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 authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary con...The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.展开更多
In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal ...In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal Multi-Objective Optimization Problems(MMOP).Locating multiple equivalent global PSs poses a significant challenge in real-world applications,especially considering the existence of local PSs.Effectively identifying and locating both global and local PSs is a major challenge.To tackle this issue,we introduce an immune-inspired reproduction strategy designed to produce more offspring in less crowded,promising regions and regulate the number of offspring in areas that have been thoroughly explored.This approach achieves a balanced trade-off between exploration and exploitation.Furthermore,we present an interval allocation strategy that adaptively assigns fitness levels to each antibody.This strategy ensures a broader survival margin for solutions in their initial stages and progressively amplifies the differences in individual fitness values as the population matures,thus fostering better population convergence.Additionally,we incorporate a multi-population mechanism that precisely manages each subpopulation through the interval allocation strategy,ensuring the preservation of both global and local PSs.Experimental results on 21 test problems,encompassing both global and local PSs,are compared with eight state-of-the-art multimodal multi-objective optimization algorithms.The results demonstrate the effectiveness of our proposed algorithm in simultaneously identifying global Pareto sets and locally high-quality PSs.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
Multi-objective optimization is a new focus of evolutionary computation research. This paper puts forward a new algorithm, which can not only converge quickly, but also keep diversity among population efficiently, in ...Multi-objective optimization is a new focus of evolutionary computation research. This paper puts forward a new algorithm, which can not only converge quickly, but also keep diversity among population efficiently, in order to find the Pareto-optimal set. This new algorithm replaces the worst individual with a newly-created one by 'multi-parent crossover' , so that the population could converge near the true Pareto-optimal solutions in the end. At the same time, this new algorithm adopts niching and fitness-sharing techniques to keep the population in a good distribution. Numerical experiments show that the algorithm is rather effective in solving some Benchmarks. No matter whether the Pareto front of problems is convex or non-convex, continuous or discontinuous, and the problems are with constraints or not, the program turns out to do well.展开更多
Airborne landing with shipboard helicopters gradually replaces surface landing to dominate joint amphibious operations.A problem with shipboard helicopter mission planning is conducted in the context of amphibious ope...Airborne landing with shipboard helicopters gradually replaces surface landing to dominate joint amphibious operations.A problem with shipboard helicopter mission planning is conducted in the context of amphibious operations.First,the typical missions of shipborne helicopters in amphibious operations are analyzed.An Amphibious Operational Mission Planning Model for Shipboard Helicopters(AOMPMSH)is established,with the objectives of minimizing the completion time of the amphibious campaign and minimizing troop and helicopter losses,taking the available operational resources and the order of the mission sub-phases into account.Then,a simulationbased amphibious operations effectiveness assessment model is constructed to calculate the optimization objectives of AOMPMSH by simulating the campaign development with an amphibious objective area situation transfer model and simulating the engagement process with a modified Lanchester model.A reference point based multi-objective optimization algorithm is designed to solve the proposed AOMPMSH.The population iteration mechanism employs an initial population generation method and a local search method to solve the problem of vast definition space.The population ranking selection mechanism employs a population distribution based reference point generation method to solve the problem of population irregular distribution.Finally,a simulation case with the background of a battalion-scaled amphibious campaign is presented.The calculation results verify the rationality of the proposed model and the superiority of the designed algorithm and have some reference value for the operational applications of shipboard helicopters in amphibious operations.展开更多
Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they prop...Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.展开更多
The multi-objective optimization problems,especially in constrained environments such as power distribution planning,demand robust strategies for discovering effective solutions.This work presents the improved variant...The multi-objective optimization problems,especially in constrained environments such as power distribution planning,demand robust strategies for discovering effective solutions.This work presents the improved variant of the Multi-population Cooperative Constrained Multi-Objective Optimization(MCCMO)Algorithm,termed Adaptive Diversity Preservation(ADP).This enhancement is primarily focused on the improvement of constraint handling strategies,local search integration,hybrid selection approaches,and adaptive parameter control.Theimproved variant was experimented on with the RWMOP50 power distribution systemplanning benchmark.As per the findings,the improved variant outperformed the original MCCMO across the eleven performance metrics,particularly in terms of convergence speed,constraint handling efficiency,and solution diversity.The results also establish that MCCMOADP consistently delivers substantial performance gains over the baseline MCCMO,demonstrating its effectiveness across performancemetrics.The new variant also excels atmaintaining the balanced trade-off between exploration and exploitation throughout the search process,making it especially suitable for complex optimization problems in multiconstrained power systems.These enhancements make MCCMO-ADP a valuable and promising candidate for handling problems such as renewable energy scheduling,logistics planning,and power system optimization.Future work will benchmark the MCCMO-ADP against widely recognized algorithms such as NSGA-Ⅱ,NSGA-Ⅲ,and MOEA/D and will also extend its validation to large-scale real-world optimization domains to further consolidate its generalizability.展开更多
Deployable Composite Thin-Walled Structures(DCTWS)are widely used in space applications due to their ability to compactly fold and self-deploy in orbit,enabled by cutouts.Cutout design is crucial for balancing structu...Deployable Composite Thin-Walled Structures(DCTWS)are widely used in space applications due to their ability to compactly fold and self-deploy in orbit,enabled by cutouts.Cutout design is crucial for balancing structural rigidity and flexibility,ensuring material integrity during large deformations,and providing adequate load-bearing capacity and stability once deployed.Most research has focused on optimizing cutout size and shape,while topology optimization offers a broader design space.However,the anisotropic properties of woven composite laminates,complex failure criteria,and multi-performance optimization needs have limited the exploration of topology optimization in this field.This work derives the sensitivities of bending stiffness,critical buckling load,and the failure index of woven composite materials with respect to element density,and formulates both single-objective and multi-objective topology optimization models using a linear weighted aggregation approach.The developed method was integrated with the commercial finite element software ABAQUS via a Python script,allowing efficient application to cutout design in various DCTWS configurations to maximize bending stiffness and critical buckling load under material failure constraints.Optimization of a classical tubular hinge resulted in improvements of 107.7%in bending stiffness and 420.5%in critical buckling load compared to level-set topology optimization results reported in the literature,validating the effectiveness of the approach.To facilitate future research and encourage the broader adoption of topology optimization techniques in DCTWS design,the source code for this work is made publicly available via a Git Hub link:https://github.com/jinhao-ok1/Topo-for-DCTWS.git.展开更多
Task scheduling in cloud computing is a multi-objective optimization problem,often involving conflicting objectives such as minimizing execution time,reducing operational cost,and maximizing resource utilization.Howev...Task scheduling in cloud computing is a multi-objective optimization problem,often involving conflicting objectives such as minimizing execution time,reducing operational cost,and maximizing resource utilization.However,traditional approaches frequently rely on single-objective optimization methods which are insufficient for capturing the complexity of such problems.To address this limitation,we introduce MDMOSA(Multi-objective Dwarf Mongoose Optimization with Simulated Annealing),a hybrid that integrates multi-objective optimization for efficient task scheduling in Infrastructure-as-a-Service(IaaS)cloud environments.MDMOSA harmonizes the exploration capabilities of the biologically inspired Dwarf Mongoose Optimization(DMO)with the exploitation strengths of Simulated Annealing(SA),achieving a balanced search process.The algorithm aims to optimize task allocation by reducing makespan and financial cost while improving system resource utilization.We evaluate MDMOSA through extensive simulations using the real-world Google Cloud Jobs(GoCJ)dataset within the CloudSim environment.Comparative analysis against benchmarked algorithms such as SMOACO,MOTSGWO,and MFPAGWO reveals that MDMOSA consistently achieves superior performance in terms of scheduling efficiency,cost-effectiveness,and scalability.These results confirm the potential of MDMOSA as a robust and adaptable solution for resource scheduling in dynamic and heterogeneous cloud computing infrastructures.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
Visible lighting and energy-saving are dual needs of energy efficiency and occupant comfort in modern buildings.In this study,a smart window based on phase-change material VO_(2) is designed and optimized to address t...Visible lighting and energy-saving are dual needs of energy efficiency and occupant comfort in modern buildings.In this study,a smart window based on phase-change material VO_(2) is designed and optimized to address the critical challenges in building energy management.The proposed phase-adaptive radiative(PAR)coating is a multilayer nanostructure consisting of TiO/VO_(2)2/TiO/Ag_(2) and polydimethylsiloxane(PDMS).For different VO_(2) phases,visible transmittance T_(vis)>0.6 and emissivity difference in the atmospheric window Δε_(AW)=0.422 can be achieved,which means the PAR window can transfer interior heat to the outside through thermal radiation for cooling or minimize thermal emission for insulation,while ensuring the transmission of visible light for natural daylighting.Compared to normal glass,the PAR window has an average temperature drop of 14.8℃.The year-round energy-saving calculation for four different cities in China indicates that the PAR window can save 22%-32% of the annual cooling and heating energy consumption by seamlessly transitioning between two phases of VO_(2)modes.The multi-objective optimization of the phase-adaptive radiative smart window provides a potential strategy for energy saving.展开更多
Rapid urbanization in China has led to spatial antagonism between urban development and farmland protection and ecological security maintenance.Multi-objective spatial collaborative optimization is a powerful method f...Rapid urbanization in China has led to spatial antagonism between urban development and farmland protection and ecological security maintenance.Multi-objective spatial collaborative optimization is a powerful method for achieving sustainable regional development.Previous studies on multi-objective spatial optimization do not involve spatial corrections to simulation results based on the natural endowment of space resources.This study proposes an Ecological Security-Food Security-Urban Sustainable Development(ES-FS-USD)spatial optimization framework.This framework combines the non-dominated sorting genetic algorithm II(NSGA-II)and patch-generating land use simulation(PLUS)model with an ecological protection importance evaluation,comprehensive agricultural productivity evaluation,and urban sustainable development potential assessment and optimizes the territorial space in the Yangtze River Delta(YRD)region in 2035.The proposed sustainable development(SD)scenario can effectively reduce the destruction of landscape patterns of various land-use types while considering both ecological and economic benefits.The simulation results were further revised by evaluating the land-use suitability of the YRD region.According to the revised spatial pattern for the YRD in 2035,the farmland area accounts for 43.59%of the total YRD,which is 5.35%less than that in 2010.Forest,grassland,and water area account for 40.46%of the total YRD—an increase of 1.42%compared with the case in 2010.Construction land accounts for 14.72%of the total YRD—an increase of 2.77%compared with the case in 2010.The ES-FS-USD spatial optimization framework ensures that spatial optimization outcomes are aligned with the natural endowments of land resources,thereby promoting the sustainable use of land resources,improving the ability of spatial management,and providing valuable insights for decision makers.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
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
Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urge...Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urgency of demand at disaster-affected sites. Firstly, urgency cost, economic cost, and transportation distance cost were identified as key objectives. The study applied fuzzy theory integration to construct a triangular fuzzy multi-objective site selection decision model. Next, the defuzzification theory transformed the fuzzy decision model into a precise one. Subsequently, an improved Chaotic Quantum Multi-Objective Harris Hawks Optimization (CQ-MOHHO) algorithm was proposed to solve the model. The CQ-MOHHO algorithm was shown to rapidly produce high-quality Pareto front solutions and identify optimal site selection schemes for emergency resource distribution centers through case studies. This outcome verified the feasibility and efficacy of the site selection decision model and the CQ-MOHHO algorithm. To further assess CQ-MOHHO’s performance, Zitzler-Deb-Thiele (ZDT) test functions, commonly used in multi-objective optimization, were employed. Comparisons with Multi-Objective Harris Hawks Optimization (MOHHO), Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Multi-Objective Grey Wolf Optimizer (MOGWO) using Generational Distance (GD), Hypervolume (HV), and Inverted Generational Distance (IGD) metrics showed that CQ-MOHHO achieved superior global search ability, faster convergence, and higher solution quality. The CQ-MOHHO algorithm efficiently achieved a balance between multiple objectives, providing decision-makers with satisfactory solutions and a valuable reference for researching and applying emergency site selection problems.展开更多
Optimizing convolutional neural networks(CNNs)for IoT attack detection remains a critical yet challenging task due to the need to balance multiple performance metrics beyond mere accuracy.This study proposes a unified...Optimizing convolutional neural networks(CNNs)for IoT attack detection remains a critical yet challenging task due to the need to balance multiple performance metrics beyond mere accuracy.This study proposes a unified and flexible optimization framework that leverages metaheuristic algorithms to automatically optimize CNN configurations for IoT attack detection.Unlike conventional single-objective approaches,the proposed method formulates a global multi-objective fitness function that integrates accuracy,precision,recall,and model size(speed/model complexity penalty)with adjustable weights.This design enables both single-objective and weightedsum multi-objective optimization,allowing adaptive selection of optimal CNN configurations for diverse deployment requirements.Two representativemetaheuristic algorithms,GeneticAlgorithm(GA)and Particle Swarm Optimization(PSO),are employed to optimize CNNhyperparameters and structure.At each generation/iteration,the best configuration is selected as themost balanced solution across optimization objectives,i.e.,the one achieving themaximum value of the global objective function.Experimental validation on two benchmark datasets,Edge-IIoT and CIC-IoT2023,demonstrates that the proposed GA-and PSO-based models significantly enhance detection accuracy(94.8%–98.3%)and generalization compared with manually tuned CNN configurations,while maintaining compact architectures.The results confirm that the multi-objective framework effectively balances predictive performance and computational efficiency.This work establishes a generalizable and adaptive optimization strategy for deep learning-based IoT attack detection and provides a foundation for future hybrid metaheuristic extensions in broader IoT security applications.展开更多
Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when ta...Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.展开更多
With the development of renewable energy technologies such as photovoltaics and wind power,it has become a research hotspot to improve the consumption rate of new energy and reduce energy costs through algorithm impro...With the development of renewable energy technologies such as photovoltaics and wind power,it has become a research hotspot to improve the consumption rate of new energy and reduce energy costs through algorithm improvement.To reduce the operational costs of micro-grid systems and the energy abandonment rate of renewable energy,while simultaneously enhancing user satisfaction on the demand side,this paper introduces an improvedmultiobjective Grey Wolf Optimizer based on Cauchy variation.The proposed approach incorporates a Cauchy variation strategy during the optimizer’s search phase to expand its exploration range and minimize the likelihood of becoming trapped in local optima.At the same time,adoptingmultiple energy storage methods to improve the consumption rate of renewable energy.Subsequently,under different energy balance orders,themulti-objective particle swarmalgorithm,multi-objective grey wolf optimizer,and Cauchy’s variant of the improvedmulti-objective grey wolf optimizer are used for example simulation,solving the Pareto solution set of the model and comparing.The analysis of the results reveals that,compared to the original optimizer,the improved optimizer decreases the daily cost by approximately 100 yuan,and reduces the energy abandonment rate to zero.Meanwhile,it enhances user satisfaction and ensures the stable operation of the micro-grid.展开更多
The multi-objective particle swarm optimization algorithm(MOPSO)is widely used to solve multi-objective optimization problems.In the article,amulti-objective particle swarm optimization algorithmbased on decomposition...The multi-objective particle swarm optimization algorithm(MOPSO)is widely used to solve multi-objective optimization problems.In the article,amulti-objective particle swarm optimization algorithmbased on decomposition and multi-selection strategy is proposed to improve the search efficiency.First,two update strategies based on decomposition are used to update the evolving population and external archive,respectively.Second,a multiselection strategy is designed.The first strategy is for the subspace without a non-dominated solution.Among the neighbor particles,the particle with the smallest penalty-based boundary intersection value is selected as the global optimal solution and the particle far away fromthe search particle and the global optimal solution is selected as the personal optimal solution to enhance global search.The second strategy is for the subspace with a non-dominated solution.In the neighbor particles,two particles are randomly selected,one as the global optimal solution and the other as the personal optimal solution,to enhance local search.The third strategy is for Pareto optimal front(PF)discontinuity,which is identified by the cumulative number of iterations of the subspace without non-dominated solutions.In the subsequent iteration,a new probability distribution is used to select from the remaining subspaces to search.Third,an adaptive inertia weight update strategy based on the dominated degree is designed to further improve the search efficiency.Finally,the proposed algorithmis compared with fivemulti-objective particle swarm optimization algorithms and five multi-objective evolutionary algorithms on 22 test problems.The results show that the proposed algorithm has better performance.展开更多
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.
文摘The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.
基金supported in part by the Science and Technology Project of Yunnan Tobacco Industrial Company under Grant JB2022YL02in part by the Natural Science Foundation of Henan Province of China under Grant 242300421413in part by the Henan Province Science and Technology Research Projects under Grants 242102110334 and 242102110375.
文摘In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal Multi-Objective Optimization Problems(MMOP).Locating multiple equivalent global PSs poses a significant challenge in real-world applications,especially considering the existence of local PSs.Effectively identifying and locating both global and local PSs is a major challenge.To tackle this issue,we introduce an immune-inspired reproduction strategy designed to produce more offspring in less crowded,promising regions and regulate the number of offspring in areas that have been thoroughly explored.This approach achieves a balanced trade-off between exploration and exploitation.Furthermore,we present an interval allocation strategy that adaptively assigns fitness levels to each antibody.This strategy ensures a broader survival margin for solutions in their initial stages and progressively amplifies the differences in individual fitness values as the population matures,thus fostering better population convergence.Additionally,we incorporate a multi-population mechanism that precisely manages each subpopulation through the interval allocation strategy,ensuring the preservation of both global and local PSs.Experimental results on 21 test problems,encompassing both global and local PSs,are compared with eight state-of-the-art multimodal multi-objective optimization algorithms.The results demonstrate the effectiveness of our proposed algorithm in simultaneously identifying global Pareto sets and locally high-quality PSs.
基金support by the Open Project of Xiangjiang Laboratory(22XJ02003)the University Fundamental Research Fund(23-ZZCX-JDZ-28,ZK21-07)+5 种基金the National Science Fund for Outstanding Young Scholars(62122093)the National Natural Science Foundation of China(72071205)the Hunan Graduate Research Innovation Project(CX20230074)the Hunan Natural Science Foundation Regional Joint Project(2023JJ50490)the Science and Technology Project for Young and Middle-aged Talents of Hunan(2023TJZ03)the Science and Technology Innovation Program of Humnan Province(2023RC1002).
文摘Sparse large-scale multi-objective optimization problems(SLMOPs)are common in science and engineering.However,the large-scale problem represents the high dimensionality of the decision space,requiring algorithms to traverse vast expanse with limited computational resources.Furthermore,in the context of sparse,most variables in Pareto optimal solutions are zero,making it difficult for algorithms to identify non-zero variables efficiently.This paper is dedicated to addressing the challenges posed by SLMOPs.To start,we introduce innovative objective functions customized to mine maximum and minimum candidate sets.This substantial enhancement dramatically improves the efficacy of frequent pattern mining.In this way,selecting candidate sets is no longer based on the quantity of nonzero variables they contain but on a higher proportion of nonzero variables within specific dimensions.Additionally,we unveil a novel approach to association rule mining,which delves into the intricate relationships between non-zero variables.This novel methodology aids in identifying sparse distributions that can potentially expedite reductions in the objective function value.We extensively tested our algorithm across eight benchmark problems and four real-world SLMOPs.The results demonstrate that our approach achieves competitive solutions across various challenges.
基金Supported by the National Natural Science Foundation of China (6013301,60073043,70071042)
文摘Multi-objective optimization is a new focus of evolutionary computation research. This paper puts forward a new algorithm, which can not only converge quickly, but also keep diversity among population efficiently, in order to find the Pareto-optimal set. This new algorithm replaces the worst individual with a newly-created one by 'multi-parent crossover' , so that the population could converge near the true Pareto-optimal solutions in the end. At the same time, this new algorithm adopts niching and fitness-sharing techniques to keep the population in a good distribution. Numerical experiments show that the algorithm is rather effective in solving some Benchmarks. No matter whether the Pareto front of problems is convex or non-convex, continuous or discontinuous, and the problems are with constraints or not, the program turns out to do well.
文摘Airborne landing with shipboard helicopters gradually replaces surface landing to dominate joint amphibious operations.A problem with shipboard helicopter mission planning is conducted in the context of amphibious operations.First,the typical missions of shipborne helicopters in amphibious operations are analyzed.An Amphibious Operational Mission Planning Model for Shipboard Helicopters(AOMPMSH)is established,with the objectives of minimizing the completion time of the amphibious campaign and minimizing troop and helicopter losses,taking the available operational resources and the order of the mission sub-phases into account.Then,a simulationbased amphibious operations effectiveness assessment model is constructed to calculate the optimization objectives of AOMPMSH by simulating the campaign development with an amphibious objective area situation transfer model and simulating the engagement process with a modified Lanchester model.A reference point based multi-objective optimization algorithm is designed to solve the proposed AOMPMSH.The population iteration mechanism employs an initial population generation method and a local search method to solve the problem of vast definition space.The population ranking selection mechanism employs a population distribution based reference point generation method to solve the problem of population irregular distribution.Finally,a simulation case with the background of a battalion-scaled amphibious campaign is presented.The calculation results verify the rationality of the proposed model and the superiority of the designed algorithm and have some reference value for the operational applications of shipboard helicopters in amphibious operations.
基金supported in part by the National Key Research and Development Program of China(2022YFD2001200)the National Natural Science Foundation of China(62176238,61976237,62206251,62106230)+3 种基金China Postdoctoral Science Foundation(2021T140616,2021M692920)the Natural Science Foundation of Henan Province(222300420088)the Program for Science&Technology Innovation Talents in Universities of Henan Province(23HASTIT023)the Program for Science&Technology Innovation Teams in Universities of Henan Province(23IRTSTHN010).
文摘Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.
文摘The multi-objective optimization problems,especially in constrained environments such as power distribution planning,demand robust strategies for discovering effective solutions.This work presents the improved variant of the Multi-population Cooperative Constrained Multi-Objective Optimization(MCCMO)Algorithm,termed Adaptive Diversity Preservation(ADP).This enhancement is primarily focused on the improvement of constraint handling strategies,local search integration,hybrid selection approaches,and adaptive parameter control.Theimproved variant was experimented on with the RWMOP50 power distribution systemplanning benchmark.As per the findings,the improved variant outperformed the original MCCMO across the eleven performance metrics,particularly in terms of convergence speed,constraint handling efficiency,and solution diversity.The results also establish that MCCMOADP consistently delivers substantial performance gains over the baseline MCCMO,demonstrating its effectiveness across performancemetrics.The new variant also excels atmaintaining the balanced trade-off between exploration and exploitation throughout the search process,making it especially suitable for complex optimization problems in multiconstrained power systems.These enhancements make MCCMO-ADP a valuable and promising candidate for handling problems such as renewable energy scheduling,logistics planning,and power system optimization.Future work will benchmark the MCCMO-ADP against widely recognized algorithms such as NSGA-Ⅱ,NSGA-Ⅲ,and MOEA/D and will also extend its validation to large-scale real-world optimization domains to further consolidate its generalizability.
基金supported by the National Natural Science Foundation of China(No.12202295)the International(Regional)Cooperation and Exchange Projects of the National Natural Science Foundation of China(No.W2421002)+2 种基金the Sichuan Science and Technology Program(No.2025ZNSFSC0845)Zhejiang Provincial Natural Science Foundation of China(No.ZCLZ24A0201)the Fundamental Research Funds for the Provincial Universities of Zhejiang(No.GK249909299001-004)。
文摘Deployable Composite Thin-Walled Structures(DCTWS)are widely used in space applications due to their ability to compactly fold and self-deploy in orbit,enabled by cutouts.Cutout design is crucial for balancing structural rigidity and flexibility,ensuring material integrity during large deformations,and providing adequate load-bearing capacity and stability once deployed.Most research has focused on optimizing cutout size and shape,while topology optimization offers a broader design space.However,the anisotropic properties of woven composite laminates,complex failure criteria,and multi-performance optimization needs have limited the exploration of topology optimization in this field.This work derives the sensitivities of bending stiffness,critical buckling load,and the failure index of woven composite materials with respect to element density,and formulates both single-objective and multi-objective topology optimization models using a linear weighted aggregation approach.The developed method was integrated with the commercial finite element software ABAQUS via a Python script,allowing efficient application to cutout design in various DCTWS configurations to maximize bending stiffness and critical buckling load under material failure constraints.Optimization of a classical tubular hinge resulted in improvements of 107.7%in bending stiffness and 420.5%in critical buckling load compared to level-set topology optimization results reported in the literature,validating the effectiveness of the approach.To facilitate future research and encourage the broader adoption of topology optimization techniques in DCTWS design,the source code for this work is made publicly available via a Git Hub link:https://github.com/jinhao-ok1/Topo-for-DCTWS.git.
文摘Task scheduling in cloud computing is a multi-objective optimization problem,often involving conflicting objectives such as minimizing execution time,reducing operational cost,and maximizing resource utilization.However,traditional approaches frequently rely on single-objective optimization methods which are insufficient for capturing the complexity of such problems.To address this limitation,we introduce MDMOSA(Multi-objective Dwarf Mongoose Optimization with Simulated Annealing),a hybrid that integrates multi-objective optimization for efficient task scheduling in Infrastructure-as-a-Service(IaaS)cloud environments.MDMOSA harmonizes the exploration capabilities of the biologically inspired Dwarf Mongoose Optimization(DMO)with the exploitation strengths of Simulated Annealing(SA),achieving a balanced search process.The algorithm aims to optimize task allocation by reducing makespan and financial cost while improving system resource utilization.We evaluate MDMOSA through extensive simulations using the real-world Google Cloud Jobs(GoCJ)dataset within the CloudSim environment.Comparative analysis against benchmarked algorithms such as SMOACO,MOTSGWO,and MFPAGWO reveals that MDMOSA consistently achieves superior performance in terms of scheduling efficiency,cost-effectiveness,and scalability.These results confirm the potential of MDMOSA as a robust and adaptable solution for resource scheduling in dynamic and heterogeneous cloud computing infrastructures.
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.
基金supported by the Fundamental Research Funds for the Provincial Universities (Grant No.2024-KYYWF-0141)the National Natural Science Foundation of China (Grant Nos.52406076,52227813)+1 种基金the National Key Research and Development Program of China (Grant No.2022YFE0133900)the China Postdoctoral Science Foundation (Grant No.2023M740905)。
文摘Visible lighting and energy-saving are dual needs of energy efficiency and occupant comfort in modern buildings.In this study,a smart window based on phase-change material VO_(2) is designed and optimized to address the critical challenges in building energy management.The proposed phase-adaptive radiative(PAR)coating is a multilayer nanostructure consisting of TiO/VO_(2)2/TiO/Ag_(2) and polydimethylsiloxane(PDMS).For different VO_(2) phases,visible transmittance T_(vis)>0.6 and emissivity difference in the atmospheric window Δε_(AW)=0.422 can be achieved,which means the PAR window can transfer interior heat to the outside through thermal radiation for cooling or minimize thermal emission for insulation,while ensuring the transmission of visible light for natural daylighting.Compared to normal glass,the PAR window has an average temperature drop of 14.8℃.The year-round energy-saving calculation for four different cities in China indicates that the PAR window can save 22%-32% of the annual cooling and heating energy consumption by seamlessly transitioning between two phases of VO_(2)modes.The multi-objective optimization of the phase-adaptive radiative smart window provides a potential strategy for energy saving.
基金National Natural Science Foundation of China,No.42301470,No.52270185,No.42171389Capacity Building Program of Local Colleges and Universities in Shanghai,No.21010503300。
文摘Rapid urbanization in China has led to spatial antagonism between urban development and farmland protection and ecological security maintenance.Multi-objective spatial collaborative optimization is a powerful method for achieving sustainable regional development.Previous studies on multi-objective spatial optimization do not involve spatial corrections to simulation results based on the natural endowment of space resources.This study proposes an Ecological Security-Food Security-Urban Sustainable Development(ES-FS-USD)spatial optimization framework.This framework combines the non-dominated sorting genetic algorithm II(NSGA-II)and patch-generating land use simulation(PLUS)model with an ecological protection importance evaluation,comprehensive agricultural productivity evaluation,and urban sustainable development potential assessment and optimizes the territorial space in the Yangtze River Delta(YRD)region in 2035.The proposed sustainable development(SD)scenario can effectively reduce the destruction of landscape patterns of various land-use types while considering both ecological and economic benefits.The simulation results were further revised by evaluating the land-use suitability of the YRD region.According to the revised spatial pattern for the YRD in 2035,the farmland area accounts for 43.59%of the total YRD,which is 5.35%less than that in 2010.Forest,grassland,and water area account for 40.46%of the total YRD—an increase of 1.42%compared with the case in 2010.Construction land accounts for 14.72%of the total YRD—an increase of 2.77%compared with the case in 2010.The ES-FS-USD spatial optimization framework ensures that spatial optimization outcomes are aligned with the natural endowments of land resources,thereby promoting the sustainable use of land resources,improving the ability of spatial management,and providing valuable insights for decision makers.
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.
文摘Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urgency of demand at disaster-affected sites. Firstly, urgency cost, economic cost, and transportation distance cost were identified as key objectives. The study applied fuzzy theory integration to construct a triangular fuzzy multi-objective site selection decision model. Next, the defuzzification theory transformed the fuzzy decision model into a precise one. Subsequently, an improved Chaotic Quantum Multi-Objective Harris Hawks Optimization (CQ-MOHHO) algorithm was proposed to solve the model. The CQ-MOHHO algorithm was shown to rapidly produce high-quality Pareto front solutions and identify optimal site selection schemes for emergency resource distribution centers through case studies. This outcome verified the feasibility and efficacy of the site selection decision model and the CQ-MOHHO algorithm. To further assess CQ-MOHHO’s performance, Zitzler-Deb-Thiele (ZDT) test functions, commonly used in multi-objective optimization, were employed. Comparisons with Multi-Objective Harris Hawks Optimization (MOHHO), Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Multi-Objective Grey Wolf Optimizer (MOGWO) using Generational Distance (GD), Hypervolume (HV), and Inverted Generational Distance (IGD) metrics showed that CQ-MOHHO achieved superior global search ability, faster convergence, and higher solution quality. The CQ-MOHHO algorithm efficiently achieved a balance between multiple objectives, providing decision-makers with satisfactory solutions and a valuable reference for researching and applying emergency site selection problems.
文摘Optimizing convolutional neural networks(CNNs)for IoT attack detection remains a critical yet challenging task due to the need to balance multiple performance metrics beyond mere accuracy.This study proposes a unified and flexible optimization framework that leverages metaheuristic algorithms to automatically optimize CNN configurations for IoT attack detection.Unlike conventional single-objective approaches,the proposed method formulates a global multi-objective fitness function that integrates accuracy,precision,recall,and model size(speed/model complexity penalty)with adjustable weights.This design enables both single-objective and weightedsum multi-objective optimization,allowing adaptive selection of optimal CNN configurations for diverse deployment requirements.Two representativemetaheuristic algorithms,GeneticAlgorithm(GA)and Particle Swarm Optimization(PSO),are employed to optimize CNNhyperparameters and structure.At each generation/iteration,the best configuration is selected as themost balanced solution across optimization objectives,i.e.,the one achieving themaximum value of the global objective function.Experimental validation on two benchmark datasets,Edge-IIoT and CIC-IoT2023,demonstrates that the proposed GA-and PSO-based models significantly enhance detection accuracy(94.8%–98.3%)and generalization compared with manually tuned CNN configurations,while maintaining compact architectures.The results confirm that the multi-objective framework effectively balances predictive performance and computational efficiency.This work establishes a generalizable and adaptive optimization strategy for deep learning-based IoT attack detection and provides a foundation for future hybrid metaheuristic extensions in broader IoT security applications.
基金funded by National Natural Science Foundation of China(Nos.12402142,11832013 and 11572134)Natural Science Foundation of Hubei Province(No.2024AFB235)+1 种基金Hubei Provincial Department of Education Science and Technology Research Project(No.Q20221714)the Opening Foundation of Hubei Key Laboratory of Digital Textile Equipment(Nos.DTL2023019 and DTL2022012).
文摘Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.
基金supported by the Open Fund of Guangxi Key Laboratory of Building New Energy and Energy Conservation(Project Number:Guike Energy 17-J-21-3).
文摘With the development of renewable energy technologies such as photovoltaics and wind power,it has become a research hotspot to improve the consumption rate of new energy and reduce energy costs through algorithm improvement.To reduce the operational costs of micro-grid systems and the energy abandonment rate of renewable energy,while simultaneously enhancing user satisfaction on the demand side,this paper introduces an improvedmultiobjective Grey Wolf Optimizer based on Cauchy variation.The proposed approach incorporates a Cauchy variation strategy during the optimizer’s search phase to expand its exploration range and minimize the likelihood of becoming trapped in local optima.At the same time,adoptingmultiple energy storage methods to improve the consumption rate of renewable energy.Subsequently,under different energy balance orders,themulti-objective particle swarmalgorithm,multi-objective grey wolf optimizer,and Cauchy’s variant of the improvedmulti-objective grey wolf optimizer are used for example simulation,solving the Pareto solution set of the model and comparing.The analysis of the results reveals that,compared to the original optimizer,the improved optimizer decreases the daily cost by approximately 100 yuan,and reduces the energy abandonment rate to zero.Meanwhile,it enhances user satisfaction and ensures the stable operation of the micro-grid.
基金supported by National Natural Science Foundations of China(nos.12271326,62102304,61806120,61502290,61672334,61673251)China Postdoctoral Science Foundation(no.2015M582606)+2 种基金Industrial Research Project of Science and Technology in Shaanxi Province(nos.2015GY016,2017JQ6063)Fundamental Research Fund for the Central Universities(no.GK202003071)Natural Science Basic Research Plan in Shaanxi Province of China(no.2022JM-354).
文摘The multi-objective particle swarm optimization algorithm(MOPSO)is widely used to solve multi-objective optimization problems.In the article,amulti-objective particle swarm optimization algorithmbased on decomposition and multi-selection strategy is proposed to improve the search efficiency.First,two update strategies based on decomposition are used to update the evolving population and external archive,respectively.Second,a multiselection strategy is designed.The first strategy is for the subspace without a non-dominated solution.Among the neighbor particles,the particle with the smallest penalty-based boundary intersection value is selected as the global optimal solution and the particle far away fromthe search particle and the global optimal solution is selected as the personal optimal solution to enhance global search.The second strategy is for the subspace with a non-dominated solution.In the neighbor particles,two particles are randomly selected,one as the global optimal solution and the other as the personal optimal solution,to enhance local search.The third strategy is for Pareto optimal front(PF)discontinuity,which is identified by the cumulative number of iterations of the subspace without non-dominated solutions.In the subsequent iteration,a new probability distribution is used to select from the remaining subspaces to search.Third,an adaptive inertia weight update strategy based on the dominated degree is designed to further improve the search efficiency.Finally,the proposed algorithmis compared with fivemulti-objective particle swarm optimization algorithms and five multi-objective evolutionary algorithms on 22 test problems.The results show that the proposed algorithm has better performance.
