Traditional large-scale multi-objective optimization algorithms(LSMOEAs)encounter difficulties when dealing with sparse large-scale multi-objective optimization problems(SLM-OPs)where most decision variables are zero....Traditional large-scale multi-objective optimization algorithms(LSMOEAs)encounter difficulties when dealing with sparse large-scale multi-objective optimization problems(SLM-OPs)where most decision variables are zero.As a result,many algorithms use a two-layer encoding approach to optimize binary variable Mask and real variable Dec separately.Nevertheless,existing optimizers often focus on locating non-zero variable posi-tions to optimize the binary variables Mask.However,approxi-mating the sparse distribution of real Pareto optimal solutions does not necessarily mean that the objective function is optimized.In data mining,it is common to mine frequent itemsets appear-ing together in a dataset to reveal the correlation between data.Inspired by this,we propose a novel two-layer encoding learning swarm optimizer based on frequent itemsets(TELSO)to address these SLMOPs.TELSO mined the frequent terms of multiple particles with better target values to find mask combinations that can obtain better objective values for fast convergence.Experi-mental results on five real-world problems and eight benchmark sets demonstrate that TELSO outperforms existing state-of-the-art sparse large-scale multi-objective evolutionary algorithms(SLMOEAs)in terms of performance and convergence speed.展开更多
During the last three decades,evolutionary algorithms(EAs)have shown superiority in solving complex optimization problems,especially those with multiple objectives and non-differentiable landscapes.However,due to the ...During the last three decades,evolutionary algorithms(EAs)have shown superiority in solving complex optimization problems,especially those with multiple objectives and non-differentiable landscapes.However,due to the stochastic search strategies,the performance of most EAs deteriorates drastically when handling a large number of decision variables.To tackle the curse of dimensionality,this work proposes an efficient EA for solving super-large-scale multi-objective optimization problems with sparse optimal solutions.The proposed algorithm estimates the sparse distribution of optimal solutions by optimizing a binary vector for each solution,and provides a fast clustering method to highly reduce the dimensionality of the search space.More importantly,all the operations related to the decision variables only contain several matrix calculations,which can be directly accelerated by GPUs.While existing EAs are capable of handling fewer than 10000 real variables,the proposed algorithm is verified to be effective in handling 1000000 real variables.Furthermore,since the proposed algorithm handles the large number of variables via accelerated matrix calculations,its runtime can be reduced to less than 10%of the runtime of existing EAs.展开更多
Sparse large-scale multi-objective optimization problems(SLMOPs)are common in science and engineering.However,the large-scale problem represents the high dimensionality of the decision space,requiring algorithms to tr...Sparse large-scale multi-objective optimization problems(SLMOPs)are common in science and engineering.However,the large-scale problem represents the high dimensionality of the decision space,requiring algorithms to traverse vast expanse with limited computational resources.Furthermore,in the context of sparse,most variables in Pareto optimal solutions are zero,making it difficult for algorithms to identify non-zero variables efficiently.This paper is dedicated to addressing the challenges posed by SLMOPs.To start,we introduce innovative objective functions customized to mine maximum and minimum candidate sets.This substantial enhancement dramatically improves the efficacy of frequent pattern mining.In this way,selecting candidate sets is no longer based on the quantity of nonzero variables they contain but on a higher proportion of nonzero variables within specific dimensions.Additionally,we unveil a novel approach to association rule mining,which delves into the intricate relationships between non-zero variables.This novel methodology aids in identifying sparse distributions that can potentially expedite reductions in the objective function value.We extensively tested our algorithm across eight benchmark problems and four real-world SLMOPs.The results demonstrate that our approach achieves competitive solutions across various challenges.展开更多
The performance of analytical derivative and sparse matrix techniques applied to a traditional dense sequential quadratic programming (SQP) is studied, and the strategy utilizing those techniques is also presented.Com...The performance of analytical derivative and sparse matrix techniques applied to a traditional dense sequential quadratic programming (SQP) is studied, and the strategy utilizing those techniques is also presented.Computational results on two typical chemical optimization problems demonstrate significant enhancement in efficiency, which shows this strategy is promising and suitable for large-scale process optimization problems.展开更多
Multi-label feature selection(MFS)is a crucial dimensionality reduction technique aimed at identifying informative features associated with multiple labels.However,traditional centralized methods face significant chal...Multi-label feature selection(MFS)is a crucial dimensionality reduction technique aimed at identifying informative features associated with multiple labels.However,traditional centralized methods face significant challenges in privacy-sensitive and distributed settings,often neglecting label dependencies and suffering from low computational efficiency.To address these issues,we introduce a novel framework,Fed-MFSDHBCPSO—federated MFS via dual-layer hybrid breeding cooperative particle swarm optimization algorithm with manifold and sparsity regularization(DHBCPSO-MSR).Leveraging the federated learning paradigm,Fed-MFSDHBCPSO allows clients to perform local feature selection(FS)using DHBCPSO-MSR.Locally selected feature subsets are encrypted with differential privacy(DP)and transmitted to a central server,where they are securely aggregated and refined through secure multi-party computation(SMPC)until global convergence is achieved.Within each client,DHBCPSO-MSR employs a dual-layer FS strategy.The inner layer constructs sample and label similarity graphs,generates Laplacian matrices to capture the manifold structure between samples and labels,and applies L2,1-norm regularization to sparsify the feature subset,yielding an optimized feature weight matrix.The outer layer uses a hybrid breeding cooperative particle swarm optimization algorithm to further refine the feature weight matrix and identify the optimal feature subset.The updated weight matrix is then fed back to the inner layer for further optimization.Comprehensive experiments on multiple real-world multi-label datasets demonstrate that Fed-MFSDHBCPSO consistently outperforms both centralized and federated baseline methods across several key evaluation metrics.展开更多
In this paper we report a sparse truncated Newton algorithm for handling large-scale simple bound nonlinear constrained minimixation problem. The truncated Newton method is used to update the variables with indices ou...In this paper we report a sparse truncated Newton algorithm for handling large-scale simple bound nonlinear constrained minimixation problem. The truncated Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At each iterative level, the search direction consists of three parts, one of which is a subspace truncated Newton direction, the other two are subspace gradient and modified gradient directions. The subspace truncated Newton direction is obtained by solving a sparse system of linear equations. The global convergence and quadratic convergence rate of the algorithm are proved and some numerical tests are given.展开更多
Formalizing complex processes and phenomena of a real-world problem may require a large number of variables and constraints,resulting in what is termed a large-scale optimization problem.Nowadays,such large-scale opti...Formalizing complex processes and phenomena of a real-world problem may require a large number of variables and constraints,resulting in what is termed a large-scale optimization problem.Nowadays,such large-scale optimization problems are solved using computing machines,leading to an enormous computational time being required,which may delay deriving timely solutions.Decomposition methods,which partition a large-scale optimization problem into lower-dimensional subproblems,represent a key approach to addressing time-efficiency issues.There has been significant progress in both applied mathematics and emerging artificial intelligence approaches on this front.This work aims at providing an overview of the decomposition methods from both the mathematics and computer science points of view.We also remark on the state-of-the-art developments and recent applications of the decomposition methods,and discuss the future research and development perspectives.展开更多
Expensive multiobjective optimization problems(EMOPs)are complex optimization problems exacted from realworld applications,where each objective function evaluation(FE)involves expensive computations or physical experi...Expensive multiobjective optimization problems(EMOPs)are complex optimization problems exacted from realworld applications,where each objective function evaluation(FE)involves expensive computations or physical experiments.Many surrogate-assisted evolutionary algorithms(SAEAs)have been designed to solve EMOPs.Nevertheless,EMOPs with large-scale decision variables remain challenging for existing SAEAs,leading to difficulties in maintaining convergence and diversity.To address this deficiency,we proposed a variable reconstructionbased SAEA(VREA)to balance convergence enhancement and diversity maintenance.Generally,a cluster-based variable reconstruction strategy reconstructs the original large-scale decision variables into low-dimensional weight variables.Thus,the population can be rapidly pushed towards the Pareto set(PS)by optimizing low-dimensional weight variables with the assistance of surrogate models.Population diversity is improved due to the cluster-based variable reconstruction strategy.An adaptive search step size strategy is proposed to balance exploration and exploitation further.Experimental comparisons with four state-of-the-art SAEAs are conducted on benchmark EMOPs with up to 1000 decision variables and an aerodynamic design task.Experimental results demonstrate that VREA obtains well-converged and diverse solutions with limited real FEs.展开更多
The research on optimization methods for constellation launch deployment strategies focused on the consideration of mission interval time constraints at the launch site.Firstly,a dynamic modeling of the constellation ...The research on optimization methods for constellation launch deployment strategies focused on the consideration of mission interval time constraints at the launch site.Firstly,a dynamic modeling of the constellation deployment process was established,and the relationship between the deployment window and the phase difference of the orbit insertion point,as well as the cost of phase adjustment after orbit insertion,was derived.Then,the combination of the constellation deployment position sequence was treated as a parameter,together with the sequence of satellite deployment intervals,as optimization variables,simplifying a highdimensional search problem within a wide range of dates to a finite-dimensional integer programming problem.An improved genetic algorithm with local search on deployment dates was introduced to optimize the launch deployment strategy.With the new description of the optimization variables,the total number of elements in the solution space was reduced by N orders of magnitude.Numerical simulation confirms that the proposed optimization method accelerates the convergence speed from hours to minutes.展开更多
Radio antenna arrays have many advantages for astronomical observations,such as high resolution,high sensitivity,multi-target simultaneous observation,and flexible beam formation.Problems surrounding key indices,such ...Radio antenna arrays have many advantages for astronomical observations,such as high resolution,high sensitivity,multi-target simultaneous observation,and flexible beam formation.Problems surrounding key indices,such as sensitivity enhancement,scanning range extension,and sidelobe level suppression,need to be solved urgently.Here,we propose a sparse optimization scheme based on a genetic algorithm for a 64-array element planar radio antenna array.As optimization targets for the iterative process of the genetic algorithm,we use the maximum sidelobe levels and beamwidth of multiple cross-section patterns that pass through the main beam in three-dimensions,with the maximum sidelobe levels of the patterns at several different scanning angles.Element positions are adjusted for iterations,to select the optimal array configuration.Following sparse layout optimization,the simulated 64-element planar radio antenna array shows that the maximum sidelobe level decreases by 1.79 dB,and the beamwidth narrows by 3°.Within the scan range of±30°,after sparse array optimization,all sidelobe levels decrease,and all beamwidths narrow.This performance improvement can potentially enhance the sensitivity and spatial resolution of radio telescope systems.展开更多
The construction of island power grids is a systematic engineering task.To ensure the safe operation of power grid systems,optimizing the line layout of island power grids is crucial.Especially in the current context ...The construction of island power grids is a systematic engineering task.To ensure the safe operation of power grid systems,optimizing the line layout of island power grids is crucial.Especially in the current context of large-scale distributed renewable energy integration into the power grid,conventional island power grid line layouts can no longer meet actual demands.It is necessary to combine the operational characteristics of island power systems and historical load data to perform load forecasting,thereby generating power grid line layout paths.This article focuses on large-scale distributed renewable energy integration,summarizing optimization strategies for island power grid line layouts,and providing a solid guarantee for the safe and stable operation of island power systems.展开更多
Sparse Large-scale Multi-objective Optimization Problems(sparse LMOPs)widely exist in various optimization applications,such as neural network training,portfolio optimization,and feature selection of classification.Al...Sparse Large-scale Multi-objective Optimization Problems(sparse LMOPs)widely exist in various optimization applications,such as neural network training,portfolio optimization,and feature selection of classification.Although numerous methods exist,automatically selecting efficient solving strategies for sparse LMOPs remains highly challenging.Given this,we propose a reinforcement learning assisted autonomous sparse multi-objective evolutionary algorithm,which aims to effectively utilize sparse knowledge for designing diversified genetic operators,and automatically select appropriate genetic operators for various problems or different situations within the same optimization process.Specifically,three sparsity-aware genetic operators are designed by utilizing sparsity statistic,sparsity clustering,and sparsity logic operation.They possess distinct advantages in terms of convergence speed,solution quality,and diversity.Furthermore,the utilization of deep Q-network enables the automatic selection of suitable operators for offspring reproduction based on the current sparse state of the population.The proposed algorithm is compared with five state-of-the-art algorithms on eight benchmark and three real-world problems.Experimental results demonstrate the superiority of the proposed algorithm and the effectiveness of the proposed sparse genetic operators for solving sparse LMOPs.展开更多
In recent decades,great progress has been made in learnable multiobjective evolutionary algorithms(MOEAs)in the field of evolutionary computations.However,existing learnable MOEAs have not been equipped with powerful ...In recent decades,great progress has been made in learnable multiobjective evolutionary algorithms(MOEAs)in the field of evolutionary computations.However,existing learnable MOEAs have not been equipped with powerful strategies for addressing the grand series associated with sparse large-scale multiobjective optimization problems(sparse LSMOPs),which include the curse of dimensionality and unknown sparsity characteristics.This work proposes a generative adversarial network(GAN)-guided evolutionary algorithm for solving sparse LSMOPs.GAN-aided offspring generation is adopted at each generation to generate high-quality sparse offspring solutions to improve the search performance,owing to the GAN’s powerful learning and generative capabilities.Specifically,random interpolation and discretization strategies are utilized to prevent mode collapse and falling into local optima,thereby generating promising sparse offspring solutions.The experimental results on both benchmark and real-world problems verify the superior performance of the proposed algorithm compared with the state-of-the-art evolutionary algorithms.展开更多
Early fault detection for spiral bevel gears is crucial to ensure normal operation and prevent accidents.The harmonic components,excited by the time-varying mesh stiffness,always appear in measured vibration signal.Ho...Early fault detection for spiral bevel gears is crucial to ensure normal operation and prevent accidents.The harmonic components,excited by the time-varying mesh stiffness,always appear in measured vibration signal.How to extract the periodical impulses that indicate gear localized fault buried in the intensive noise and interfered by harmonics is a challenging task.In this paper,a novel Periodical Sparse-Assisted Decoupling(PSAD)method is proposed as an optimization problem to extract fault feature from noisy vibration signal.The PSAD method decouples the impulsive fault feature and harmonic components based on the sparse representation method.The sparsity within and across groups property and the periodicity of the fault feature are incorporated into the regularizer as the prior information.The nonconvex penalty is employed to highlight the sparsity of fault features.Meanwhile,the weight factor based on2norm of each group is constructed to strengthen the amplitude of fault feature.An iterative algorithm with Majorization-Minimization(MM)is derived to solve the optimization problem.Simulation study and experimental analysis confirm the performance of the proposed PSAD method in extracting and enhancing defect impulses from noisy signal.The suggested method surpasses other comparative methods in extracting and enhancing fault features.展开更多
Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms a...Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.展开更多
Large-scale multi-objective optimization problems(MOPs)that involve a large number of decision variables,have emerged from many real-world applications.While evolutionary algorithms(EAs)have been widely acknowledged a...Large-scale multi-objective optimization problems(MOPs)that involve a large number of decision variables,have emerged from many real-world applications.While evolutionary algorithms(EAs)have been widely acknowledged as a mainstream method for MOPs,most research progress and successful applications of EAs have been restricted to MOPs with small-scale decision variables.More recently,it has been reported that traditional multi-objective EAs(MOEAs)suffer severe deterioration with the increase of decision variables.As a result,and motivated by the emergence of real-world large-scale MOPs,investigation of MOEAs in this aspect has attracted much more attention in the past decade.This paper reviews the progress of evolutionary computation for large-scale multi-objective optimization from two angles.From the key difficulties of the large-scale MOPs,the scalability analysis is discussed by focusing on the performance of existing MOEAs and the challenges induced by the increase of the number of decision variables.From the perspective of methodology,the large-scale MOEAs are categorized into three classes and introduced respectively:divide and conquer based,dimensionality reduction based and enhanced search-based approaches.Several future research directions are also discussed.展开更多
Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studi...Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.展开更多
Massive multiple-input multiple-output(MIMO)technology enables higher data rate transmission in the future mobile communications.However,exploiting a large number of antenna elements at base station(BS)makes effective...Massive multiple-input multiple-output(MIMO)technology enables higher data rate transmission in the future mobile communications.However,exploiting a large number of antenna elements at base station(BS)makes effective implementation of massive MIMO challenging,due to the size and weight limits of the masssive MIMO that are located on each BS.Therefore,in order to miniaturize the massive MIMO,it is crucial to reduce the number of antenna elements via effective methods such as sparse array synthesis.In this paper,a multiple-pattern synthesis is considered towards convex optimization(CO).The joint convex optimization(JCO)based synthesis is proposed to construct a codebook for beamforming.Then,a criterion containing multiple constraints is developed,in which the sparse array is required to fullfill all constraints.Finally,extensive evaluations are performed under realistic simulation settings.The results show that with the same number of antenna elements,sparse array using the proposed JCO-based synthesis outperforms not only the uniform array,but also the sparse array with the existing CO-based synthesis method.Furthermore,with a half of the number of antenna elements that on the uniform array,the performance of the JCO-based sparse array approaches to that of the uniform array.展开更多
To solve large-scale optimization problems,Fragrance coefficient and variant Particle Swarm local search Butterfly Optimization Algorithm(FPSBOA)is proposed.In the position update stage of Butterfly Optimization Algor...To solve large-scale optimization problems,Fragrance coefficient and variant Particle Swarm local search Butterfly Optimization Algorithm(FPSBOA)is proposed.In the position update stage of Butterfly Optimization Algorithm(BOA),the fragrance coefficient is designed to balance the exploration and exploitation of BOA.The variant particle swarm local search strategy is proposed to improve the local search ability of the current optimal butterfly and prevent the algorithm from falling into local optimality.192000-dimensional functions and 201000-dimensional CEC 2010 large-scale functions are used to verify FPSBOA for complex large-scale optimization problems.The experimental results are statistically analyzed by Friedman test and Wilcoxon rank-sum test.All attained results demonstrated that FPSBOA can better solve more challenging scientific and industrial real-world problems with thousands of variables.Finally,four mechanical engineering problems and one ten-dimensional process synthesis and design problem are applied to FPSBOA,which shows FPSBOA has the feasibility and effectiveness in real-world application problems.展开更多
In isogeometric analysis,it is frequently required to handle the geometric models enclosed by four-sided or non-four-sided boundary patches,such as trimmed surfaces.In this paper,we develop a Gregory solid based metho...In isogeometric analysis,it is frequently required to handle the geometric models enclosed by four-sided or non-four-sided boundary patches,such as trimmed surfaces.In this paper,we develop a Gregory solid based method to parameterize those models.First,we extend the Gregory patch representation to the trivariate Gregory solid representation.Second,the trivariate Gregory solid representation is employed to interpolate the boundary patches of a geometric model,thus generating the polyhedral volume parametrization.To improve the regularity of the polyhedral volume parametrization,we formulate the construction of the trivariate Gregory solid as a sparse optimization problem,where the optimization objective function is a linear combination of some terms,including a sparse term aiming to reduce the negative Jacobian area of the Gregory solid.Then,the alternating direction method of multipliers(ADMM)is used to solve the sparse optimization problem.Lots of experimental examples illustrated in this paper demonstrate the effectiveness and efficiency of the developed method.展开更多
基金supported by the Scientific Research Project of Xiang Jiang Lab(22XJ02003)the University Fundamental Research Fund(23-ZZCX-JDZ-28)+5 种基金the National Science Fund for Outstanding Young Scholars(62122093)the National Natural Science Foundation of China(72071205)the Hunan Graduate Research Innovation Project(ZC23112101-10)the Hunan Natural Science Foundation Regional Joint Project(2023JJ50490)the Science and Technology Project for Young and Middle-aged Talents of Hunan(2023TJ-Z03)the Science and Technology Innovation Program of Humnan Province(2023RC1002)。
文摘Traditional large-scale multi-objective optimization algorithms(LSMOEAs)encounter difficulties when dealing with sparse large-scale multi-objective optimization problems(SLM-OPs)where most decision variables are zero.As a result,many algorithms use a two-layer encoding approach to optimize binary variable Mask and real variable Dec separately.Nevertheless,existing optimizers often focus on locating non-zero variable posi-tions to optimize the binary variables Mask.However,approxi-mating the sparse distribution of real Pareto optimal solutions does not necessarily mean that the objective function is optimized.In data mining,it is common to mine frequent itemsets appear-ing together in a dataset to reveal the correlation between data.Inspired by this,we propose a novel two-layer encoding learning swarm optimizer based on frequent itemsets(TELSO)to address these SLMOPs.TELSO mined the frequent terms of multiple particles with better target values to find mask combinations that can obtain better objective values for fast convergence.Experi-mental results on five real-world problems and eight benchmark sets demonstrate that TELSO outperforms existing state-of-the-art sparse large-scale multi-objective evolutionary algorithms(SLMOEAs)in terms of performance and convergence speed.
基金This work was supported in part by the National Key Research and Development Program of China(2018AAA0100100)the National Natural Science Foundation of China(61822301,61876123,61906001)+2 种基金the Collaborative Innovation Program of Universities in Anhui Province(GXXT-2020-051)the Hong Kong Scholars Program(XJ2019035)Anhui Provincial Natural Science Foundation(1908085QF271).
文摘During the last three decades,evolutionary algorithms(EAs)have shown superiority in solving complex optimization problems,especially those with multiple objectives and non-differentiable landscapes.However,due to the stochastic search strategies,the performance of most EAs deteriorates drastically when handling a large number of decision variables.To tackle the curse of dimensionality,this work proposes an efficient EA for solving super-large-scale multi-objective optimization problems with sparse optimal solutions.The proposed algorithm estimates the sparse distribution of optimal solutions by optimizing a binary vector for each solution,and provides a fast clustering method to highly reduce the dimensionality of the search space.More importantly,all the operations related to the decision variables only contain several matrix calculations,which can be directly accelerated by GPUs.While existing EAs are capable of handling fewer than 10000 real variables,the proposed algorithm is verified to be effective in handling 1000000 real variables.Furthermore,since the proposed algorithm handles the large number of variables via accelerated matrix calculations,its runtime can be reduced to less than 10%of the runtime of existing EAs.
基金support by the Open Project of Xiangjiang Laboratory(22XJ02003)the University Fundamental Research Fund(23-ZZCX-JDZ-28,ZK21-07)+5 种基金the National Science Fund for Outstanding Young Scholars(62122093)the National Natural Science Foundation of China(72071205)the Hunan Graduate Research Innovation Project(CX20230074)the Hunan Natural Science Foundation Regional Joint Project(2023JJ50490)the Science and Technology Project for Young and Middle-aged Talents of Hunan(2023TJZ03)the Science and Technology Innovation Program of Humnan Province(2023RC1002).
文摘Sparse large-scale multi-objective optimization problems(SLMOPs)are common in science and engineering.However,the large-scale problem represents the high dimensionality of the decision space,requiring algorithms to traverse vast expanse with limited computational resources.Furthermore,in the context of sparse,most variables in Pareto optimal solutions are zero,making it difficult for algorithms to identify non-zero variables efficiently.This paper is dedicated to addressing the challenges posed by SLMOPs.To start,we introduce innovative objective functions customized to mine maximum and minimum candidate sets.This substantial enhancement dramatically improves the efficacy of frequent pattern mining.In this way,selecting candidate sets is no longer based on the quantity of nonzero variables they contain but on a higher proportion of nonzero variables within specific dimensions.Additionally,we unveil a novel approach to association rule mining,which delves into the intricate relationships between non-zero variables.This novel methodology aids in identifying sparse distributions that can potentially expedite reductions in the objective function value.We extensively tested our algorithm across eight benchmark problems and four real-world SLMOPs.The results demonstrate that our approach achieves competitive solutions across various challenges.
基金Supported by the National Natural Science Foundation of China(No.29906010).
文摘The performance of analytical derivative and sparse matrix techniques applied to a traditional dense sequential quadratic programming (SQP) is studied, and the strategy utilizing those techniques is also presented.Computational results on two typical chemical optimization problems demonstrate significant enhancement in efficiency, which shows this strategy is promising and suitable for large-scale process optimization problems.
文摘Multi-label feature selection(MFS)is a crucial dimensionality reduction technique aimed at identifying informative features associated with multiple labels.However,traditional centralized methods face significant challenges in privacy-sensitive and distributed settings,often neglecting label dependencies and suffering from low computational efficiency.To address these issues,we introduce a novel framework,Fed-MFSDHBCPSO—federated MFS via dual-layer hybrid breeding cooperative particle swarm optimization algorithm with manifold and sparsity regularization(DHBCPSO-MSR).Leveraging the federated learning paradigm,Fed-MFSDHBCPSO allows clients to perform local feature selection(FS)using DHBCPSO-MSR.Locally selected feature subsets are encrypted with differential privacy(DP)and transmitted to a central server,where they are securely aggregated and refined through secure multi-party computation(SMPC)until global convergence is achieved.Within each client,DHBCPSO-MSR employs a dual-layer FS strategy.The inner layer constructs sample and label similarity graphs,generates Laplacian matrices to capture the manifold structure between samples and labels,and applies L2,1-norm regularization to sparsify the feature subset,yielding an optimized feature weight matrix.The outer layer uses a hybrid breeding cooperative particle swarm optimization algorithm to further refine the feature weight matrix and identify the optimal feature subset.The updated weight matrix is then fed back to the inner layer for further optimization.Comprehensive experiments on multiple real-world multi-label datasets demonstrate that Fed-MFSDHBCPSO consistently outperforms both centralized and federated baseline methods across several key evaluation metrics.
基金The research was supported by the State Education Grant for Retumed Scholars
文摘In this paper we report a sparse truncated Newton algorithm for handling large-scale simple bound nonlinear constrained minimixation problem. The truncated Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At each iterative level, the search direction consists of three parts, one of which is a subspace truncated Newton direction, the other two are subspace gradient and modified gradient directions. The subspace truncated Newton direction is obtained by solving a sparse system of linear equations. The global convergence and quadratic convergence rate of the algorithm are proved and some numerical tests are given.
基金The Australian Research Council(DP200101197,DP230101107).
文摘Formalizing complex processes and phenomena of a real-world problem may require a large number of variables and constraints,resulting in what is termed a large-scale optimization problem.Nowadays,such large-scale optimization problems are solved using computing machines,leading to an enormous computational time being required,which may delay deriving timely solutions.Decomposition methods,which partition a large-scale optimization problem into lower-dimensional subproblems,represent a key approach to addressing time-efficiency issues.There has been significant progress in both applied mathematics and emerging artificial intelligence approaches on this front.This work aims at providing an overview of the decomposition methods from both the mathematics and computer science points of view.We also remark on the state-of-the-art developments and recent applications of the decomposition methods,and discuss the future research and development perspectives.
基金supported by the National Natural Science Foundation of China(U20A20306,62276191)the Fundamental Research Funds for the Central Universities(HUST2023JYCXJJ011).
文摘Expensive multiobjective optimization problems(EMOPs)are complex optimization problems exacted from realworld applications,where each objective function evaluation(FE)involves expensive computations or physical experiments.Many surrogate-assisted evolutionary algorithms(SAEAs)have been designed to solve EMOPs.Nevertheless,EMOPs with large-scale decision variables remain challenging for existing SAEAs,leading to difficulties in maintaining convergence and diversity.To address this deficiency,we proposed a variable reconstructionbased SAEA(VREA)to balance convergence enhancement and diversity maintenance.Generally,a cluster-based variable reconstruction strategy reconstructs the original large-scale decision variables into low-dimensional weight variables.Thus,the population can be rapidly pushed towards the Pareto set(PS)by optimizing low-dimensional weight variables with the assistance of surrogate models.Population diversity is improved due to the cluster-based variable reconstruction strategy.An adaptive search step size strategy is proposed to balance exploration and exploitation further.Experimental comparisons with four state-of-the-art SAEAs are conducted on benchmark EMOPs with up to 1000 decision variables and an aerodynamic design task.Experimental results demonstrate that VREA obtains well-converged and diverse solutions with limited real FEs.
文摘The research on optimization methods for constellation launch deployment strategies focused on the consideration of mission interval time constraints at the launch site.Firstly,a dynamic modeling of the constellation deployment process was established,and the relationship between the deployment window and the phase difference of the orbit insertion point,as well as the cost of phase adjustment after orbit insertion,was derived.Then,the combination of the constellation deployment position sequence was treated as a parameter,together with the sequence of satellite deployment intervals,as optimization variables,simplifying a highdimensional search problem within a wide range of dates to a finite-dimensional integer programming problem.An improved genetic algorithm with local search on deployment dates was introduced to optimize the launch deployment strategy.With the new description of the optimization variables,the total number of elements in the solution space was reduced by N orders of magnitude.Numerical simulation confirms that the proposed optimization method accelerates the convergence speed from hours to minutes.
基金supported by the Ministry of Science and Technology SKA Special Project(2020SKA0110202)the Special Project on Building a Science and Technology Innovation Center for South and Southeast Asia–International Joint Innovation Platform in Yunnan Province:"Yunnan Sino-Malaysian International Joint Laboratory of HF-VHF Advanced Radio Astronomy Technology"(202303AP140003)+4 种基金the National Natural Science Foundation of China (NSFC) Joint Fund for Astronomy (JFA) incubator program (U2031133)the International Partnership Program Project of the International Cooperation Bureau of the Chinese Academy of Sciences:"Belt and Road"Cooperation (114A11KYSB20200001)the Kunming Foreign (International) Cooperation Base Program:"Yunnan Observatory of the Chinese Academy of Sciences-University of Malaya Joint R&D Cooperation Base for Advanced Radio Astronomy Technology"(GHJD-2021022)the China-Malaysia Collaborative Research on Space Remote Sensing and Radio Astronomy Observation of Space Weather at Low and Middle Latitudes under the Key Special Project of the State Key R&D Program of the Ministry of Science and Technology for International Cooperation in Science,Technology and Innovation among Governments (2022YFE0140000)the High-precision calibration method for low-frequency radio interferometric arrays for the SKA project of the Ministry of Science and Technology(2020SKA0110300).
文摘Radio antenna arrays have many advantages for astronomical observations,such as high resolution,high sensitivity,multi-target simultaneous observation,and flexible beam formation.Problems surrounding key indices,such as sensitivity enhancement,scanning range extension,and sidelobe level suppression,need to be solved urgently.Here,we propose a sparse optimization scheme based on a genetic algorithm for a 64-array element planar radio antenna array.As optimization targets for the iterative process of the genetic algorithm,we use the maximum sidelobe levels and beamwidth of multiple cross-section patterns that pass through the main beam in three-dimensions,with the maximum sidelobe levels of the patterns at several different scanning angles.Element positions are adjusted for iterations,to select the optimal array configuration.Following sparse layout optimization,the simulated 64-element planar radio antenna array shows that the maximum sidelobe level decreases by 1.79 dB,and the beamwidth narrows by 3°.Within the scan range of±30°,after sparse array optimization,all sidelobe levels decrease,and all beamwidths narrow.This performance improvement can potentially enhance the sensitivity and spatial resolution of radio telescope systems.
文摘The construction of island power grids is a systematic engineering task.To ensure the safe operation of power grid systems,optimizing the line layout of island power grids is crucial.Especially in the current context of large-scale distributed renewable energy integration into the power grid,conventional island power grid line layouts can no longer meet actual demands.It is necessary to combine the operational characteristics of island power systems and historical load data to perform load forecasting,thereby generating power grid line layout paths.This article focuses on large-scale distributed renewable energy integration,summarizing optimization strategies for island power grid line layouts,and providing a solid guarantee for the safe and stable operation of island power systems.
基金supported by the National Natural Science Foundation of China(Nos.62303013,62276001,and U21A20512).
文摘Sparse Large-scale Multi-objective Optimization Problems(sparse LMOPs)widely exist in various optimization applications,such as neural network training,portfolio optimization,and feature selection of classification.Although numerous methods exist,automatically selecting efficient solving strategies for sparse LMOPs remains highly challenging.Given this,we propose a reinforcement learning assisted autonomous sparse multi-objective evolutionary algorithm,which aims to effectively utilize sparse knowledge for designing diversified genetic operators,and automatically select appropriate genetic operators for various problems or different situations within the same optimization process.Specifically,three sparsity-aware genetic operators are designed by utilizing sparsity statistic,sparsity clustering,and sparsity logic operation.They possess distinct advantages in terms of convergence speed,solution quality,and diversity.Furthermore,the utilization of deep Q-network enables the automatic selection of suitable operators for offspring reproduction based on the current sparse state of the population.The proposed algorithm is compared with five state-of-the-art algorithms on eight benchmark and three real-world problems.Experimental results demonstrate the superiority of the proposed algorithm and the effectiveness of the proposed sparse genetic operators for solving sparse LMOPs.
基金supported in part by National Natural Science Foundation of China(Nos.61906002,62076005,and U20A20398)the Natural Science Foundation of Anhui Province,China(Nos.2008085MF191 and 2508085 MF157)the University Synergy Innovation Program of Anhui Province,China(No.GXXT-2021-002).
文摘In recent decades,great progress has been made in learnable multiobjective evolutionary algorithms(MOEAs)in the field of evolutionary computations.However,existing learnable MOEAs have not been equipped with powerful strategies for addressing the grand series associated with sparse large-scale multiobjective optimization problems(sparse LSMOPs),which include the curse of dimensionality and unknown sparsity characteristics.This work proposes a generative adversarial network(GAN)-guided evolutionary algorithm for solving sparse LSMOPs.GAN-aided offspring generation is adopted at each generation to generate high-quality sparse offspring solutions to improve the search performance,owing to the GAN’s powerful learning and generative capabilities.Specifically,random interpolation and discretization strategies are utilized to prevent mode collapse and falling into local optima,thereby generating promising sparse offspring solutions.The experimental results on both benchmark and real-world problems verify the superior performance of the proposed algorithm compared with the state-of-the-art evolutionary algorithms.
基金supported by the National Science Foundationof China(Nos.52305127 and 52475130)。
文摘Early fault detection for spiral bevel gears is crucial to ensure normal operation and prevent accidents.The harmonic components,excited by the time-varying mesh stiffness,always appear in measured vibration signal.How to extract the periodical impulses that indicate gear localized fault buried in the intensive noise and interfered by harmonics is a challenging task.In this paper,a novel Periodical Sparse-Assisted Decoupling(PSAD)method is proposed as an optimization problem to extract fault feature from noisy vibration signal.The PSAD method decouples the impulsive fault feature and harmonic components based on the sparse representation method.The sparsity within and across groups property and the periodicity of the fault feature are incorporated into the regularizer as the prior information.The nonconvex penalty is employed to highlight the sparsity of fault features.Meanwhile,the weight factor based on2norm of each group is constructed to strengthen the amplitude of fault feature.An iterative algorithm with Majorization-Minimization(MM)is derived to solve the optimization problem.Simulation study and experimental analysis confirm the performance of the proposed PSAD method in extracting and enhancing defect impulses from noisy signal.The suggested method surpasses other comparative methods in extracting and enhancing fault features.
基金supported in part by the National Key Research and Development Program of China(2018AAA0100100)the National Natural Science Foundation of China(61906001,62136008,U21A20512)+1 种基金the Key Program of Natural Science Project of Educational Commission of Anhui Province(KJ2020A0036)Alexander von Humboldt Professorship for Artificial Intelligence Funded by the Federal Ministry of Education and Research,Germany。
文摘Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.
基金This work was supported by the Natural Science Foundation of China(Nos.61672478 and 61806090)the National Key Research and Development Program of China(No.2017YFB1003102)+4 种基金the Guangdong Provincial Key Laboratory(No.2020B121201001)the Shenzhen Peacock Plan(No.KQTD2016112514355531)the Guangdong-Hong Kong-Macao Greater Bay Area Center for Brain Science and Brain-inspired Intelligence Fund(No.2019028)the Fellowship of China Postdoctoral Science Foundation(No.2020M671900)the National Leading Youth Talent Support Program of China.
文摘Large-scale multi-objective optimization problems(MOPs)that involve a large number of decision variables,have emerged from many real-world applications.While evolutionary algorithms(EAs)have been widely acknowledged as a mainstream method for MOPs,most research progress and successful applications of EAs have been restricted to MOPs with small-scale decision variables.More recently,it has been reported that traditional multi-objective EAs(MOEAs)suffer severe deterioration with the increase of decision variables.As a result,and motivated by the emergence of real-world large-scale MOPs,investigation of MOEAs in this aspect has attracted much more attention in the past decade.This paper reviews the progress of evolutionary computation for large-scale multi-objective optimization from two angles.From the key difficulties of the large-scale MOPs,the scalability analysis is discussed by focusing on the performance of existing MOEAs and the challenges induced by the increase of the number of decision variables.From the perspective of methodology,the large-scale MOEAs are categorized into three classes and introduced respectively:divide and conquer based,dimensionality reduction based and enhanced search-based approaches.Several future research directions are also discussed.
文摘Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.
文摘Massive multiple-input multiple-output(MIMO)technology enables higher data rate transmission in the future mobile communications.However,exploiting a large number of antenna elements at base station(BS)makes effective implementation of massive MIMO challenging,due to the size and weight limits of the masssive MIMO that are located on each BS.Therefore,in order to miniaturize the massive MIMO,it is crucial to reduce the number of antenna elements via effective methods such as sparse array synthesis.In this paper,a multiple-pattern synthesis is considered towards convex optimization(CO).The joint convex optimization(JCO)based synthesis is proposed to construct a codebook for beamforming.Then,a criterion containing multiple constraints is developed,in which the sparse array is required to fullfill all constraints.Finally,extensive evaluations are performed under realistic simulation settings.The results show that with the same number of antenna elements,sparse array using the proposed JCO-based synthesis outperforms not only the uniform array,but also the sparse array with the existing CO-based synthesis method.Furthermore,with a half of the number of antenna elements that on the uniform array,the performance of the JCO-based sparse array approaches to that of the uniform array.
基金funded by the National Natural Science Foundation of China(No.72104069)the Science and Technology Department of Henan Province,China(No.182102310886 and 162102110109)the Postgraduate Meritocracy Scheme,hina(No.SYL19060145).
文摘To solve large-scale optimization problems,Fragrance coefficient and variant Particle Swarm local search Butterfly Optimization Algorithm(FPSBOA)is proposed.In the position update stage of Butterfly Optimization Algorithm(BOA),the fragrance coefficient is designed to balance the exploration and exploitation of BOA.The variant particle swarm local search strategy is proposed to improve the local search ability of the current optimal butterfly and prevent the algorithm from falling into local optimality.192000-dimensional functions and 201000-dimensional CEC 2010 large-scale functions are used to verify FPSBOA for complex large-scale optimization problems.The experimental results are statistically analyzed by Friedman test and Wilcoxon rank-sum test.All attained results demonstrated that FPSBOA can better solve more challenging scientific and industrial real-world problems with thousands of variables.Finally,four mechanical engineering problems and one ten-dimensional process synthesis and design problem are applied to FPSBOA,which shows FPSBOA has the feasibility and effectiveness in real-world application problems.
基金supported by the National Natural Science Foundation of China(No.61872316)the National Key R&D Program of China(No.2016YFB1001501)the Fundamental Research Funds for the Central Universities(No.2017XZZX009-03)
文摘In isogeometric analysis,it is frequently required to handle the geometric models enclosed by four-sided or non-four-sided boundary patches,such as trimmed surfaces.In this paper,we develop a Gregory solid based method to parameterize those models.First,we extend the Gregory patch representation to the trivariate Gregory solid representation.Second,the trivariate Gregory solid representation is employed to interpolate the boundary patches of a geometric model,thus generating the polyhedral volume parametrization.To improve the regularity of the polyhedral volume parametrization,we formulate the construction of the trivariate Gregory solid as a sparse optimization problem,where the optimization objective function is a linear combination of some terms,including a sparse term aiming to reduce the negative Jacobian area of the Gregory solid.Then,the alternating direction method of multipliers(ADMM)is used to solve the sparse optimization problem.Lots of experimental examples illustrated in this paper demonstrate the effectiveness and efficiency of the developed method.
