Time series clustering is a challenging problem due to the large-volume,high-dimensional,and warping characteristics of time series data.Traditional clustering methods often use a single criterion or distance measure,...Time series clustering is a challenging problem due to the large-volume,high-dimensional,and warping characteristics of time series data.Traditional clustering methods often use a single criterion or distance measure,which may not capture all the features of the data.This paper proposes a novel method for time series clustering based on evolutionary multi-tasking optimization,termed i-MFEA,which uses an improved multifactorial evolutionary algorithm to optimize multiple clustering tasks simultaneously,each with a different validity index or distance measure.Therefore,i-MFEA can produce diverse and robust clustering solutions that satisfy various preferences of decision-makers.Experiments on two artificial datasets show that i-MFEA outperforms single-objective evolutionary algorithms and traditional clustering methods in terms of convergence speed and clustering quality.The paper also discusses how i-MFEA can address two long-standing issues in time series clustering:the choice of appropriate similarity measure and the number of clusters.展开更多
Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they prop...Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.展开更多
Meta-heuristic evolutionary algorithms have become widely used for solving complex optimization problems.However,their effectiveness in real-world applications is often limited by the need for many evaluations,which c...Meta-heuristic evolutionary algorithms have become widely used for solving complex optimization problems.However,their effectiveness in real-world applications is often limited by the need for many evaluations,which can be both costly and time-consuming.This is especially true for large-scale transportation networks,where the size of the problem and the high computational cost can hinder the algorithm’s performance.To address these challenges,recent research has focused on using surrogate-assisted models.These models aim to reduce the number of expensive evaluations and improve the efficiency of solving time-consuming optimization problems.This paper presents a new two-layer Surrogate-Assisted Fish Migration Optimization(SA-FMO)algorithm designed to tackle high-dimensional and computationally heavy problems.The global surrogate model offers a good approximation of the entire problem space,while the local surrogate model focuses on refining the solution near the current best option,improving local optimization.To test the effectiveness of the SA-FMO algorithm,we first conduct experiments using six benchmark functions in a 50-dimensional space.We then apply the algorithm to optimize urban rail transit routes,focusing on the Train Routing Optimization problem.This aims to improve operational efficiency and vehicle turnover in situations with uneven passenger flow during transit disruptions.The results show that SA-FMO can effectively improve optimization outcomes in complex transportation scenarios.展开更多
In recent years, particle swarm optimization (PSO) has received widespread attention in feature selection due to its simplicity and potential for global search. However, in traditional PSO, particles primarily update ...In recent years, particle swarm optimization (PSO) has received widespread attention in feature selection due to its simplicity and potential for global search. However, in traditional PSO, particles primarily update based on two extreme values: personal best and global best, which limits the diversity of information. Ideally, particles should learn from multiple advantageous particles to enhance interactivity and optimization efficiency. Accordingly, this paper proposes a PSO that simulates the evolutionary dynamics of species survival in mountain peak ecology (PEPSO) for feature selection. Based on the pyramid topology, the algorithm simulates the features of mountain peak ecology in nature and the competitive-cooperative strategies among species. According to the principles of the algorithm, the population is first adaptively divided into many subgroups based on the fitness level of particles. Then, particles within each subgroup are divided into three different types based on their evolutionary levels, employing different adaptive inertia weight rules and dynamic learning mechanisms to define distinct learning modes. Consequently, all particles play their respective roles in promoting the global optimization performance of the algorithm, similar to different species in the ecological pattern of mountain peaks. Experimental validation of the PEPSO performance was conducted on 18 public datasets. The experimental results demonstrate that the PEPSO outperforms other PSO variant-based feature selection methods and mainstream feature selection methods based on intelligent optimization algorithms in terms of overall performance in global search capability, classification accuracy, and reduction of feature space dimensions. Wilcoxon signed-rank test also confirms the excellent performance of the PEPSO.展开更多
In recent years,surrogate models derived from genuine data samples have proven to be efficient in addressing optimization challenges that are costly or time⁃intensive.However,the individuals in the population become i...In recent years,surrogate models derived from genuine data samples have proven to be efficient in addressing optimization challenges that are costly or time⁃intensive.However,the individuals in the population become indistinguishable as the curse of dimensionality increases in the objective space and the accumulation of surrogate approximated errors.Therefore,in this paper,each objective function is modeled using a radial basis function approach,and the optimal solution set of the surrogate model is located by the multi⁃objective evolutionary algorithm of strengthened dominance relation.The original objective function values of the true evaluations are converted to two indicator values,and then the surrogate models are set up for the two performance indicators.Finally,an adaptive infill sampling strategy that relies on approximate performance indicators is proposed to assist in selecting individuals for real evaluations from the potential optimal solution set.The algorithm is contrasted against several advanced surrogate⁃assisted evolutionary algorithms on two suites of test cases,and the experimental findings prove that the approach is competitive in solving expensive many⁃objective optimization problems.展开更多
Evolutionary computation is a rapidly evolving field and the related algorithms have been successfully used to solve various real-world optimization problems.The past decade has also witnessed their fast progress to s...Evolutionary computation is a rapidly evolving field and the related algorithms have been successfully used to solve various real-world optimization problems.The past decade has also witnessed their fast progress to solve a class of challenging optimization problems called high-dimensional expensive problems(HEPs).The evaluation of their objective fitness requires expensive resource due to their use of time-consuming physical experiments or computer simulations.Moreover,it is hard to traverse the huge search space within reasonable resource as problem dimension increases.Traditional evolutionary algorithms(EAs)tend to fail to solve HEPs competently because they need to conduct many such expensive evaluations before achieving satisfactory results.To reduce such evaluations,many novel surrogate-assisted algorithms emerge to cope with HEPs in recent years.Yet there lacks a thorough review of the state of the art in this specific and important area.This paper provides a comprehensive survey of these evolutionary algorithms for HEPs.We start with a brief introduction to the research status and the basic concepts of HEPs.Then,we present surrogate-assisted evolutionary algorithms for HEPs from four main aspects.We also give comparative results of some representative algorithms and application examples.Finally,we indicate open challenges and several promising directions to advance the progress in evolutionary optimization algorithms for HEPs.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
Task scheduling plays a key role in effectively managing and allocating computing resources to meet various computing tasks in a cloud computing environment.Short execution time and low load imbalance may be the chall...Task scheduling plays a key role in effectively managing and allocating computing resources to meet various computing tasks in a cloud computing environment.Short execution time and low load imbalance may be the challenges for some algorithms in resource scheduling scenarios.In this work,the Hierarchical Particle Swarm Optimization-Evolutionary Artificial Bee Colony Algorithm(HPSO-EABC)has been proposed,which hybrids our presented Evolutionary Artificial Bee Colony(EABC),and Hierarchical Particle Swarm Optimization(HPSO)algorithm.The HPSO-EABC algorithm incorporates both the advantages of the HPSO and the EABC algorithm.Comprehensive testing including evaluations of algorithm convergence speed,resource execution time,load balancing,and operational costs has been done.The results indicate that the EABC algorithm exhibits greater parallelism compared to the Artificial Bee Colony algorithm.Compared with the Particle Swarm Optimization algorithm,the HPSO algorithmnot only improves the global search capability but also effectively mitigates getting stuck in local optima.As a result,the hybrid HPSO-EABC algorithm demonstrates significant improvements in terms of stability and convergence speed.Moreover,it exhibits enhanced resource scheduling performance in both homogeneous and heterogeneous environments,effectively reducing execution time and cost,which also is verified by the ablation experimental.展开更多
The evolutionary strategy with a dynamic weighting schedule is proposed to find all the compromised solutions of the multi-objective integrated structure and control optimization problem, where the optimal system perf...The evolutionary strategy with a dynamic weighting schedule is proposed to find all the compromised solutions of the multi-objective integrated structure and control optimization problem, where the optimal system performance and control cost are defined by H2 or H∞ norms. During this optimization process, the weights are varying with the increasing generation instead of fixed values. The proposed strategy together with the linear matrix inequality （LMI） or the Riccati controller design method can find a series of uniformly distributed nondominated solutions in a single run. Therefore, this method can greatly reduce the computation intensity of the integrated optimization problem compared with the weight-based single objective genetic algorithm. Active automotive suspension is adopted as an example to illustrate the effectiveness of the proposed method.展开更多
In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However,...In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.展开更多
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
The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly...The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.展开更多
A new algorithm based on genetic algorithm(GA) is developed for solving function optimization problems with inequality constraints. This algorithm has been used to a series of standard test problems and exhibited good...A new algorithm based on genetic algorithm(GA) is developed for solving function optimization problems with inequality constraints. This algorithm has been used to a series of standard test problems and exhibited good performance. The computation results show that its generality, precision, robustness, simplicity and performance are all satisfactory.展开更多
This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search pro...This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.展开更多
Computational time complexity analyzes of evolutionary algorithms （EAs） have been performed since the mid-nineties. The first results were related to very simple algorithms, such as the （1＋1）-EA, on toy problems....Computational time complexity analyzes of evolutionary algorithms （EAs） have been performed since the mid-nineties. The first results were related to very simple algorithms, such as the （1＋1）-EA, on toy problems. These efforts produced a deeper understanding of how EAs perform on different kinds of fitness landscapes and general mathematical tools that may be extended to the analysis of more complicated EAs on more realistic problems. In fact, in recent years, it has been possible to analyze the （1＋1）-EA on combinatorial optimization problems with practical applications and more realistic population-based EAs on structured toy problems. This paper presents a survey of the results obtained in the last decade along these two research lines. The most common mathematical techniques are introduced, the basic ideas behind them are discussed and their elective applications are highlighted. Solved problems that were still open are enumerated as are those still awaiting for a solution. New questions and problems arisen in the meantime are also considered.展开更多
Evolutionary algorithms have been shown to be very successful in solving multi-objective optimization problems(MOPs).However,their performance often deteriorates when solving MOPs with irregular Pareto fronts.To remed...Evolutionary algorithms have been shown to be very successful in solving multi-objective optimization problems(MOPs).However,their performance often deteriorates when solving MOPs with irregular Pareto fronts.To remedy this issue,a large body of research has been performed in recent years and many new algorithms have been proposed.This paper provides a comprehensive survey of the research on MOPs with irregular Pareto fronts.We start with a brief introduction to the basic concepts,followed by a summary of the benchmark test problems with irregular problems,an analysis of the causes of the irregularity,and real-world optimization problems with irregular Pareto fronts.Then,a taxonomy of the existing methodologies for handling irregular problems is given and representative algorithms are reviewed with a discussion of their strengths and weaknesses.Finally,open challenges are pointed out and a few promising future directions are suggested.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
The K-means algorithm is one of the most popular techniques in clustering. Nevertheless, the performance of the Kmeans algorithm depends highly on initial cluster centers and converges to local minima. This paper prop...The K-means algorithm is one of the most popular techniques in clustering. Nevertheless, the performance of the Kmeans algorithm depends highly on initial cluster centers and converges to local minima. This paper proposes a hybrid evolutionary programming based clustering algorithm, called PSO-SA, by combining particle swarm optimization (PSO) and simulated annealing (SA). The basic idea is to search around the global solution by SA and to increase the information exchange among particles using a mutation operator to escape local optima. Three datasets, Iris, Wisconsin Breast Cancer, and Ripley's Glass, have been considered to show the effectiveness of the proposed clustering algorithm in providing optimal clusters. The simulation results show that the PSO-SA clustering algorithm not only has a better response but also converges more quickly than the K-means, PSO, and SA algorithms.展开更多
This paper presents a parallel two-level evolutionary algorithm based on domain decomposition for solving function optimization problem containing multiple solutions. By combining the characteristics of the global sea...This paper presents a parallel two-level evolutionary algorithm based on domain decomposition for solving function optimization problem containing multiple solutions. By combining the characteristics of the global search and local search in each sub-domain, the former enables individual to draw closer to each optima and keeps the diversity of individuals, while the latter selects local optimal solutions known as latent solutions in sub-domain. In the end, by selecting the global optimal solutions from latent solutions in each sub-domain, we can discover all the optimal solutions easily and quickly.展开更多
Application of the multiobjective evolutionary algorithms to the aerodynamicoptimization design of a centrifugal impeller is presented. The aerodynamic performance of acentrifugal impeller is evaluated by using the th...Application of the multiobjective evolutionary algorithms to the aerodynamicoptimization design of a centrifugal impeller is presented. The aerodynamic performance of acentrifugal impeller is evaluated by using the three-dimensional Navier-Stokes solutions. Thetypical centrifugal impeller is redesigned for maximization of the pressure rise and blade load andminimization of the rotational total pressure loss at the given flow conditions. The Bezier curvesare used to parameterize the three-dimensional impeller blade shape. The present method obtains manyreasonable Pareto optimal designs that outperform the original centrifugal impeller. Detailedobservation of the certain Pareto optimal design demonstrates the feasibility of the presentmultiobjective optimization method tool for turbomachinery design.展开更多
基金supported by the Open Project of Xiangjiang Laboratory(No.22XJ02003)the National Natural Science Foundation of China(No.62122093).
文摘Time series clustering is a challenging problem due to the large-volume,high-dimensional,and warping characteristics of time series data.Traditional clustering methods often use a single criterion or distance measure,which may not capture all the features of the data.This paper proposes a novel method for time series clustering based on evolutionary multi-tasking optimization,termed i-MFEA,which uses an improved multifactorial evolutionary algorithm to optimize multiple clustering tasks simultaneously,each with a different validity index or distance measure.Therefore,i-MFEA can produce diverse and robust clustering solutions that satisfy various preferences of decision-makers.Experiments on two artificial datasets show that i-MFEA outperforms single-objective evolutionary algorithms and traditional clustering methods in terms of convergence speed and clustering quality.The paper also discusses how i-MFEA can address two long-standing issues in time series clustering:the choice of appropriate similarity measure and the number of clusters.
基金supported in part by the National Key Research and Development Program of China(2022YFD2001200)the National Natural Science Foundation of China(62176238,61976237,62206251,62106230)+3 种基金China Postdoctoral Science Foundation(2021T140616,2021M692920)the Natural Science Foundation of Henan Province(222300420088)the Program for Science&Technology Innovation Talents in Universities of Henan Province(23HASTIT023)the Program for Science&Technology Innovation Teams in Universities of Henan Province(23IRTSTHN010).
文摘Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.
基金supported by the National Natural Science Foundation of China(Project No.52172321,52102391)Sichuan Province Science and Technology Innovation Talent Project(2024JDRC0020)+1 种基金China Shenhua Energy Company Limited Technology Project(GJNY-22-7/2300-K1220053)Key science and technology projects in the transportation industry of the Ministry of Transport(2022-ZD7-132).
文摘Meta-heuristic evolutionary algorithms have become widely used for solving complex optimization problems.However,their effectiveness in real-world applications is often limited by the need for many evaluations,which can be both costly and time-consuming.This is especially true for large-scale transportation networks,where the size of the problem and the high computational cost can hinder the algorithm’s performance.To address these challenges,recent research has focused on using surrogate-assisted models.These models aim to reduce the number of expensive evaluations and improve the efficiency of solving time-consuming optimization problems.This paper presents a new two-layer Surrogate-Assisted Fish Migration Optimization(SA-FMO)algorithm designed to tackle high-dimensional and computationally heavy problems.The global surrogate model offers a good approximation of the entire problem space,while the local surrogate model focuses on refining the solution near the current best option,improving local optimization.To test the effectiveness of the SA-FMO algorithm,we first conduct experiments using six benchmark functions in a 50-dimensional space.We then apply the algorithm to optimize urban rail transit routes,focusing on the Train Routing Optimization problem.This aims to improve operational efficiency and vehicle turnover in situations with uneven passenger flow during transit disruptions.The results show that SA-FMO can effectively improve optimization outcomes in complex transportation scenarios.
文摘In recent years, particle swarm optimization (PSO) has received widespread attention in feature selection due to its simplicity and potential for global search. However, in traditional PSO, particles primarily update based on two extreme values: personal best and global best, which limits the diversity of information. Ideally, particles should learn from multiple advantageous particles to enhance interactivity and optimization efficiency. Accordingly, this paper proposes a PSO that simulates the evolutionary dynamics of species survival in mountain peak ecology (PEPSO) for feature selection. Based on the pyramid topology, the algorithm simulates the features of mountain peak ecology in nature and the competitive-cooperative strategies among species. According to the principles of the algorithm, the population is first adaptively divided into many subgroups based on the fitness level of particles. Then, particles within each subgroup are divided into three different types based on their evolutionary levels, employing different adaptive inertia weight rules and dynamic learning mechanisms to define distinct learning modes. Consequently, all particles play their respective roles in promoting the global optimization performance of the algorithm, similar to different species in the ecological pattern of mountain peaks. Experimental validation of the PEPSO performance was conducted on 18 public datasets. The experimental results demonstrate that the PEPSO outperforms other PSO variant-based feature selection methods and mainstream feature selection methods based on intelligent optimization algorithms in terms of overall performance in global search capability, classification accuracy, and reduction of feature space dimensions. Wilcoxon signed-rank test also confirms the excellent performance of the PEPSO.
基金Sponsored by Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(Grant No.2022L294)Taiyuan University of Science and Technology Scientific Research Initial Funding(Grant Nos.W2022018,W20242012)Foundamental Research Program of Shanxi Province(Grant No.202403021212170).
文摘In recent years,surrogate models derived from genuine data samples have proven to be efficient in addressing optimization challenges that are costly or time⁃intensive.However,the individuals in the population become indistinguishable as the curse of dimensionality increases in the objective space and the accumulation of surrogate approximated errors.Therefore,in this paper,each objective function is modeled using a radial basis function approach,and the optimal solution set of the surrogate model is located by the multi⁃objective evolutionary algorithm of strengthened dominance relation.The original objective function values of the true evaluations are converted to two indicator values,and then the surrogate models are set up for the two performance indicators.Finally,an adaptive infill sampling strategy that relies on approximate performance indicators is proposed to assist in selecting individuals for real evaluations from the potential optimal solution set.The algorithm is contrasted against several advanced surrogate⁃assisted evolutionary algorithms on two suites of test cases,and the experimental findings prove that the approach is competitive in solving expensive many⁃objective optimization problems.
基金supported in part by the Natural Science Foundation of Jiangsu Province(BK20230923,BK20221067)the National Natural Science Foundation of China(62206113,62203093)+1 种基金Institutional Fund Projects Provided by the Ministry of Education and King Abdulaziz University(IFPIP-1532-135-1443)FDCT(Fundo para o Desen-volvimento das Ciencias e da Tecnologia)(0047/2021/A1)。
文摘Evolutionary computation is a rapidly evolving field and the related algorithms have been successfully used to solve various real-world optimization problems.The past decade has also witnessed their fast progress to solve a class of challenging optimization problems called high-dimensional expensive problems(HEPs).The evaluation of their objective fitness requires expensive resource due to their use of time-consuming physical experiments or computer simulations.Moreover,it is hard to traverse the huge search space within reasonable resource as problem dimension increases.Traditional evolutionary algorithms(EAs)tend to fail to solve HEPs competently because they need to conduct many such expensive evaluations before achieving satisfactory results.To reduce such evaluations,many novel surrogate-assisted algorithms emerge to cope with HEPs in recent years.Yet there lacks a thorough review of the state of the art in this specific and important area.This paper provides a comprehensive survey of these evolutionary algorithms for HEPs.We start with a brief introduction to the research status and the basic concepts of HEPs.Then,we present surrogate-assisted evolutionary algorithms for HEPs from four main aspects.We also give comparative results of some representative algorithms and application examples.Finally,we indicate open challenges and several promising directions to advance the progress in evolutionary optimization algorithms for HEPs.
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jointly supported by the Jiangsu Postgraduate Research and Practice Innovation Project under Grant KYCX22_1030,SJCX22_0283 and SJCX23_0293the NUPTSF under Grant NY220201.
文摘Task scheduling plays a key role in effectively managing and allocating computing resources to meet various computing tasks in a cloud computing environment.Short execution time and low load imbalance may be the challenges for some algorithms in resource scheduling scenarios.In this work,the Hierarchical Particle Swarm Optimization-Evolutionary Artificial Bee Colony Algorithm(HPSO-EABC)has been proposed,which hybrids our presented Evolutionary Artificial Bee Colony(EABC),and Hierarchical Particle Swarm Optimization(HPSO)algorithm.The HPSO-EABC algorithm incorporates both the advantages of the HPSO and the EABC algorithm.Comprehensive testing including evaluations of algorithm convergence speed,resource execution time,load balancing,and operational costs has been done.The results indicate that the EABC algorithm exhibits greater parallelism compared to the Artificial Bee Colony algorithm.Compared with the Particle Swarm Optimization algorithm,the HPSO algorithmnot only improves the global search capability but also effectively mitigates getting stuck in local optima.As a result,the hybrid HPSO-EABC algorithm demonstrates significant improvements in terms of stability and convergence speed.Moreover,it exhibits enhanced resource scheduling performance in both homogeneous and heterogeneous environments,effectively reducing execution time and cost,which also is verified by the ablation experimental.
文摘The evolutionary strategy with a dynamic weighting schedule is proposed to find all the compromised solutions of the multi-objective integrated structure and control optimization problem, where the optimal system performance and control cost are defined by H2 or H∞ norms. During this optimization process, the weights are varying with the increasing generation instead of fixed values. The proposed strategy together with the linear matrix inequality （LMI） or the Riccati controller design method can find a series of uniformly distributed nondominated solutions in a single run. Therefore, this method can greatly reduce the computation intensity of the integrated optimization problem compared with the weight-based single objective genetic algorithm. Active automotive suspension is adopted as an example to illustrate the effectiveness of the proposed method.
基金partly supported by the National Natural Science Foundation of China(62076225)。
文摘In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.
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the Liaoning Province Nature Fundation Project(2022-MS-291)the National Programme for Foreign Expert Projects(G2022006008L)+2 种基金the Basic Research Projects of Liaoning Provincial Department of Education(LJKMZ20220781,LJKMZ20220783,LJKQZ20222457)King Saud University funded this study through theResearcher Support Program Number(RSPD2023R704)King Saud University,Riyadh,Saudi Arabia.
文摘The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.
文摘A new algorithm based on genetic algorithm(GA) is developed for solving function optimization problems with inequality constraints. This algorithm has been used to a series of standard test problems and exhibited good performance. The computation results show that its generality, precision, robustness, simplicity and performance are all satisfactory.
文摘This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.
基金This work was supported by an EPSRC grant (No.EP/C520696/1).
文摘Computational time complexity analyzes of evolutionary algorithms （EAs） have been performed since the mid-nineties. The first results were related to very simple algorithms, such as the （1＋1）-EA, on toy problems. These efforts produced a deeper understanding of how EAs perform on different kinds of fitness landscapes and general mathematical tools that may be extended to the analysis of more complicated EAs on more realistic problems. In fact, in recent years, it has been possible to analyze the （1＋1）-EA on combinatorial optimization problems with practical applications and more realistic population-based EAs on structured toy problems. This paper presents a survey of the results obtained in the last decade along these two research lines. The most common mathematical techniques are introduced, the basic ideas behind them are discussed and their elective applications are highlighted. Solved problems that were still open are enumerated as are those still awaiting for a solution. New questions and problems arisen in the meantime are also considered.
基金supported in part by the National Natural Science Foundation of China(61806051,61903078)Natural Science Foundation of Shanghai(20ZR1400400)+2 种基金Agricultural Project of the Shanghai Committee of Science and Technology(16391902800)the Fundamental Research Funds for the Central Universities(2232020D-48)the Project of the Humanities and Social Sciences on Young Fund of the Ministry of Education in China(Research on swarm intelligence collaborative robust optimization scheduling for high-dimensional dynamic decisionmaking system(20YJCZH052))。
文摘Evolutionary algorithms have been shown to be very successful in solving multi-objective optimization problems(MOPs).However,their performance often deteriorates when solving MOPs with irregular Pareto fronts.To remedy this issue,a large body of research has been performed in recent years and many new algorithms have been proposed.This paper provides a comprehensive survey of the research on MOPs with irregular Pareto fronts.We start with a brief introduction to the basic concepts,followed by a summary of the benchmark test problems with irregular problems,an analysis of the causes of the irregularity,and real-world optimization problems with irregular Pareto fronts.Then,a taxonomy of the existing methodologies for handling irregular problems is given and representative algorithms are reviewed with a discussion of their strengths and weaknesses.Finally,open challenges are pointed out and a few promising future directions are suggested.
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.
文摘The K-means algorithm is one of the most popular techniques in clustering. Nevertheless, the performance of the Kmeans algorithm depends highly on initial cluster centers and converges to local minima. This paper proposes a hybrid evolutionary programming based clustering algorithm, called PSO-SA, by combining particle swarm optimization (PSO) and simulated annealing (SA). The basic idea is to search around the global solution by SA and to increase the information exchange among particles using a mutation operator to escape local optima. Three datasets, Iris, Wisconsin Breast Cancer, and Ripley's Glass, have been considered to show the effectiveness of the proposed clustering algorithm in providing optimal clusters. The simulation results show that the PSO-SA clustering algorithm not only has a better response but also converges more quickly than the K-means, PSO, and SA algorithms.
基金Supported by the National Natural Science Foundation of China(60133010,60073043,70071042)
文摘This paper presents a parallel two-level evolutionary algorithm based on domain decomposition for solving function optimization problem containing multiple solutions. By combining the characteristics of the global search and local search in each sub-domain, the former enables individual to draw closer to each optima and keeps the diversity of individuals, while the latter selects local optimal solutions known as latent solutions in sub-domain. In the end, by selecting the global optimal solutions from latent solutions in each sub-domain, we can discover all the optimal solutions easily and quickly.
文摘Application of the multiobjective evolutionary algorithms to the aerodynamicoptimization design of a centrifugal impeller is presented. The aerodynamic performance of acentrifugal impeller is evaluated by using the three-dimensional Navier-Stokes solutions. Thetypical centrifugal impeller is redesigned for maximization of the pressure rise and blade load andminimization of the rotational total pressure loss at the given flow conditions. The Bezier curvesare used to parameterize the three-dimensional impeller blade shape. The present method obtains manyreasonable Pareto optimal designs that outperform the original centrifugal impeller. Detailedobservation of the certain Pareto optimal design demonstrates the feasibility of the presentmultiobjective optimization method tool for turbomachinery design.
