A novel multi-objective optimization algorithm incorporating vector method and evolution strategies,referred as vector dominant multi-objective evolutionary algorithm(VD-MOEA),is developed and applied to the aerodynam...A novel multi-objective optimization algorithm incorporating vector method and evolution strategies,referred as vector dominant multi-objective evolutionary algorithm(VD-MOEA),is developed and applied to the aerodynamic-structural integrative design of wind turbine blades.A set of virtual vectors are elaborately constructed,guiding population to fast move forward to the Pareto optimal front and dominating the distribution uniformity with high efficiency.In comparison to conventional evolution algorithms,VD-MOEA displays dramatic improvement of algorithm performance in both convergence and diversity preservation when handling complex problems of multi-variables,multi-objectives and multi-constraints.As an example,a 1.5 MW wind turbine blade is subsequently designed taking the maximum annual energy production,the minimum blade mass,and the minimum blade root thrust as the optimization objectives.The results show that the Pareto optimal set can be obtained in one single simulation run and that the obtained solutions in the optimal set are distributed quite uniformly,maximally maintaining the population diversity.The efficiency of VD-MOEA has been elevated by two orders of magnitude compared with the classical NSGA-II.This provides a reliable high-performance optimization approach for the aerodynamic-structural integrative design of wind turbine blade.展开更多
Community detection is one of the most fundamental applications in understanding the structure of complicated networks.Furthermore,it is an important approach to identifying closely linked clusters of nodes that may r...Community detection is one of the most fundamental applications in understanding the structure of complicated networks.Furthermore,it is an important approach to identifying closely linked clusters of nodes that may represent underlying patterns and relationships.Networking structures are highly sensitive in social networks,requiring advanced techniques to accurately identify the structure of these communities.Most conventional algorithms for detecting communities perform inadequately with complicated networks.In addition,they miss out on accurately identifying clusters.Since single-objective optimization cannot always generate accurate and comprehensive results,as multi-objective optimization can.Therefore,we utilized two objective functions that enable strong connections between communities and weak connections between them.In this study,we utilized the intra function,which has proven effective in state-of-the-art research studies.We proposed a new inter-function that has demonstrated its effectiveness by making the objective of detecting external connections between communities is to make them more distinct and sparse.Furthermore,we proposed a Multi-Objective community strength enhancement algorithm(MOCSE).The proposed algorithm is based on the framework of the Multi-Objective Evolutionary Algorithm with Decomposition(MOEA/D),integrated with a new heuristic mutation strategy,community strength enhancement(CSE).The results demonstrate that the model is effective in accurately identifying community structures while also being computationally efficient.The performance measures used to evaluate the MOEA/D algorithm in our work are normalized mutual information(NMI)and modularity(Q).It was tested using five state-of-the-art algorithms on social networks,comprising real datasets(Zachary,Dolphin,Football,Krebs,SFI,Jazz,and Netscience),as well as twenty synthetic datasets.These results provide the robustness and practical value of the proposed algorithm in multi-objective community identification.展开更多
In a wide range of engineering applications,complex constrained multi-objective optimization problems(CMOPs)present significant challenges,as the complexity of constraints often hampers algorithmic convergence and red...In a wide range of engineering applications,complex constrained multi-objective optimization problems(CMOPs)present significant challenges,as the complexity of constraints often hampers algorithmic convergence and reduces population diversity.To address these challenges,we propose a novel algorithm named Constraint IntensityDriven Evolutionary Multitasking(CIDEMT),which employs a two-stage,tri-task framework to dynamically integrates problem structure and knowledge transfer.In the first stage,three cooperative tasks are designed to explore the Constrained Pareto Front(CPF),the Unconstrained Pareto Front(UPF),and theε-relaxed constraint boundary,respectively.A CPF-UPF relationship classifier is employed to construct a problem-type-aware evolutionary strategy pool.At the end of the first stage,each task selects strategies from this strategy pool based on the specific type of problem,thereby guiding the subsequent evolutionary process.In the second stage,while each task continues to evolve,aτ-driven knowledge transfer mechanism is introduced to selectively incorporate effective solutions across tasks.enhancing the convergence and feasibility of the main task.Extensive experiments conducted on 32 benchmark problems from three test suites(LIRCMOP,DASCMOP,and DOC)demonstrate that CIDEMT achieves the best Inverted Generational Distance(IGD)values on 24 problems and the best Hypervolume values(HV)on 22 problems.Furthermore,CIDEMT significantly outperforms six state-of-the-art constrained multi-objective evolutionary algorithms(CMOEAs).These results confirm CIDEMT’s superiority in promoting convergence,diversity,and robustness in solving complex CMOPs.展开更多
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
In reliability analyses,the absence of a priori information on the most probable point of failure(MPP)may result in overlooking critical points,thereby leading to biased assessment outcomes.Moreover,second-order relia...In reliability analyses,the absence of a priori information on the most probable point of failure(MPP)may result in overlooking critical points,thereby leading to biased assessment outcomes.Moreover,second-order reliability methods exhibit limited accuracy in highly nonlinear scenarios.To overcome these challenges,a novel reliability analysis strategy based on a multimodal differential evolution algorithm and a hypersphere integration method is proposed.Initially,the penalty function method is employed to reformulate the MPP search problem as a conditionally constrained optimization task.Subsequently,a differential evolution algorithm incorporating a population delineation strategy is utilized to identify all MPPs.Finally,a paraboloid equation is constructed based on the curvature of the limit-state function at the MPPs,and the failure probability of the structure is calculated by using the hypersphere integration method.The localization effectiveness of the MPPs is compared through multiple numerical cases and two engineering examples,with accuracy comparisons of failure probabilities against the first-order reliability method(FORM)and the secondorder reliability method(SORM).The results indicate that the method effectively identifies existing MPPs and achieves higher solution precision.展开更多
Welding deformation adversely affects the quality and precision of structural components,and traditional methods require significant material resources and time.Machine learning has demonstrated exceptional ac-curacy ...Welding deformation adversely affects the quality and precision of structural components,and traditional methods require significant material resources and time.Machine learning has demonstrated exceptional ac-curacy and efficiency in solving complex problems.Thus,the use of machine learning to predict welding de-formations is a novel approach.In this study,laser welding experiments were conducted on a TC4 titanium alloy to establish a welding deformation dataset.The deep neural network(DNN)and convolutional neural network(CNN)models were designed and constructed,with average prediction errors of 0.85 mm and 0.94 mm on the validation set,respectively.To further optimize the network parameters,a differential evolution algorithm was employed through mutation,crossover,and selection.The results indicated that after optimization,the pre-diction errors of the DNN and CNN models reduced to 0.75 mm and 0.85 mm,respectively.These represent accuracy improvements of 14.8%and 9.6%,respectively.The optimized models exhibited superior predictive performances for the validation set.展开更多
Dimensional synthesis is one of the most difficult issues in the field of parallel robots with actuation redundancy. To deal with the optimal design of a redundantly actuated parallel robot used for ankle rehabilitati...Dimensional synthesis is one of the most difficult issues in the field of parallel robots with actuation redundancy. To deal with the optimal design of a redundantly actuated parallel robot used for ankle rehabilitation, a methodology of dimensional synthesis based on multi-objective optimization is presented. First, the dimensional synthesis of the redundant parallel robot is formulated as a nonlinear constrained multi-objective optimization problem. Then four objective functions, separately reflecting occupied space, input/output transmission and torque performances, and multi-criteria constraints, such as dimension, interference and kinematics, are defined. In consideration of the passive exercise of plantar/dorsiflexion requiring large output moment, a torque index is proposed. To cope with the actuation redundancy of the parallel robot, a new output transmission index is defined as well. The multi-objective optimization problem is solved by using a modified Differential Evolution（DE） algorithm, which is characterized by new selection and mutation strategies. Meanwhile, a special penalty method is presented to tackle the multi-criteria constraints. Finally, numerical experiments for different optimization algorithms are implemented. The computation results show that the proposed indices of output transmission and torque, and constraint handling are effective for the redundant parallel robot; the modified DE algorithm is superior to the other tested algorithms, in terms of the ability of global search and the number of non-dominated solutions. The proposed methodology of multi-objective optimization can be also applied to the dimensional synthesis of other redundantly actuated parallel robots only with rotational movements.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
The continuous growth of air traffic has led to acute airspace congestion and severe delays, which threatens operation safety and cause enormous economic loss. Flight assignment is an economical and effective strategi...The continuous growth of air traffic has led to acute airspace congestion and severe delays, which threatens operation safety and cause enormous economic loss. Flight assignment is an economical and effective strategic plan to reduce the flight delay and airspace congestion by rea- sonably regulating the air traffic flow of China. However, it is a large-scale combinatorial optimiza- tion problem which is difficult to solve. In order to improve the quality of solutions, an effective multi-objective parallel evolution algorithm （MPEA） framework with dynamic migration interval strategy is presented in this work. Firstly, multiple evolution populations are constructed to solve the problem simultaneously to enhance the optimization capability. Then a new strategy is pro- posed to dynamically change the migration interval among different evolution populations to improve the efficiency of the cooperation of populations. Finally, the cooperative co-evolution （CC） algorithm combined with non-dominated sorting genetic algorithm II （NSGA-II） is intro- duced for each population. Empirical studies using the real air traffic data of the Chinese air route network and daily flight plans show that our method outperforms the existing approaches, multi- objective genetic algorithm （MOGA）, multi-objective evolutionary algorithm based on decom- position （MOEA/D）, CC-based multi-objective algorithm （CCMA） as well as other two MPEAs with different migration interval strategies.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
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
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
The overall performance of multi-robot collaborative systems is significantly affected by the multi-robot task allocation.To improve the effectiveness,robustness,and safety of multi-robot collaborative systems,a multi...The overall performance of multi-robot collaborative systems is significantly affected by the multi-robot task allocation.To improve the effectiveness,robustness,and safety of multi-robot collaborative systems,a multimodal multi-objective evolutionary algorithm based on deep reinforcement learning is proposed in this paper.The improved multimodal multi-objective evolutionary algorithm is used to solve multi-robot task allo-cation problems.Moreover,a deep reinforcement learning strategy is used in the last generation to provide a high-quality path for each assigned robot via an end-to-end manner.Comparisons with three popular multimodal multi-objective evolutionary algorithms on three different scenarios of multi-robot task allocation problems are carried out to verify the performance of the proposed algorithm.The experimental test results show that the proposed algorithm can generate sufficient equivalent schemes to improve the availability and robustness of multi-robot collaborative systems in uncertain environments,and also produce the best scheme to improve the overall task execution efficiency of multi-robot collaborative systems.展开更多
In this paper, a new hybrid multi-objective evolutionary algorithm （MOEA）, the niched Pareto tabu search combined with a genetic algorithm （NPTSGA）, is proposed for the management of groundwater resources under va...In this paper, a new hybrid multi-objective evolutionary algorithm （MOEA）, the niched Pareto tabu search combined with a genetic algorithm （NPTSGA）, is proposed for the management of groundwater resources under variable density conditions. Relatively few MOEAs can possess global search ability contenting with intensified search in a local area. Moreover, the overall searching ability of tabu search （TS） based MOEAs is very sensitive to the neighborhood step size. The NPTSGA is developed on the thought of integrating the genetic algorithm （GA） with a TS based MOEA, the niched Pareto tabu search （NPTS）, which helps to alleviate both of the above difficulties. Here, the global search ability of the NPTS is improved by the diversification of candidate solutions arising from the evolving genetic algorithm population. Furthermore, the proposed methodology coupled with a density-dependent groundwater flow and solute transport simulator, SEAWAT, is developed and its performance is evaluated through a synthetic seawater intrusion management problem. Optimization results indicate that the NPTSGA offers a tradeoff between the two conflicting objectives. A key conclusion of this study is that the NPTSGA keeps the balance between the intensification of nondomination and the diversification of near Pareto-optimal solutions along the tradeoff curves and is a stable and robust method for implementing the multi-objective design of variable-density groundwater resources.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
Due to the intermittency and instability of Wind-Solar energy and easy compensation of hydropower, this study proposes a Wind-Solar-Hydro power optimal scheduling model. This model is aimed at maximizing the total sys...Due to the intermittency and instability of Wind-Solar energy and easy compensation of hydropower, this study proposes a Wind-Solar-Hydro power optimal scheduling model. This model is aimed at maximizing the total system power generation and the minimum ten-day joint output. To effectively optimize the multi-objective model, a new algorithm named non-dominated sorting culture differential evolution algorithm(NSCDE) is proposed. The feasibility of NSCDE was verified through several well-known benchmark problems. It was then applied to the Jinping Wind-Solar-Hydro complementary power generation system. The results demonstrate that NSCDE can provide decision makers a series of optimized scheduling schemes.展开更多
This work proposes a novel approach for multi-type optimal placement of flexible AC transmission system(FACTS) devices so as to optimize multi-objective voltage stability problem. The current study discusses a way for...This work proposes a novel approach for multi-type optimal placement of flexible AC transmission system(FACTS) devices so as to optimize multi-objective voltage stability problem. The current study discusses a way for locating and setting of thyristor controlled series capacitor(TCSC) and static var compensator(SVC) using the multi-objective optimization approach named strength pareto multi-objective evolutionary algorithm(SPMOEA). Maximization of the static voltage stability margin(SVSM) and minimizations of real power losses(RPL) and load voltage deviation(LVD) are taken as the goals or three objective functions, when optimally locating multi-type FACTS devices. The performance and effectiveness of the proposed approach has been validated by the simulation results of the IEEE 30-bus and IEEE 118-bus test systems. The proposed approach is compared with non-dominated sorting particle swarm optimization(NSPSO) algorithm. This comparison confirms the usefulness of the multi-objective proposed technique that makes it promising for determination of combinatorial problems of FACTS devices location and setting in large scale power systems.展开更多
Multi-objective optimal evolutionary algorithms (MOEAs) are a kind of new effective algorithms to solve Multi-objective optimal problem (MOP). Because ranking, a method which is used by most MOEAs to solve MOP, has so...Multi-objective optimal evolutionary algorithms (MOEAs) are a kind of new effective algorithms to solve Multi-objective optimal problem (MOP). Because ranking, a method which is used by most MOEAs to solve MOP, has some shortcoming s, in this paper, we proposed a new method using tree structure to express the relationship of solutions. Experiments prove that the method can reach the Pare-to front, retain the diversity of the population, and use less time.展开更多
This research paper presents a comprehensive investigation into the effectiveness of the DeepSurNet-NSGA II(Deep Surrogate Model-Assisted Non-dominated Sorting Genetic Algorithm II)for solving complex multiobjective o...This research paper presents a comprehensive investigation into the effectiveness of the DeepSurNet-NSGA II(Deep Surrogate Model-Assisted Non-dominated Sorting Genetic Algorithm II)for solving complex multiobjective optimization problems,with a particular focus on robotic leg-linkage design.The study introduces an innovative approach that integrates deep learning-based surrogate models with the robust Non-dominated Sorting Genetic Algorithm II,aiming to enhance the efficiency and precision of the optimization process.Through a series of empirical experiments and algorithmic analyses,the paper demonstrates a high degree of correlation between solutions generated by the DeepSurNet-NSGA II and those obtained from direct experimental methods,underscoring the algorithm’s capability to accurately approximate the Pareto-optimal frontier while significantly reducing computational demands.The methodology encompasses a detailed exploration of the algorithm’s configuration,the experimental setup,and the criteria for performance evaluation,ensuring the reproducibility of results and facilitating future advancements in the field.The findings of this study not only confirm the practical applicability and theoretical soundness of the DeepSurNet-NSGA II in navigating the intricacies of multi-objective optimization but also highlight its potential as a transformative tool in engineering and design optimization.By bridging the gap between complex optimization challenges and achievable solutions,this research contributes valuable insights into the optimization domain,offering a promising direction for future inquiries and technological innovations.展开更多
Tourism route planning is widely applied in the smart tourism field.The Pareto-optimal front obtained by the traditional multi-objective evolutionary algorithm exhibits long tails,sharp peaks and disconnected regions ...Tourism route planning is widely applied in the smart tourism field.The Pareto-optimal front obtained by the traditional multi-objective evolutionary algorithm exhibits long tails,sharp peaks and disconnected regions problems,which leads to uneven distribution and weak diversity of optimization solutions of tourism routes.Inspired by these limitations,we propose a multi-objective evolutionary algorithm for tourism route recommendation(MOTRR)with two-stage and Pareto layering based on decomposition.The method decomposes the multiobjective problem into several subproblems,and improves the distribution of solutions through a two-stage method.The crowding degree mechanism between extreme and intermediate populations is used in the two-stage method.The neighborhood is determined according to the weight of the subproblem for crossover mutation.Finally,Pareto layering is used to improve the updating efficiency and population diversity of the solution.The two-stage method is combined with the Pareto layering structure,which not only maintains the distribution and diversity of the algorithm,but also avoids the same solutions.Compared with several classical benchmark algorithms,the experimental results demonstrate competitive advantages on five test functions,hypervolume(HV)and inverted generational distance(IGD)metrics.Using the experimental results of real scenic spot datasets from two famous tourism social networking sites with vast amounts of users and large-scale online comments in Beijing,our proposed algorithm shows better distribution.It proves that the tourism routes recommended by our proposed algorithm have better distribution and diversity,so that the recommended routes can better meet the personalized needs of tourists.展开更多
基金funded jointly by the National Basic Research Program of China(″973″Program)(No2014CB046200)the National Natural Science Foundation of China(No.51506089)+1 种基金the Jiangsu Provincial Natural Science Foundation(No.BK20140059)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘A novel multi-objective optimization algorithm incorporating vector method and evolution strategies,referred as vector dominant multi-objective evolutionary algorithm(VD-MOEA),is developed and applied to the aerodynamic-structural integrative design of wind turbine blades.A set of virtual vectors are elaborately constructed,guiding population to fast move forward to the Pareto optimal front and dominating the distribution uniformity with high efficiency.In comparison to conventional evolution algorithms,VD-MOEA displays dramatic improvement of algorithm performance in both convergence and diversity preservation when handling complex problems of multi-variables,multi-objectives and multi-constraints.As an example,a 1.5 MW wind turbine blade is subsequently designed taking the maximum annual energy production,the minimum blade mass,and the minimum blade root thrust as the optimization objectives.The results show that the Pareto optimal set can be obtained in one single simulation run and that the obtained solutions in the optimal set are distributed quite uniformly,maximally maintaining the population diversity.The efficiency of VD-MOEA has been elevated by two orders of magnitude compared with the classical NSGA-II.This provides a reliable high-performance optimization approach for the aerodynamic-structural integrative design of wind turbine blade.
文摘Community detection is one of the most fundamental applications in understanding the structure of complicated networks.Furthermore,it is an important approach to identifying closely linked clusters of nodes that may represent underlying patterns and relationships.Networking structures are highly sensitive in social networks,requiring advanced techniques to accurately identify the structure of these communities.Most conventional algorithms for detecting communities perform inadequately with complicated networks.In addition,they miss out on accurately identifying clusters.Since single-objective optimization cannot always generate accurate and comprehensive results,as multi-objective optimization can.Therefore,we utilized two objective functions that enable strong connections between communities and weak connections between them.In this study,we utilized the intra function,which has proven effective in state-of-the-art research studies.We proposed a new inter-function that has demonstrated its effectiveness by making the objective of detecting external connections between communities is to make them more distinct and sparse.Furthermore,we proposed a Multi-Objective community strength enhancement algorithm(MOCSE).The proposed algorithm is based on the framework of the Multi-Objective Evolutionary Algorithm with Decomposition(MOEA/D),integrated with a new heuristic mutation strategy,community strength enhancement(CSE).The results demonstrate that the model is effective in accurately identifying community structures while also being computationally efficient.The performance measures used to evaluate the MOEA/D algorithm in our work are normalized mutual information(NMI)and modularity(Q).It was tested using five state-of-the-art algorithms on social networks,comprising real datasets(Zachary,Dolphin,Football,Krebs,SFI,Jazz,and Netscience),as well as twenty synthetic datasets.These results provide the robustness and practical value of the proposed algorithm in multi-objective community identification.
基金supported by the National Natural Science Foundation of China under Grant No.61972040the Science and Technology Research and Development Project funded by China Railway Material Trade Group Luban Company.
文摘In a wide range of engineering applications,complex constrained multi-objective optimization problems(CMOPs)present significant challenges,as the complexity of constraints often hampers algorithmic convergence and reduces population diversity.To address these challenges,we propose a novel algorithm named Constraint IntensityDriven Evolutionary Multitasking(CIDEMT),which employs a two-stage,tri-task framework to dynamically integrates problem structure and knowledge transfer.In the first stage,three cooperative tasks are designed to explore the Constrained Pareto Front(CPF),the Unconstrained Pareto Front(UPF),and theε-relaxed constraint boundary,respectively.A CPF-UPF relationship classifier is employed to construct a problem-type-aware evolutionary strategy pool.At the end of the first stage,each task selects strategies from this strategy pool based on the specific type of problem,thereby guiding the subsequent evolutionary process.In the second stage,while each task continues to evolve,aτ-driven knowledge transfer mechanism is introduced to selectively incorporate effective solutions across tasks.enhancing the convergence and feasibility of the main task.Extensive experiments conducted on 32 benchmark problems from three test suites(LIRCMOP,DASCMOP,and DOC)demonstrate that CIDEMT achieves the best Inverted Generational Distance(IGD)values on 24 problems and the best Hypervolume values(HV)on 22 problems.Furthermore,CIDEMT significantly outperforms six state-of-the-art constrained multi-objective evolutionary algorithms(CMOEAs).These results confirm CIDEMT’s superiority in promoting convergence,diversity,and robustness in solving complex CMOPs.
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.
基金National Natural Science Foundation of China(No.52375236)Fundamental Research Funds for the Central Universities of China(No.23D110316)。
文摘In reliability analyses,the absence of a priori information on the most probable point of failure(MPP)may result in overlooking critical points,thereby leading to biased assessment outcomes.Moreover,second-order reliability methods exhibit limited accuracy in highly nonlinear scenarios.To overcome these challenges,a novel reliability analysis strategy based on a multimodal differential evolution algorithm and a hypersphere integration method is proposed.Initially,the penalty function method is employed to reformulate the MPP search problem as a conditionally constrained optimization task.Subsequently,a differential evolution algorithm incorporating a population delineation strategy is utilized to identify all MPPs.Finally,a paraboloid equation is constructed based on the curvature of the limit-state function at the MPPs,and the failure probability of the structure is calculated by using the hypersphere integration method.The localization effectiveness of the MPPs is compared through multiple numerical cases and two engineering examples,with accuracy comparisons of failure probabilities against the first-order reliability method(FORM)and the secondorder reliability method(SORM).The results indicate that the method effectively identifies existing MPPs and achieves higher solution precision.
基金Supported by Defense Industrial Technology Development Program of China(Grant No.JCKY2021605B015).
文摘Welding deformation adversely affects the quality and precision of structural components,and traditional methods require significant material resources and time.Machine learning has demonstrated exceptional ac-curacy and efficiency in solving complex problems.Thus,the use of machine learning to predict welding de-formations is a novel approach.In this study,laser welding experiments were conducted on a TC4 titanium alloy to establish a welding deformation dataset.The deep neural network(DNN)and convolutional neural network(CNN)models were designed and constructed,with average prediction errors of 0.85 mm and 0.94 mm on the validation set,respectively.To further optimize the network parameters,a differential evolution algorithm was employed through mutation,crossover,and selection.The results indicated that after optimization,the pre-diction errors of the DNN and CNN models reduced to 0.75 mm and 0.85 mm,respectively.These represent accuracy improvements of 14.8%and 9.6%,respectively.The optimized models exhibited superior predictive performances for the validation set.
基金Supported by National Natural Science Foundation of China(Grant No.51175029)Beijing Municipal Natural Science Foundation of China(Grant No.3132019)
文摘Dimensional synthesis is one of the most difficult issues in the field of parallel robots with actuation redundancy. To deal with the optimal design of a redundantly actuated parallel robot used for ankle rehabilitation, a methodology of dimensional synthesis based on multi-objective optimization is presented. First, the dimensional synthesis of the redundant parallel robot is formulated as a nonlinear constrained multi-objective optimization problem. Then four objective functions, separately reflecting occupied space, input/output transmission and torque performances, and multi-criteria constraints, such as dimension, interference and kinematics, are defined. In consideration of the passive exercise of plantar/dorsiflexion requiring large output moment, a torque index is proposed. To cope with the actuation redundancy of the parallel robot, a new output transmission index is defined as well. The multi-objective optimization problem is solved by using a modified Differential Evolution（DE） algorithm, which is characterized by new selection and mutation strategies. Meanwhile, a special penalty method is presented to tackle the multi-criteria constraints. Finally, numerical experiments for different optimization algorithms are implemented. The computation results show that the proposed indices of output transmission and torque, and constraint handling are effective for the redundant parallel robot; the modified DE algorithm is superior to the other tested algorithms, in terms of the ability of global search and the number of non-dominated solutions. The proposed methodology of multi-objective optimization can be also applied to the dimensional synthesis of other redundantly actuated parallel robots only with rotational movements.
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co-supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (No. 60921001)
文摘The continuous growth of air traffic has led to acute airspace congestion and severe delays, which threatens operation safety and cause enormous economic loss. Flight assignment is an economical and effective strategic plan to reduce the flight delay and airspace congestion by rea- sonably regulating the air traffic flow of China. However, it is a large-scale combinatorial optimiza- tion problem which is difficult to solve. In order to improve the quality of solutions, an effective multi-objective parallel evolution algorithm （MPEA） framework with dynamic migration interval strategy is presented in this work. Firstly, multiple evolution populations are constructed to solve the problem simultaneously to enhance the optimization capability. Then a new strategy is pro- posed to dynamically change the migration interval among different evolution populations to improve the efficiency of the cooperation of populations. Finally, the cooperative co-evolution （CC） algorithm combined with non-dominated sorting genetic algorithm II （NSGA-II） is intro- duced for each population. Empirical studies using the real air traffic data of the Chinese air route network and daily flight plans show that our method outperforms the existing approaches, multi- objective genetic algorithm （MOGA）, multi-objective evolutionary algorithm based on decom- position （MOEA/D）, CC-based multi-objective algorithm （CCMA） as well as other two MPEAs with different migration interval strategies.
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 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the Shanghai Pujiang Program (No.22PJD030),the National Natural Science Foundation of China (Nos.61603244 and 71904116)the National Natural Science Foundation of China-Shandong Joint Fund (No.U2006228)。
文摘The overall performance of multi-robot collaborative systems is significantly affected by the multi-robot task allocation.To improve the effectiveness,robustness,and safety of multi-robot collaborative systems,a multimodal multi-objective evolutionary algorithm based on deep reinforcement learning is proposed in this paper.The improved multimodal multi-objective evolutionary algorithm is used to solve multi-robot task allo-cation problems.Moreover,a deep reinforcement learning strategy is used in the last generation to provide a high-quality path for each assigned robot via an end-to-end manner.Comparisons with three popular multimodal multi-objective evolutionary algorithms on three different scenarios of multi-robot task allocation problems are carried out to verify the performance of the proposed algorithm.The experimental test results show that the proposed algorithm can generate sufficient equivalent schemes to improve the availability and robustness of multi-robot collaborative systems in uncertain environments,and also produce the best scheme to improve the overall task execution efficiency of multi-robot collaborative systems.
基金funded by the National Basic Research Program of China(the 973 Program,No.2010CB428803)the National Natural Science Foundation of China(Nos.41072175,40902069 and 40725010)
文摘In this paper, a new hybrid multi-objective evolutionary algorithm （MOEA）, the niched Pareto tabu search combined with a genetic algorithm （NPTSGA）, is proposed for the management of groundwater resources under variable density conditions. Relatively few MOEAs can possess global search ability contenting with intensified search in a local area. Moreover, the overall searching ability of tabu search （TS） based MOEAs is very sensitive to the neighborhood step size. The NPTSGA is developed on the thought of integrating the genetic algorithm （GA） with a TS based MOEA, the niched Pareto tabu search （NPTS）, which helps to alleviate both of the above difficulties. Here, the global search ability of the NPTS is improved by the diversification of candidate solutions arising from the evolving genetic algorithm population. Furthermore, the proposed methodology coupled with a density-dependent groundwater flow and solute transport simulator, SEAWAT, is developed and its performance is evaluated through a synthetic seawater intrusion management problem. Optimization results indicate that the NPTSGA offers a tradeoff between the two conflicting objectives. A key conclusion of this study is that the NPTSGA keeps the balance between the intensification of nondomination and the diversification of near Pareto-optimal solutions along the tradeoff curves and is a stable and robust method for implementing the multi-objective design of variable-density groundwater resources.
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supported by the National Key R&D Program of China (2016YFC0402209)the Major Research Plan of the National Natural Science Foundation of China (No. 91647114)
文摘Due to the intermittency and instability of Wind-Solar energy and easy compensation of hydropower, this study proposes a Wind-Solar-Hydro power optimal scheduling model. This model is aimed at maximizing the total system power generation and the minimum ten-day joint output. To effectively optimize the multi-objective model, a new algorithm named non-dominated sorting culture differential evolution algorithm(NSCDE) is proposed. The feasibility of NSCDE was verified through several well-known benchmark problems. It was then applied to the Jinping Wind-Solar-Hydro complementary power generation system. The results demonstrate that NSCDE can provide decision makers a series of optimized scheduling schemes.
文摘This work proposes a novel approach for multi-type optimal placement of flexible AC transmission system(FACTS) devices so as to optimize multi-objective voltage stability problem. The current study discusses a way for locating and setting of thyristor controlled series capacitor(TCSC) and static var compensator(SVC) using the multi-objective optimization approach named strength pareto multi-objective evolutionary algorithm(SPMOEA). Maximization of the static voltage stability margin(SVSM) and minimizations of real power losses(RPL) and load voltage deviation(LVD) are taken as the goals or three objective functions, when optimally locating multi-type FACTS devices. The performance and effectiveness of the proposed approach has been validated by the simulation results of the IEEE 30-bus and IEEE 118-bus test systems. The proposed approach is compared with non-dominated sorting particle swarm optimization(NSPSO) algorithm. This comparison confirms the usefulness of the multi-objective proposed technique that makes it promising for determination of combinatorial problems of FACTS devices location and setting in large scale power systems.
基金Supported by the National Natural Science Foundation of China(60073043,70071042,60133010)
文摘Multi-objective optimal evolutionary algorithms (MOEAs) are a kind of new effective algorithms to solve Multi-objective optimal problem (MOP). Because ranking, a method which is used by most MOEAs to solve MOP, has some shortcoming s, in this paper, we proposed a new method using tree structure to express the relationship of solutions. Experiments prove that the method can reach the Pare-to front, retain the diversity of the population, and use less time.
文摘This research paper presents a comprehensive investigation into the effectiveness of the DeepSurNet-NSGA II(Deep Surrogate Model-Assisted Non-dominated Sorting Genetic Algorithm II)for solving complex multiobjective optimization problems,with a particular focus on robotic leg-linkage design.The study introduces an innovative approach that integrates deep learning-based surrogate models with the robust Non-dominated Sorting Genetic Algorithm II,aiming to enhance the efficiency and precision of the optimization process.Through a series of empirical experiments and algorithmic analyses,the paper demonstrates a high degree of correlation between solutions generated by the DeepSurNet-NSGA II and those obtained from direct experimental methods,underscoring the algorithm’s capability to accurately approximate the Pareto-optimal frontier while significantly reducing computational demands.The methodology encompasses a detailed exploration of the algorithm’s configuration,the experimental setup,and the criteria for performance evaluation,ensuring the reproducibility of results and facilitating future advancements in the field.The findings of this study not only confirm the practical applicability and theoretical soundness of the DeepSurNet-NSGA II in navigating the intricacies of multi-objective optimization but also highlight its potential as a transformative tool in engineering and design optimization.By bridging the gap between complex optimization challenges and achievable solutions,this research contributes valuable insights into the optimization domain,offering a promising direction for future inquiries and technological innovations.
基金partially supported by the National Natural Science Foundation of China(41930644,61972439)the Collaborative Innovation Project of Anhui Province(GXXT-2022-093)the Key Program in the Youth Elite Support Plan in Universities of Anhui Province(gxyqZD2019010)。
文摘Tourism route planning is widely applied in the smart tourism field.The Pareto-optimal front obtained by the traditional multi-objective evolutionary algorithm exhibits long tails,sharp peaks and disconnected regions problems,which leads to uneven distribution and weak diversity of optimization solutions of tourism routes.Inspired by these limitations,we propose a multi-objective evolutionary algorithm for tourism route recommendation(MOTRR)with two-stage and Pareto layering based on decomposition.The method decomposes the multiobjective problem into several subproblems,and improves the distribution of solutions through a two-stage method.The crowding degree mechanism between extreme and intermediate populations is used in the two-stage method.The neighborhood is determined according to the weight of the subproblem for crossover mutation.Finally,Pareto layering is used to improve the updating efficiency and population diversity of the solution.The two-stage method is combined with the Pareto layering structure,which not only maintains the distribution and diversity of the algorithm,but also avoids the same solutions.Compared with several classical benchmark algorithms,the experimental results demonstrate competitive advantages on five test functions,hypervolume(HV)and inverted generational distance(IGD)metrics.Using the experimental results of real scenic spot datasets from two famous tourism social networking sites with vast amounts of users and large-scale online comments in Beijing,our proposed algorithm shows better distribution.It proves that the tourism routes recommended by our proposed algorithm have better distribution and diversity,so that the recommended routes can better meet the personalized needs of tourists.
