Multi-Objective Evolutionary Algorithms(MOEAs)have significantly advanced the domain of MultiObjective Optimization(MOO),facilitating solutions for complex problems with multiple conflicting objectives.This review exp...Multi-Objective Evolutionary Algorithms(MOEAs)have significantly advanced the domain of MultiObjective Optimization(MOO),facilitating solutions for complex problems with multiple conflicting objectives.This review explores the historical development of MOEAs,beginning with foundational concepts in multi-objective optimization,basic types of MOEAs,and the evolution of Pareto-based selection and niching methods.Further advancements,including decom-position-based approaches and hybrid algorithms,are discussed.Applications are analyzed in established domains such as engineering and economics,as well as in emerging fields like advanced analytics and machine learning.The significance of MOEAs in addressing real-world problems is emphasized,highlighting their role in facilitating informed decision-making.Finally,the development trajectory of MOEAs is compared with evolutionary processes,offering insights into their progress and future potential.展开更多
Steady-state non-dominated sorting genetic algorithm (SNSGA), a new form of multi-objective genetic algorithm, is implemented by combining the steady-state idea in steady-state genetic algorithms (SSGA) and the fitnes...Steady-state non-dominated sorting genetic algorithm (SNSGA), a new form of multi-objective genetic algorithm, is implemented by combining the steady-state idea in steady-state genetic algorithms (SSGA) and the fitness assignment strategy of non-dominated sorting genetic algorithm (NSGA). The fitness assignment strategy is improved and a new self-adjustment scheme of is proposed. This algorithm is proved to be very efficient both computationally and in terms of the quality of the Pareto fronts produced with five test problems including GA difficult problem and GA deceptive one. Finally, SNSGA is introduced to solve multi-objective mixed integer linear programming (MILP) and mixed integer non-linear programming (MINLP) problems in process synthesis.展开更多
Multi-objective Evolutionary Algorithm (MOEA) is becoming a hot research area and quite a few aspects of MOEAs have been studied and discussed. However there are still few literatures discussing the roles of search an...Multi-objective Evolutionary Algorithm (MOEA) is becoming a hot research area and quite a few aspects of MOEAs have been studied and discussed. However there are still few literatures discussing the roles of search and selection operators in MOEAs. This paper studied their roles by solving a case of discrete Multi-objective Optimization Problem (MOP): Multi-objective TSP with a new MOEA. In the new MOEA, We adopt an efficient search operator, which has the properties of both crossover and mutation, to generate the new individuals and chose two selection operators: Family Competition and Population Competition with probabilities to realize selection. The simulation experiments showed that this new MOEA could get good uniform solutions representing the Pareto Front and outperformed SPEA in almost every simulation run on this problem. Furthermore, we analyzed its convergence property using finite Markov chain and proved that it could converge to Pareto Front with probability 1. We also find that the convergence property of MOEAs has much relationship with search and selection operators.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
Data structures used for an algorithm can have a great impact on its performance, particularly for the solution of large and complex problems, such as multi-objective optimization problems （MOPs）. Multi-objective ev...Data structures used for an algorithm can have a great impact on its performance, particularly for the solution of large and complex problems, such as multi-objective optimization problems （MOPs）. Multi-objective evolutionary algorithms （MOEAs） are considered an attractive approach for solving MOPs~ since they are able to explore several parts of the Pareto front simultaneously. The data structures for storing and updating populations and non-dominated solutions （archives） may affect the efficiency of the search process. This article describes data structures used in MOEAs for realizing populations and archives in a comparative way, emphasizing their computational requirements and general applicability reported in the original work.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
Today's volatile market conditions in electronic industries have lead to a new production system,seru(which is the Japanese pronunciation for cell),and has been widely implemented in hundreds of Japanese and other...Today's volatile market conditions in electronic industries have lead to a new production system,seru(which is the Japanese pronunciation for cell),and has been widely implemented in hundreds of Japanese and other Asia companies.In particular,the rotating seru has been widely implemented,where workers are fully cross-trained with the same skill level but may be different on the proficiency of performing tasks.The rotating seru production problem,which determines the rotating sequence of workers as well as the assembling sequence of jobs,is difficult to solve due to conflicting objectives and dynamic release of customer demands.To solve this problem,we propose a dynamic multiobjective NSGA-II based memetic algorithm.Moreover,to preserve desirable population diversity and improve the searching efficiency,we propose different problem-specific evolutionary strategies.Finally,we test the performance of our proposed memetic algorithm with other state-of-the-art multi-objective evolutionary algorithms and demonstrate the effectiveness of our proposed algorithm.展开更多
In this paper, a multi-objective particle swarm optimization （MOPSO） algorithm and a nondominated sorting genetic algorithm II （NSGA-II） are used to optimize the operating parameters of a 1.6 L, spark ignition （S...In this paper, a multi-objective particle swarm optimization （MOPSO） algorithm and a nondominated sorting genetic algorithm II （NSGA-II） are used to optimize the operating parameters of a 1.6 L, spark ignition （SI） gasoline engine. The aim of this optimization is to reduce engine emissions in terms of carbon monoxide （CO）, hydrocarbons （HC）, and nitrogen oxides （NOx）, which are the causes of diverse environmental problems such as air pollution and global warming. Stationary engine tests were performed for data generation, covering 60 operating conditions. Artificial neural networks （ANNs） were used to predict exhaust emissions, whose inputs were from six engine operating parameters, and the outputs were three resulting exhaust emissions. The outputs of ANNs were used to evaluate objective functions within the optimization algorithms： NSGA-II and MOPSO. Then a decision-making process was conducted, using a fuzzy method to select a Pareto solution with which the best emission reductions can be achieved. The NSGA-II algorithm achieved reductions of at least 9.84%, 82.44%, and 13.78% for CO, HC, and NOx, respectively. With a MOPSO algorithm the reached reductions were at least 13.68%, 83.80%, and 7.67% for CO, HC, and NOx, respectively.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
Cloud computing has become an essential technology for the management and processing of large datasets,offering scalability,high availability,and fault tolerance.However,optimizing data replication across multiple dat...Cloud computing has become an essential technology for the management and processing of large datasets,offering scalability,high availability,and fault tolerance.However,optimizing data replication across multiple data centers poses a significant challenge,especially when balancing opposing goals such as latency,storage costs,energy consumption,and network efficiency.This study introduces a novel Dynamic Optimization Algorithm called Dynamic Multi-Objective Gannet Optimization(DMGO),designed to enhance data replication efficiency in cloud environments.Unlike traditional static replication systems,DMGO adapts dynamically to variations in network conditions,system demand,and resource availability.The approach utilizes multi-objective optimization approaches to efficiently balance data access latency,storage efficiency,and operational costs.DMGO consistently evaluates data center performance and adjusts replication algorithms in real time to guarantee optimal system efficiency.Experimental evaluations conducted in a simulated cloud environment demonstrate that DMGO significantly outperforms conventional static algorithms,achieving faster data access,lower storage overhead,reduced energy consumption,and improved scalability.The proposed methodology offers a robust and adaptable solution for modern cloud systems,ensuring efficient resource consumption while maintaining high performance.展开更多
In recent years,the development of new types of nuclear reactors,such as transportable,marine,and space reactors,has presented new challenges for the optimization of reactor radiation-shielding design.Shielding struct...In recent years,the development of new types of nuclear reactors,such as transportable,marine,and space reactors,has presented new challenges for the optimization of reactor radiation-shielding design.Shielding structures typically need to be lightweight,miniaturized,and radiation-protected,which is a multi-parameter and multi-objective optimization problem.The conventional multi-objective(two or three objectives)optimization method for radiation-shielding design exhibits limitations for a number of optimization objectives and variable parameters,as well as a deficiency in achieving a global optimal solution,thereby failing to meet the requirements of shielding optimization for newly developed reactors.In this study,genetic and artificial bee-colony algorithms are combined with a reference-point-selection strategy and applied to the many-objective(having four or more objectives)optimal design of reactor radiation shielding.To validate the reliability of the methods,an optimization simulation is conducted on three-dimensional shielding structures and another complicated shielding-optimization problem.The numerical results demonstrate that the proposed algorithms outperform conventional shielding-design methods in terms of optimization performance,and they exhibit their reliability in practical engineering problems.The many-objective optimization algorithms developed in this study are proven to efficiently and consistently search for Pareto-front shielding schemes.Therefore,the algorithms proposed in this study offer novel insights into improving the shielding-design performance and shielding quality of new reactor types.展开更多
This paper introduces a hybrid multi-objective optimization algorithm,designated HMODESFO,which amalgamates the exploratory prowess of Differential Evolution(DE)with the rapid convergence attributes of the Sailfish Op...This paper introduces a hybrid multi-objective optimization algorithm,designated HMODESFO,which amalgamates the exploratory prowess of Differential Evolution(DE)with the rapid convergence attributes of the Sailfish Optimization(SFO)algorithm.The primary objective is to address multi-objective optimization challenges within mechanical engineering,with a specific emphasis on planetary gearbox optimization.The algorithm is equipped with the ability to dynamically select the optimal mutation operator,contingent upon an adaptive normalized population spacing parameter.The efficacy of HMODESFO has been substantiated through rigorous validation against estab-lished industry benchmarks,including a suite of Zitzler-Deb-Thiele(ZDT)and Zeb-Thiele-Laumanns-Zitzler(DTLZ)problems,where it exhibited superior performance.The outcomes underscore the algorithm’s markedly enhanced optimization capabilities relative to existing methods,particularly in tackling highly intricate multi-objective planetary gearbox optimization problems.Additionally,the performance of HMODESFO is evaluated against selected well-known mechanical engineering test problems,further accentuating its adeptness in resolving complex optimization challenges within this domain.展开更多
The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency...The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency. A multi-objective model was presented for the material distribution routing problem in mixed manufacturing systems, and it was solved by a hybrid multi-objective evolutionary algorithm (HMOEA). The characteristics of the HMOEA are as follows: 1) A route pool is employed to preserve the best routes for the population initiation; 2) A specialized best?worst route crossover (BWRC) mode is designed to perform the crossover operators for selecting the best route from Chromosomes 1 to exchange with the worst one in Chromosomes 2, so that the better genes are inherited to the offspring; 3) A route swap mode is used to perform the mutation for improving the convergence speed and preserving the better gene; 4) Local heuristics search methods are applied in this algorithm. Computational study of a practical case shows that the proposed algorithm can decrease the total travel distance by 51.66%, enhance the average vehicle load rate by 37.85%, cut down 15 routes and reduce a deliver vehicle. The convergence speed of HMOEA is faster than that of famous NSGA-II.展开更多
Finding an optimal isolator arrangement for asymmetric structures using traditional conceptual design methods that can significantly minimize torsional response while ensuring efficient horizontal seismic isolation is...Finding an optimal isolator arrangement for asymmetric structures using traditional conceptual design methods that can significantly minimize torsional response while ensuring efficient horizontal seismic isolation is cumbersome and inefficient.Thus,this work develops a multi-objective optimization method to enhance the torsional resistance of asymmetric base-isolated structures.The primary objective is to simultaneously minimize the interstory rotation of the superstructure,the rotation of the isolation layer,and the interstory displacement of the superstructure without exceeding the isolator displacement limits.A fast non-dominated sorting genetic algorithm(NSGA-Ⅱ)is employed to satisfy this optimization objective.Subsequently,the isolator arrangement,encompassing both positions and categories,is optimized according to this multi-objective optimization method.Additionally,an optimization design platform is developed to streamline the design operation.This platform integrates the input of optimization parameters,the output of optimization results,the finite element analysis,and the multi-objective optimization method proposed herein.Finally,the application of this multi-objective optimization method and its associated platform are demonstrated on two asymmetric base-isolated structures of varying heights and plan configurations.The results indicate that the optimal isolator arrangement derived from the optimization method can further improve the control over the lateral and torsional responses of asymmetric base-isolated structures compared to conventional conceptual design methods.Notably,the interstory rotation of the optimal base-isolated structure is significantly reduced,constituting only approximately 33.7%of that observed in the original base-isolated structure.The proposed platform facilitates the automatic generation of the optimal design scheme for the isolators of asymmetric base-isolated structures,offering valuable insights and guidance for the burgeoning field of intelligent civil engineering design.展开更多
Multi-objective optimization is critical for problem-solving in engineering,economics,and AI.This study introduces the Multi-Objective Chef-Based Optimization Algorithm(MOCBOA),an upgraded version of the Chef-Based Op...Multi-objective optimization is critical for problem-solving in engineering,economics,and AI.This study introduces the Multi-Objective Chef-Based Optimization Algorithm(MOCBOA),an upgraded version of the Chef-Based Optimization Algorithm(CBOA)that addresses distinct objectives.Our approach is unique in systematically examining four dominance relations—Pareto,Epsilon,Cone-epsilon,and Strengthened dominance—to evaluate their influence on sustaining solution variety and driving convergence toward the Pareto front.Our comparison investigation,which was conducted on fifty test problems from the CEC 2021 benchmark and applied to areas such as chemical engineering,mechanical design,and power systems,reveals that the dominance approach used has a considerable impact on the key optimization measures such as the hypervolume metric.This paper provides a solid foundation for determining themost effective dominance approach and significant insights for both theoretical research and practical applications in multi-objective optimization.展开更多
Accurate determination of rock mass parameters is essential for ensuring the accuracy of numericalsimulations. Displacement back-analysis is the most widely used method;however, the reliability of thecurrent approache...Accurate determination of rock mass parameters is essential for ensuring the accuracy of numericalsimulations. Displacement back-analysis is the most widely used method;however, the reliability of thecurrent approaches remains unsatisfactory. Therefore, in this paper, a multistage rock mass parameterback-analysis method, that considers the construction process and displacement losses is proposed andimplemented through the coupling of numerical simulation, auto-machine learning (AutoML), andmulti-objective optimization algorithms (MOOAs). First, a parametric modeling platform for mechanizedtwin tunnels is developed, generating a dataset through extensive numerical simulations. Next, theAutoML method is utilized to establish a surrogate model linking rock parameters and displacements.The tunnel construction process is divided into multiple stages, transforming the rock mass parameterback-analysis into a multi-objective optimization problem, for which multi-objective optimization algorithmsare introduced to obtain the rock mass parameters. The newly proposed rock mass parameterback-analysis method is validated in a mechanized twin tunnel project, and its accuracy and effectivenessare demonstrated. Compared with traditional single-stage back-analysis methods, the proposedmodel decreases the average absolute percentage error from 12.73% to 4.34%, significantly improving theaccuracy of the back-analysis. Moreover, although the accuracy of back analysis significantly increaseswith the number of construction stages considered, the back analysis time is acceptable. This studyprovides a new method for displacement back analysis that is efficient and accurate, thereby paving theway for precise parameter determination in numerical simulations.展开更多
As two independent problems,scheduling for parts fabrication line and sequencing for mixed-model assembly line have been addressed respectively by many researchers.However,these two problems should be considered simul...As two independent problems,scheduling for parts fabrication line and sequencing for mixed-model assembly line have been addressed respectively by many researchers.However,these two problems should be considered simultaneously to improve the efficiency of the whole fabrication/assembly systems.By far,little research effort is devoted to sequencing problems for mixed-model fabrication/assembly systems.This paper is concerned about the sequencing problems in pull production systems which are composed of one mixed-model assembly line with limited intermediate buffers and two flexible parts fabrication flow lines with identical parallel machines and limited intermediate buffers.Two objectives are considered simultaneously：minimizing the total variation in parts consumption in the assembly line and minimizing the total makespan cost in the fabrication/assembly system.The integrated optimization framework,mathematical models and the method to construct the complete schedules for the fabrication lines according to the production sequences for the first stage in fabrication lines are presented.Since the above problems are non-deterministic polynomial-hard（NP-hard）,a modified multi-objective genetic algorithm is proposed for solving the models,in which a method to generate the production sequences for the fabrication lines from the production sequences for the assembly line and a method to generate the initial population are put forward,new selection,crossover and mutation operators are designed,and Pareto ranking method and sharing function method are employed to evaluate the individuals＇ fitness.The feasibility and efficiency of the multi-objective genetic algorithm is shown by computational comparison with a multi-objective simulated annealing algorithm.The sequencing problems for mixed-model production systems can be solved effectively by the proposed modified multi-objective genetic algorithm.展开更多
In recent years,feature selection(FS)optimization of high-dimensional gene expression data has become one of the most promising approaches for cancer prediction and classification.This work reviews FS and classificati...In recent years,feature selection(FS)optimization of high-dimensional gene expression data has become one of the most promising approaches for cancer prediction and classification.This work reviews FS and classification methods that utilize evolutionary algorithms(EAs)for gene expression profiles in cancer or medical applications based on research motivations,challenges,and recommendations.Relevant studies were retrieved from four major academic databases-IEEE,Scopus,Springer,and ScienceDirect-using the keywords‘cancer classification’,‘optimization’,‘FS’,and‘gene expression profile’.A total of 67 papers were finally selected with key advancements identified as follows:(1)The majority of papers(44.8%)focused on developing algorithms and models for FS and classification.(2)The second category encompassed studies on biomarker identification by EAs,including 20 papers(30%).(3)The third category comprised works that applied FS to cancer data for decision support system purposes,addressing high-dimensional data and the formulation of chromosome length.These studies accounted for 12%of the total number of studies.(4)The remaining three papers(4.5%)were reviews and surveys focusing on models and developments in prediction and classification optimization for cancer classification under current technical conditions.This review highlights the importance of optimizing FS in EAs to manage high-dimensional data effectively.Despite recent advancements,significant limitations remain:the dynamic formulation of chromosome length remains an underexplored area.Thus,further research is needed on dynamic-length chromosome techniques for more sophisticated biomarker gene selection techniques.The findings suggest that further advancements in dynamic chromosome length formulations and adaptive algorithms could enhance cancer classification accuracy and efficiency.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
To address issues such as poor initial population diversity, low stability and local convergence accuracy, and easy local optima in the traditional Multi-Objective Artificial Hummingbird Algorithm (MOAHA), an Improved...To address issues such as poor initial population diversity, low stability and local convergence accuracy, and easy local optima in the traditional Multi-Objective Artificial Hummingbird Algorithm (MOAHA), an Improved MOAHA (IMOAHA) was proposed. The improvements involve Tent mapping based on random variables to initialize the population, a logarithmic decrease strategy for inertia weight to balance search capability, and the improved search operators in the territory foraging phase to enhance the ability to escape from local optima and increase convergence accuracy. The effectiveness of IMOAHA was verified through Matlab/Simulink. The results demonstrate that IMOAHA exhibits superior convergence, diversity, uniformity, and coverage of solutions across 6 test functions, outperforming 4 comparative algorithms. A Wilcoxon rank-sum test further confirmed its exceptional performance. To assess IMOAHA’s ability to solve engineering problems, an optimization model for a multi-track, multi-train urban rail traction power supply system with Supercapacitor Energy Storage Systems (SCESSs) was established, and IMOAHA was successfully applied to solving the capacity allocation problem of SCESSs, demonstrating that it is an effective tool for solving complex Multi-Objective Optimization Problems (MOOPs) in engineering domains.展开更多
文摘Multi-Objective Evolutionary Algorithms(MOEAs)have significantly advanced the domain of MultiObjective Optimization(MOO),facilitating solutions for complex problems with multiple conflicting objectives.This review explores the historical development of MOEAs,beginning with foundational concepts in multi-objective optimization,basic types of MOEAs,and the evolution of Pareto-based selection and niching methods.Further advancements,including decom-position-based approaches and hybrid algorithms,are discussed.Applications are analyzed in established domains such as engineering and economics,as well as in emerging fields like advanced analytics and machine learning.The significance of MOEAs in addressing real-world problems is emphasized,highlighting their role in facilitating informed decision-making.Finally,the development trajectory of MOEAs is compared with evolutionary processes,offering insights into their progress and future potential.
文摘Steady-state non-dominated sorting genetic algorithm (SNSGA), a new form of multi-objective genetic algorithm, is implemented by combining the steady-state idea in steady-state genetic algorithms (SSGA) and the fitness assignment strategy of non-dominated sorting genetic algorithm (NSGA). The fitness assignment strategy is improved and a new self-adjustment scheme of is proposed. This algorithm is proved to be very efficient both computationally and in terms of the quality of the Pareto fronts produced with five test problems including GA difficult problem and GA deceptive one. Finally, SNSGA is introduced to solve multi-objective mixed integer linear programming (MILP) and mixed integer non-linear programming (MINLP) problems in process synthesis.
基金Supported by the National Natural Science Foundation of China(60133010,70071042,60073043)
文摘Multi-objective Evolutionary Algorithm (MOEA) is becoming a hot research area and quite a few aspects of MOEAs have been studied and discussed. However there are still few literatures discussing the roles of search and selection operators in MOEAs. This paper studied their roles by solving a case of discrete Multi-objective Optimization Problem (MOP): Multi-objective TSP with a new MOEA. In the new MOEA, We adopt an efficient search operator, which has the properties of both crossover and mutation, to generate the new individuals and chose two selection operators: Family Competition and Population Competition with probabilities to realize selection. The simulation experiments showed that this new MOEA could get good uniform solutions representing the Pareto Front and outperformed SPEA in almost every simulation run on this problem. Furthermore, we analyzed its convergence property using finite Markov chain and proved that it could converge to Pareto Front with probability 1. We also find that the convergence property of MOEAs has much relationship with search and selection operators.
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supported by the Research Center of College of Computer and Information Sciences,King Saud University,Saudi Arabia
文摘Data structures used for an algorithm can have a great impact on its performance, particularly for the solution of large and complex problems, such as multi-objective optimization problems （MOPs）. Multi-objective evolutionary algorithms （MOEAs） are considered an attractive approach for solving MOPs~ since they are able to explore several parts of the Pareto front simultaneously. The data structures for storing and updating populations and non-dominated solutions （archives） may affect the efficiency of the search process. This article describes data structures used in MOEAs for realizing populations and archives in a comparative way, emphasizing their computational requirements and general applicability reported in the original work.
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We thank Professor Wei Jiang and two anonymous reviewers for their suggestions and comments.Feng Liu and Jiafu Tang were supported by the NSFC[grant numbers 71872033,71420107028]Kan Fang was supported by the NSFC[grant number 71701144]+1 种基金Yong Yin was supported by the Omron research fund.Feng Liu was also supported by the 2020 LiaoNing Revitalization Talents Program(XLYC2007061)the Dalian High Level Talents Innovation Support Plan(2019RQ107).
文摘Today's volatile market conditions in electronic industries have lead to a new production system,seru(which is the Japanese pronunciation for cell),and has been widely implemented in hundreds of Japanese and other Asia companies.In particular,the rotating seru has been widely implemented,where workers are fully cross-trained with the same skill level but may be different on the proficiency of performing tasks.The rotating seru production problem,which determines the rotating sequence of workers as well as the assembling sequence of jobs,is difficult to solve due to conflicting objectives and dynamic release of customer demands.To solve this problem,we propose a dynamic multiobjective NSGA-II based memetic algorithm.Moreover,to preserve desirable population diversity and improve the searching efficiency,we propose different problem-specific evolutionary strategies.Finally,we test the performance of our proposed memetic algorithm with other state-of-the-art multi-objective evolutionary algorithms and demonstrate the effectiveness of our proposed algorithm.
文摘In this paper, a multi-objective particle swarm optimization （MOPSO） algorithm and a nondominated sorting genetic algorithm II （NSGA-II） are used to optimize the operating parameters of a 1.6 L, spark ignition （SI） gasoline engine. The aim of this optimization is to reduce engine emissions in terms of carbon monoxide （CO）, hydrocarbons （HC）, and nitrogen oxides （NOx）, which are the causes of diverse environmental problems such as air pollution and global warming. Stationary engine tests were performed for data generation, covering 60 operating conditions. Artificial neural networks （ANNs） were used to predict exhaust emissions, whose inputs were from six engine operating parameters, and the outputs were three resulting exhaust emissions. The outputs of ANNs were used to evaluate objective functions within the optimization algorithms： NSGA-II and MOPSO. Then a decision-making process was conducted, using a fuzzy method to select a Pareto solution with which the best emission reductions can be achieved. The NSGA-II algorithm achieved reductions of at least 9.84%, 82.44%, and 13.78% for CO, HC, and NOx, respectively. With a MOPSO algorithm the reached reductions were at least 13.68%, 83.80%, and 7.67% for CO, HC, and NOx, respectively.
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.
文摘Cloud computing has become an essential technology for the management and processing of large datasets,offering scalability,high availability,and fault tolerance.However,optimizing data replication across multiple data centers poses a significant challenge,especially when balancing opposing goals such as latency,storage costs,energy consumption,and network efficiency.This study introduces a novel Dynamic Optimization Algorithm called Dynamic Multi-Objective Gannet Optimization(DMGO),designed to enhance data replication efficiency in cloud environments.Unlike traditional static replication systems,DMGO adapts dynamically to variations in network conditions,system demand,and resource availability.The approach utilizes multi-objective optimization approaches to efficiently balance data access latency,storage efficiency,and operational costs.DMGO consistently evaluates data center performance and adjusts replication algorithms in real time to guarantee optimal system efficiency.Experimental evaluations conducted in a simulated cloud environment demonstrate that DMGO significantly outperforms conventional static algorithms,achieving faster data access,lower storage overhead,reduced energy consumption,and improved scalability.The proposed methodology offers a robust and adaptable solution for modern cloud systems,ensuring efficient resource consumption while maintaining high performance.
基金supported by the National Natural Science Foundation of China(Nos.12475174 and 12175101)Yue Lu Shan Center Industrial Innovation(No.2024YCII0108)。
文摘In recent years,the development of new types of nuclear reactors,such as transportable,marine,and space reactors,has presented new challenges for the optimization of reactor radiation-shielding design.Shielding structures typically need to be lightweight,miniaturized,and radiation-protected,which is a multi-parameter and multi-objective optimization problem.The conventional multi-objective(two or three objectives)optimization method for radiation-shielding design exhibits limitations for a number of optimization objectives and variable parameters,as well as a deficiency in achieving a global optimal solution,thereby failing to meet the requirements of shielding optimization for newly developed reactors.In this study,genetic and artificial bee-colony algorithms are combined with a reference-point-selection strategy and applied to the many-objective(having four or more objectives)optimal design of reactor radiation shielding.To validate the reliability of the methods,an optimization simulation is conducted on three-dimensional shielding structures and another complicated shielding-optimization problem.The numerical results demonstrate that the proposed algorithms outperform conventional shielding-design methods in terms of optimization performance,and they exhibit their reliability in practical engineering problems.The many-objective optimization algorithms developed in this study are proven to efficiently and consistently search for Pareto-front shielding schemes.Therefore,the algorithms proposed in this study offer novel insights into improving the shielding-design performance and shielding quality of new reactor types.
基金supported by the Serbian Ministry of Education and Science under Grant No.TR35006 and COST Action:CA23155—A Pan-European Network of Ocean Tribology(OTC)The research of B.Rosic and M.Rosic was supported by the Serbian Ministry of Education and Science under Grant TR35029.
文摘This paper introduces a hybrid multi-objective optimization algorithm,designated HMODESFO,which amalgamates the exploratory prowess of Differential Evolution(DE)with the rapid convergence attributes of the Sailfish Optimization(SFO)algorithm.The primary objective is to address multi-objective optimization challenges within mechanical engineering,with a specific emphasis on planetary gearbox optimization.The algorithm is equipped with the ability to dynamically select the optimal mutation operator,contingent upon an adaptive normalized population spacing parameter.The efficacy of HMODESFO has been substantiated through rigorous validation against estab-lished industry benchmarks,including a suite of Zitzler-Deb-Thiele(ZDT)and Zeb-Thiele-Laumanns-Zitzler(DTLZ)problems,where it exhibited superior performance.The outcomes underscore the algorithm’s markedly enhanced optimization capabilities relative to existing methods,particularly in tackling highly intricate multi-objective planetary gearbox optimization problems.Additionally,the performance of HMODESFO is evaluated against selected well-known mechanical engineering test problems,further accentuating its adeptness in resolving complex optimization challenges within this domain.
基金Project(50775089)supported by the National Natural Science Foundation of ChinaProject(2007AA04Z190,2009AA043301)supported by the National High Technology Research and Development Program of ChinaProject(2005CB724100)supported by the National Basic Research Program of China
文摘The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency. A multi-objective model was presented for the material distribution routing problem in mixed manufacturing systems, and it was solved by a hybrid multi-objective evolutionary algorithm (HMOEA). The characteristics of the HMOEA are as follows: 1) A route pool is employed to preserve the best routes for the population initiation; 2) A specialized best?worst route crossover (BWRC) mode is designed to perform the crossover operators for selecting the best route from Chromosomes 1 to exchange with the worst one in Chromosomes 2, so that the better genes are inherited to the offspring; 3) A route swap mode is used to perform the mutation for improving the convergence speed and preserving the better gene; 4) Local heuristics search methods are applied in this algorithm. Computational study of a practical case shows that the proposed algorithm can decrease the total travel distance by 51.66%, enhance the average vehicle load rate by 37.85%, cut down 15 routes and reduce a deliver vehicle. The convergence speed of HMOEA is faster than that of famous NSGA-II.
基金National Natural Science Foundation of China under Grant No.52278490。
文摘Finding an optimal isolator arrangement for asymmetric structures using traditional conceptual design methods that can significantly minimize torsional response while ensuring efficient horizontal seismic isolation is cumbersome and inefficient.Thus,this work develops a multi-objective optimization method to enhance the torsional resistance of asymmetric base-isolated structures.The primary objective is to simultaneously minimize the interstory rotation of the superstructure,the rotation of the isolation layer,and the interstory displacement of the superstructure without exceeding the isolator displacement limits.A fast non-dominated sorting genetic algorithm(NSGA-Ⅱ)is employed to satisfy this optimization objective.Subsequently,the isolator arrangement,encompassing both positions and categories,is optimized according to this multi-objective optimization method.Additionally,an optimization design platform is developed to streamline the design operation.This platform integrates the input of optimization parameters,the output of optimization results,the finite element analysis,and the multi-objective optimization method proposed herein.Finally,the application of this multi-objective optimization method and its associated platform are demonstrated on two asymmetric base-isolated structures of varying heights and plan configurations.The results indicate that the optimal isolator arrangement derived from the optimization method can further improve the control over the lateral and torsional responses of asymmetric base-isolated structures compared to conventional conceptual design methods.Notably,the interstory rotation of the optimal base-isolated structure is significantly reduced,constituting only approximately 33.7%of that observed in the original base-isolated structure.The proposed platform facilitates the automatic generation of the optimal design scheme for the isolators of asymmetric base-isolated structures,offering valuable insights and guidance for the burgeoning field of intelligent civil engineering design.
基金funded by Researchers Supporting Programnumber(RSPD2024R809),King Saud University,Riyadh,Saudi Arabia.
文摘Multi-objective optimization is critical for problem-solving in engineering,economics,and AI.This study introduces the Multi-Objective Chef-Based Optimization Algorithm(MOCBOA),an upgraded version of the Chef-Based Optimization Algorithm(CBOA)that addresses distinct objectives.Our approach is unique in systematically examining four dominance relations—Pareto,Epsilon,Cone-epsilon,and Strengthened dominance—to evaluate their influence on sustaining solution variety and driving convergence toward the Pareto front.Our comparison investigation,which was conducted on fifty test problems from the CEC 2021 benchmark and applied to areas such as chemical engineering,mechanical design,and power systems,reveals that the dominance approach used has a considerable impact on the key optimization measures such as the hypervolume metric.This paper provides a solid foundation for determining themost effective dominance approach and significant insights for both theoretical research and practical applications in multi-objective optimization.
基金supported by the National Natural Science Foundation of China(Grant Nos.52090081,52079068)the State Key Laboratory of Hydroscience and Hydraulic Engineering(Grant No.2021-KY-04).
文摘Accurate determination of rock mass parameters is essential for ensuring the accuracy of numericalsimulations. Displacement back-analysis is the most widely used method;however, the reliability of thecurrent approaches remains unsatisfactory. Therefore, in this paper, a multistage rock mass parameterback-analysis method, that considers the construction process and displacement losses is proposed andimplemented through the coupling of numerical simulation, auto-machine learning (AutoML), andmulti-objective optimization algorithms (MOOAs). First, a parametric modeling platform for mechanizedtwin tunnels is developed, generating a dataset through extensive numerical simulations. Next, theAutoML method is utilized to establish a surrogate model linking rock parameters and displacements.The tunnel construction process is divided into multiple stages, transforming the rock mass parameterback-analysis into a multi-objective optimization problem, for which multi-objective optimization algorithmsare introduced to obtain the rock mass parameters. The newly proposed rock mass parameterback-analysis method is validated in a mechanized twin tunnel project, and its accuracy and effectivenessare demonstrated. Compared with traditional single-stage back-analysis methods, the proposedmodel decreases the average absolute percentage error from 12.73% to 4.34%, significantly improving theaccuracy of the back-analysis. Moreover, although the accuracy of back analysis significantly increaseswith the number of construction stages considered, the back analysis time is acceptable. This studyprovides a new method for displacement back analysis that is efficient and accurate, thereby paving theway for precise parameter determination in numerical simulations.
基金supported by National Natural Science Foundation of China (Grant No.50875101)National Hi-tech Research and Development Program of China (863 Program,Grant No.2007AA04Z186)
文摘As two independent problems,scheduling for parts fabrication line and sequencing for mixed-model assembly line have been addressed respectively by many researchers.However,these two problems should be considered simultaneously to improve the efficiency of the whole fabrication/assembly systems.By far,little research effort is devoted to sequencing problems for mixed-model fabrication/assembly systems.This paper is concerned about the sequencing problems in pull production systems which are composed of one mixed-model assembly line with limited intermediate buffers and two flexible parts fabrication flow lines with identical parallel machines and limited intermediate buffers.Two objectives are considered simultaneously：minimizing the total variation in parts consumption in the assembly line and minimizing the total makespan cost in the fabrication/assembly system.The integrated optimization framework,mathematical models and the method to construct the complete schedules for the fabrication lines according to the production sequences for the first stage in fabrication lines are presented.Since the above problems are non-deterministic polynomial-hard（NP-hard）,a modified multi-objective genetic algorithm is proposed for solving the models,in which a method to generate the production sequences for the fabrication lines from the production sequences for the assembly line and a method to generate the initial population are put forward,new selection,crossover and mutation operators are designed,and Pareto ranking method and sharing function method are employed to evaluate the individuals＇ fitness.The feasibility and efficiency of the multi-objective genetic algorithm is shown by computational comparison with a multi-objective simulated annealing algorithm.The sequencing problems for mixed-model production systems can be solved effectively by the proposed modified multi-objective genetic algorithm.
基金funded by the Ministry of Higher Education of Malaysia,grant number FRGS/1/2022/ICT02/UPSI/02/1.
文摘In recent years,feature selection(FS)optimization of high-dimensional gene expression data has become one of the most promising approaches for cancer prediction and classification.This work reviews FS and classification methods that utilize evolutionary algorithms(EAs)for gene expression profiles in cancer or medical applications based on research motivations,challenges,and recommendations.Relevant studies were retrieved from four major academic databases-IEEE,Scopus,Springer,and ScienceDirect-using the keywords‘cancer classification’,‘optimization’,‘FS’,and‘gene expression profile’.A total of 67 papers were finally selected with key advancements identified as follows:(1)The majority of papers(44.8%)focused on developing algorithms and models for FS and classification.(2)The second category encompassed studies on biomarker identification by EAs,including 20 papers(30%).(3)The third category comprised works that applied FS to cancer data for decision support system purposes,addressing high-dimensional data and the formulation of chromosome length.These studies accounted for 12%of the total number of studies.(4)The remaining three papers(4.5%)were reviews and surveys focusing on models and developments in prediction and classification optimization for cancer classification under current technical conditions.This review highlights the importance of optimizing FS in EAs to manage high-dimensional data effectively.Despite recent advancements,significant limitations remain:the dynamic formulation of chromosome length remains an underexplored area.Thus,further research is needed on dynamic-length chromosome techniques for more sophisticated biomarker gene selection techniques.The findings suggest that further advancements in dynamic chromosome length formulations and adaptive algorithms could enhance cancer classification accuracy and efficiency.
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by National Natural Science Foundation of China(62373142,62033014)Natural Science Foundation of Hunan Province(2025JJ70017,2022JJ50074).
文摘To address issues such as poor initial population diversity, low stability and local convergence accuracy, and easy local optima in the traditional Multi-Objective Artificial Hummingbird Algorithm (MOAHA), an Improved MOAHA (IMOAHA) was proposed. The improvements involve Tent mapping based on random variables to initialize the population, a logarithmic decrease strategy for inertia weight to balance search capability, and the improved search operators in the territory foraging phase to enhance the ability to escape from local optima and increase convergence accuracy. The effectiveness of IMOAHA was verified through Matlab/Simulink. The results demonstrate that IMOAHA exhibits superior convergence, diversity, uniformity, and coverage of solutions across 6 test functions, outperforming 4 comparative algorithms. A Wilcoxon rank-sum test further confirmed its exceptional performance. To assess IMOAHA’s ability to solve engineering problems, an optimization model for a multi-track, multi-train urban rail traction power supply system with Supercapacitor Energy Storage Systems (SCESSs) was established, and IMOAHA was successfully applied to solving the capacity allocation problem of SCESSs, demonstrating that it is an effective tool for solving complex Multi-Objective Optimization Problems (MOOPs) in engineering domains.
