proposed method is validated through three different structural examples,demonstrating its superior performance.Observed that the computational that,compared to the traditional Solid Isotropic Material with Penalization(SIMP)method,the proposed approach reduces the upper bound of structural compliance by approximately 30%.Additionally,the optimized results exhibit clear material interfaces without grayscale elements,and the stress concentration factor is reduced by approximately 42%.Consequently,the computational results fromdifferent examples verify the effectiveness and superiority of this study across various fields,achieving the goal of providing more precise optimization results within a shorter timeframe.
基金funded by the National Research Foundation of the RSA(reference and grant number RA22102965959)and supported by the University of the Free State(UFS).
摘要This psychobiography aimed to uncover the characteristics of optimal personality functioning(OPF)across the lifespan of Chabani Manganyi(1940–2024),the first Black South African clinical psychologist.The methodology used in this study encompassed an existential Franklian scholarly psychobiography.Sources of data on Manganyi included only publicly available primary and secondary data.Primary sources included Manganyi’s own writings,such as his autobiography,as well as his academic publications,including the biographies he wrote on creative individuals such as Gordimer,Sekoto and Mphahlele.Secondary sources included scholarly publications by academics and colleagues who knew him,as well as tributes,historical accounts,and archival records related to South African psychology scholarship during apartheid and the country’s transition to democracy.The study’s data sources were captured using online research platforms and search engines that included EBSCOhost,ResearchGate,Google Scholar,the University of the Free State’s Kovsie Catalogue and ProQuest.Alexander’s(1988,1990)biographical approach,which lists nine indicators of thematic salience(i.e.,uniqueness,negation,emphasis,primacy,frequency,error or distortion,isolation,incompletion,and omission)were utilized for the identification,extraction and compilation of salient data for analysis,alongside Frankl’s proposed nine characteristics of optimal personality functioning.Findings revealed that Manganyi personified characteristics of self-determining action,which were consistently evident in his pursuit of education,his intellectual independence,and his scholarly innovations in the field of South African psychology.Manganyi also personified a sense of self-transcendence,primarily expressed through his scholarship,mentorship,and social advocacy.He consistently positioned his dedication to work in his search for broader societal comprehension and transformation,beyond his personal advancement.Manganyi also exhibited qualities of future-directedness,work as vocation,and the search for meaning in resilient living,serving as a role model in managing challenging life and historical circumstances in transformative ways.The findings align with Frankl’s existential characteristics of optimal personality functioning as applied within this scholarly psychobiographical approach,highlighting its cross-cultural transportability in studying historical figures.
基金supported by National Key Research and Development Program of China(2024YFE0214000)National Natural Science Foundation of China(62173308)+3 种基金Natural Science Foundation of Zhejiang Province of China(LRG25F030002)Zhejiang Province Leading Geese Plan(2025C01056)Jinhua Science and Technology Project(2022-1-042)Natural Science Foundation of Jiangsu Province(BK20240009).
摘要Dear Editor,This letter addresses distributed optimization for resource allocation problems with time-varying objective functions and time-varying constraints.Inspired by the distributed average tracking(DAT)approach,a distributed control protocol is proposed for optimal resource allocation.The convergence to a time-varying optimal solution within a predefined time is proved.Two numerical examples are given to illustrate the effectiveness of the proposed approach.
基金supported by National Key Research and Development Program of China under Grant 2024YFE0210800National Natural Science Foundation of China under Grant 62495062Beijing Natural Science Foundation under Grant L242017.
摘要The Dynamical Density Functional Theory(DDFT)algorithm,derived by associating classical Density Functional Theory(DFT)with the fundamental Smoluchowski dynamical equation,describes the evolution of inhomo-geneous fluid density distributions over time.It plays a significant role in studying the evolution of density distributions over time in inhomogeneous systems.The Sunway Bluelight II supercomputer,as a new generation of China’s developed supercomputer,possesses powerful computational capabilities.Porting and optimizing industrial software on this platform holds significant importance.For the optimization of the DDFT algorithm,based on the Sunway Bluelight II supercomputer and the unique hardware architecture of the SW39000 processor,this work proposes three acceleration strategies to enhance computational efficiency and performance,including direct parallel optimization,local-memory constrained optimization for CPEs,and multi-core groups collaboration and communication optimization.This method combines the characteristics of the program’s algorithm with the unique hardware architecture of the Sunway Bluelight II supercomputer,optimizing the storage and transmission structures to achieve a closer integration of software and hardware.For the first time,this paper presents Sunway-Dynamical Density Functional Theory(SW-DDFT).Experimental results show that SW-DDFT achieves a speedup of 6.67 times within a single-core group compared to the original DDFT implementation,with six core groups(a total of 384 CPEs),the maximum speedup can reach 28.64 times,and parallel efficiency can reach 71%,demonstrating excellent acceleration performance.
基金funded by the National Key Research and Development Program of China(No.2023YFD2201300)the Key Research and Development Program of Zhejiang Province(2023C02042),China.
摘要Corosolic acid,a naturally occurring pentacyclic triterpenic acid,is widely recognized for its broad spectrum of biological activities,particularly its antidiabetic properties,making it a popular ingredient in dietary supplements for regulating blood sugar levels.Beyond its anti-diabetic effects,recent studies have revealed its therapeutic potential in areas such as anti-cancer,anti-inflammatory,and antibacterial activities.However,its clinical application is hindered by poor water solubility and low bioavailability due to its molecular structure.This review systematically examines the pharmacological activities of corosolic acid,emphasizing its mechanisms of action in disease intervention.Emerging strategies to overcome its inherent limitations,including chemical modifications,microbial transformations,and advanced delivery systems,are also discussed.Notably,some chemical derivatives exhibitα-glucosidase inhibition with IC50 values half that of corosolic acid.Microbial transformations have been shown to enhance its bioavailability while reducing cancer cell toxicity.Additionally,corosolic acid-based delivery systems have demonstrated significant improvements in solubility,stability,and biological activity.By consolidating current insights into its functional properties and biological activity enhancement methods,this review aims to emphasize the practical application values in food and medicine and the future development of corosolic acid as a versatile bioactive compound.
基金supported by the Innovation Fund Project of the Gansu Education Department(Grant No.2021B-099).
摘要The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.
基金Funded by the Deep Underground National Science&Technology Major Project gram of China(No.2024ZD1003704)the National Natural Science Foundation of China(Nos.51834001 and 52374111)。
摘要The multi-objective optimization of backfill effect based on response surface methodology and desirability function(RSM-DF)was conducted.Firstly,the test results show that the uniaxial compressive strength(UCS)increases with cement sand ratio(CSR),slurry concentration(SC),and curing age(CA),while flow resistance(FR)increases with SC and backfill flow rate(BFR),and decreases with CSR.Then the regression models of UCS and FR as response values were established through RSM.Multi-factor interaction found that CSR-CA impacted UCS most,while SC-BFR impacted FR most.By introducing the desirability function,the optimal backfill parameters were obtained based on RSM-DF(CSR is 1:6.25,SC is 69%,CA is 11.5 d,and BFR is 90 m3/h),showing close results of Design Expert and high reliability for optimization.For a copper mine in China,RSM-DF optimization will reduce cement consumption by 4758 t per year,increase tailings consumption by about 6700 t,and reduce CO2emission by about 4758 t.Thus,RSM-DF provides a new approach for backfill parameters optimization,which has important theoretical and practical values.