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
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
Aimed to address the multi-objective scheduling problem in printing workshops,a hybrid optimization algorithm combining Particle Swarm Optimization(PSO),Genetic Algorithm(GA),and Simulated Annealing(SA)was by proposed...Aimed to address the multi-objective scheduling problem in printing workshops,a hybrid optimization algorithm combining Particle Swarm Optimization(PSO),Genetic Algorithm(GA),and Simulated Annealing(SA)was by proposed which called PGA-PSO-SA(Parallel Genetic Algorithm-Particle Swarm Optimization-Simulated Annealing).Firstly,PSO algorithm was used for global search to quickly find the initial solution.Then,GA optimization selection and crossover operations were used to enhance population diversity.Then,SA algorithm was employed for local search to further improve the solution quality.Experimental results showed that this method achieves better results in terms of job completion time,energy consumption,and machine load distribution.Compared to single algorithms,PGA-PSO-SA hybrid algorithm can more effectively find the global optimal solution,enhancing the overall performance of the scheduling scheme.The research results provides new ideas and methods for scheduling optimization in printing workshops.展开更多
A new hang-off system has been proposed to improve the security of risers in hang-off modes during typhoons.However,efficient anti-typhoon evacuation strategies have not been investigated.Optimiza-tion model and metho...A new hang-off system has been proposed to improve the security of risers in hang-off modes during typhoons.However,efficient anti-typhoon evacuation strategies have not been investigated.Optimiza-tion model and method for the anti-typhoon evacuation strategies should be researched.Therefore,multi-objective functions are proposed based on operation time,evacuation speed stability,and steering stability.An evacuation path model and a dynamic model of risers with the new hang-off system are developed for design variables and constraints.A multi-objective optimization model with high-dimensional variables and complex constraints is established.Finally,a three-stage optimization method based on genetic algorithm,least square method,and the penalty function method is proposed to solve the multi-objective optimization model.Optimization results show that the operation time can be reduced through operation parameter optimization,especially evacuation heading optimization.The optimal anti-typhoon strategy is evacuation with all risers suspended along a variable path when the direction angle is large,while evacuation with all risers suspended along a straight path at another di-rection angle.Besides,the influencing factors on anti-typhoon evacuation strategies indicate that the proposed optimization model and method have strong applicability to working conditions and remarkable optimization effects.展开更多
This paper presents an improved virtual coupling train set(VCTS)operation control framework to deal with the lack of opti-mization of speed curves in the traditional techniques.The framework takes into account the tem...This paper presents an improved virtual coupling train set(VCTS)operation control framework to deal with the lack of opti-mization of speed curves in the traditional techniques.The framework takes into account the temporary speed limit on the railway line and the communication delay between trains,and it uses a VCTS consisting of three trains as an experimental object.It creates the virtual coupling train tracking and control process by improving the driving strategy of the leader train and using the leader-follower model.The follower train uses the improved speed curve of the leader train as its speed refer-ence curve through knowledge migration,and this completes the multi-objective optimization of the driving strategy for the VCTS.The experimental results confirm that the deep reinforcement learning algorithm effectively achieves the optimization goal of the train driving strategy.They also reveal that the intrinsic curiosity module prioritized experience replay dueling double deep Q-network(ICM-PER-D3QN)algorithm outperforms the deep Q-network(DQN)algorithm in optimizing the driving strategy of the leader train.The ICM-PER-D3QN algorithm enhances the leader train driving strategy by an average of 57%when compared to the DQN algorithm.Furthermore,the particle swarm optimization(PSO)-based model predictive control(MPC)algorithm has also demonstrated tracking accuracy and further improved safety during VCTS operation,with an average increase of 37.7%in tracking accuracy compared to the traditional MPC algorithm.展开更多
To achieve low-carbon regulation of electric vehicle(EV)charging loads under the“dual carbon”goals,this paper proposes a coordinated scheduling strategy that integrates dynamic carbon factor prediction and multiobje...To achieve low-carbon regulation of electric vehicle(EV)charging loads under the“dual carbon”goals,this paper proposes a coordinated scheduling strategy that integrates dynamic carbon factor prediction and multiobjective optimization.First,a dual-convolution enhanced improved Crossformer prediction model is constructed,which employs parallel 1×1 global and 3×3 local convolutionmodules(Integrated Convolution Block,ICB)formultiscale feature extraction,combinedwith anAdaptive Spectral Block(ASB)to enhance time-series fluctuationmodeling.Based on high-precision predictions,a carbon-electricity cost joint optimization model is further designed to balance economic,environmental,and grid-friendly objectives.The model’s superiority was validated through a case study using real-world data from a renewable-heavy grid.Simulation results show that the proposed multi-objective strategy demonstrated a superior balance compared to baseline and benchmark models,achieving a 15.8%reduction in carbon emissions and a 5.2%reduction in economic costs,while still providing a substantial 22.2%reduction in the peak-valley difference.Its balanced performance significantly outperformed both a single-objective strategy and a state-of-the-art Model Predictive Control(MPC)benchmark,highlighting the advantage of a global optimization approach.This study provides theoretical and technical pathways for dynamic carbon factor-driven EV charging optimization.展开更多
The evolutionary strategy with a dynamic weighting schedule is proposed to find all the compromised solutions of the multi-objective integrated structure and control optimization problem, where the optimal system perf...The evolutionary strategy with a dynamic weighting schedule is proposed to find all the compromised solutions of the multi-objective integrated structure and control optimization problem, where the optimal system performance and control cost are defined by H2 or H∞ norms. During this optimization process, the weights are varying with the increasing generation instead of fixed values. The proposed strategy together with the linear matrix inequality （LMI） or the Riccati controller design method can find a series of uniformly distributed nondominated solutions in a single run. Therefore, this method can greatly reduce the computation intensity of the integrated optimization problem compared with the weight-based single objective genetic algorithm. Active automotive suspension is adopted as an example to illustrate the effectiveness of the proposed method.展开更多
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
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 lack of systematic and scientific top-level arrangement in the field of civil aircraft flight test leads to the problems of long duration and high cost.Based on the flight test activity,mathematical models of flig...The lack of systematic and scientific top-level arrangement in the field of civil aircraft flight test leads to the problems of long duration and high cost.Based on the flight test activity,mathematical models of flight test duration and cost are established to set up the framework of flight test process.The top-level arrangement for flight test is optimized by multi-objective algorithm to reduce the duration and cost of flight test.In order to verify the necessity and validity of the mathematical models and the optimization algorithm of top-level arrangement,real flight test data is used to make an example calculation.Results show that the multi-objective optimization results of the top-level flight arrangement are better than the initial arrangement data,which can shorten the duration,reduce the cost,and improve the efficiency of flight test.展开更多
Cloud computing has become an essential technology for the management and processing of large datasets,offering scalability,high availability,and fault tolerance.However,optimizing data replication across multiple dat...Cloud computing has become an essential technology for the management and processing of large datasets,offering scalability,high availability,and fault tolerance.However,optimizing data replication across multiple data centers poses a significant challenge,especially when balancing opposing goals such as latency,storage costs,energy consumption,and network efficiency.This study introduces a novel Dynamic Optimization Algorithm called Dynamic Multi-Objective Gannet Optimization(DMGO),designed to enhance data replication efficiency in cloud environments.Unlike traditional static replication systems,DMGO adapts dynamically to variations in network conditions,system demand,and resource availability.The approach utilizes multi-objective optimization approaches to efficiently balance data access latency,storage efficiency,and operational costs.DMGO consistently evaluates data center performance and adjusts replication algorithms in real time to guarantee optimal system efficiency.Experimental evaluations conducted in a simulated cloud environment demonstrate that DMGO significantly outperforms conventional static algorithms,achieving faster data access,lower storage overhead,reduced energy consumption,and improved scalability.The proposed methodology offers a robust and adaptable solution for modern cloud systems,ensuring efficient resource consumption while maintaining high performance.展开更多
The intermittency and volatility of wind and photovoltaic power generation exacerbate issues such as wind and solar curtailment,hindering the efficient utilization of renewable energy and the low-carbon development of...The intermittency and volatility of wind and photovoltaic power generation exacerbate issues such as wind and solar curtailment,hindering the efficient utilization of renewable energy and the low-carbon development of energy systems.To enhance the consumption capacity of green power,the green power system consumption optimization scheduling model(GPS-COSM)is proposed,which comprehensively integrates green power system,electric boiler,combined heat and power unit,thermal energy storage,and electrical energy storage.The optimization objectives are to minimize operating cost,minimize carbon emission,and maximize the consumption of wind and solar curtailment.The multi-objective particle swarm optimization algorithm is employed to solve the model,and a fuzzy membership function is introduced to evaluate the satisfaction level of the Pareto optimal solution set,thereby selecting the optimal compromise solution to achieve a dynamic balance among economic efficiency,environmental friendliness,and energy utilization efficiency.Three typical operating modes are designed for comparative analysis.The results demonstrate that the mode involving the coordinated operation of electric boiler,thermal energy storage,and electrical energy storage performs the best in terms of economic efficiency,environmental friendliness,and renewable energy utilization efficiency,achieving the wind and solar curtailment consumption rate of 99.58%.The application of electric boiler significantly enhances the direct accommodation capacity of the green power system.Thermal energy storage optimizes intertemporal regulation,while electrical energy storage strengthens the system’s dynamic regulation capability.The coordinated optimization of multiple devices significantly reduces reliance on fossil fuels.展开更多
Impinging jet arrays are extensively used in numerous industrial operations,including the cooling of electronics,turbine blades,and other high-heat flux systems because of their superior heat transfer capabilities.Opt...Impinging jet arrays are extensively used in numerous industrial operations,including the cooling of electronics,turbine blades,and other high-heat flux systems because of their superior heat transfer capabilities.Optimizing the design and operating parameters of such systems is essential to enhance cooling efficiency and achieve uniform pressure distribution,which can lead to improved system performance and energy savings.This paper presents two multi-objective optimization methodologies for a turbulent air jet impingement cooling system.The governing equations are resolved employing the commercial computational fluid dynamics(CFD)software ANSYS Fluent v17.The study focuses on four controlling parameters:Reynolds number(Re),swirl number(S),jet-to-jet separation distance(Z/D),and impingement height(H/D).The effects of these parameters on heat transfer and impingement pressure distribution are investigated.Non-dominated Sorting Genetic Algorithm(NSGA-II)and Weighted Sum Method(WSM)are employed to optimize the controlling parameters for maximum cooling performance.The aim is to identify optimal design parameters and system configurations that enhance heat transfer efficiency while achieving a uniform impingement pressure distribution.These findings have practical implications for applications requiring efficient cooling.The optimized design achieved a 12.28%increase in convective heat transfer efficiency with a local Nusselt number of 113.05 compared to 100.69 in the reference design.Enhanced convective cooling and heat flux were observed in the optimized configuration,particularly in areas of direct jet impingement.Additionally,the optimized design maintained lower wall temperatures,demonstrating more effective thermal dissipation.展开更多
This work addresses the cut order planning(COP)problem for multi-color garment production,which is the first step in the clothing industry.First,a multi-objective optimization model of multicolor COP(MCOP)is establish...This work addresses the cut order planning(COP)problem for multi-color garment production,which is the first step in the clothing industry.First,a multi-objective optimization model of multicolor COP(MCOP)is established with production error and production cost as optimization objectives,combined with constraints such as the number of equipment and the number of layers.Second,a decoupled multi-objective optimization algorithm(DMOA)is proposed based on the linear programming decoupling strategy and non-dominated sorting in genetic algorithmsⅡ(NSGAII).The size-combination matrix and the fabric-layer matrix are decoupled to improve the accuracy of the algorithm.Meanwhile,an improved NSGAII algorithm is designed to obtain the optimal Pareto solution to the MCOP problem,thereby constructing a practical intelligent production optimization algorithm.Finally,the effectiveness and superiority of the proposed DMOA are verified through practical cases and comparative experiments,which can effectively optimize the production process for garment enterprises.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
In recent years,decomposition-based evolutionary algorithms have become popular algorithms for solving multi-objective problems in real-life scenarios.In these algorithms,the reference vectors of the Penalty-Based bou...In recent years,decomposition-based evolutionary algorithms have become popular algorithms for solving multi-objective problems in real-life scenarios.In these algorithms,the reference vectors of the Penalty-Based boundary intersection(PBI)are distributed parallelly while those based on the normal boundary intersection(NBI)are distributed radially in a conical shape in the objective space.To improve the problem-solving effectiveness of multi-objective optimization algorithms in engineering applications,this paper addresses the improvement of the Collaborative Decomposition(CoD)method,a multi-objective decomposition technique that integrates PBI and NBI,and combines it with the Elephant Clan Optimization Algorithm,introducing the Collaborative Decomposition Multi-objective Improved Elephant Clan Optimization Algorithm(CoDMOIECO).Specifically,a novel subpopulation construction method with adaptive changes following the number of iterations and a novel individual merit ranking based onNBI and angle are proposed.,enabling the creation of subpopulations closely linked to weight vectors and the identification of diverse individuals within them.Additionally,new update strategies for the clan leader,male elephants,and juvenile elephants are introduced to boost individual exploitation capabilities and further enhance the algorithm’s convergence.Finally,a new CoD-based environmental selection method is proposed,introducing adaptive dynamically adjusted angle coefficients and individual angles on corresponding weight vectors,significantly improving both the convergence and distribution of the algorithm.Experimental comparisons on the ZDT,DTLZ,and WFG function sets with four benchmark multi-objective algorithms—MOEA/D,CAMOEA,VaEA,and MOEA/D-UR—demonstrate that CoDMOIECO achieves superior performance in both convergence and distribution.展开更多
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 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.
文摘Aimed to address the multi-objective scheduling problem in printing workshops,a hybrid optimization algorithm combining Particle Swarm Optimization(PSO),Genetic Algorithm(GA),and Simulated Annealing(SA)was by proposed which called PGA-PSO-SA(Parallel Genetic Algorithm-Particle Swarm Optimization-Simulated Annealing).Firstly,PSO algorithm was used for global search to quickly find the initial solution.Then,GA optimization selection and crossover operations were used to enhance population diversity.Then,SA algorithm was employed for local search to further improve the solution quality.Experimental results showed that this method achieves better results in terms of job completion time,energy consumption,and machine load distribution.Compared to single algorithms,PGA-PSO-SA hybrid algorithm can more effectively find the global optimal solution,enhancing the overall performance of the scheduling scheme.The research results provides new ideas and methods for scheduling optimization in printing workshops.
基金supported by the National Natural Science Foundation of China(Grant No:52271300,52071337)National Key Research and Development Program of China(2022YFC2806501)+1 种基金High-tech Ship Research Projects Sponsored by MIIT(CBG2N21-4-25)Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT14R58).
文摘A new hang-off system has been proposed to improve the security of risers in hang-off modes during typhoons.However,efficient anti-typhoon evacuation strategies have not been investigated.Optimiza-tion model and method for the anti-typhoon evacuation strategies should be researched.Therefore,multi-objective functions are proposed based on operation time,evacuation speed stability,and steering stability.An evacuation path model and a dynamic model of risers with the new hang-off system are developed for design variables and constraints.A multi-objective optimization model with high-dimensional variables and complex constraints is established.Finally,a three-stage optimization method based on genetic algorithm,least square method,and the penalty function method is proposed to solve the multi-objective optimization model.Optimization results show that the operation time can be reduced through operation parameter optimization,especially evacuation heading optimization.The optimal anti-typhoon strategy is evacuation with all risers suspended along a variable path when the direction angle is large,while evacuation with all risers suspended along a straight path at another di-rection angle.Besides,the influencing factors on anti-typhoon evacuation strategies indicate that the proposed optimization model and method have strong applicability to working conditions and remarkable optimization effects.
基金supported by the National Natural Science Foundation of China under Grant 52162050.
文摘This paper presents an improved virtual coupling train set(VCTS)operation control framework to deal with the lack of opti-mization of speed curves in the traditional techniques.The framework takes into account the temporary speed limit on the railway line and the communication delay between trains,and it uses a VCTS consisting of three trains as an experimental object.It creates the virtual coupling train tracking and control process by improving the driving strategy of the leader train and using the leader-follower model.The follower train uses the improved speed curve of the leader train as its speed refer-ence curve through knowledge migration,and this completes the multi-objective optimization of the driving strategy for the VCTS.The experimental results confirm that the deep reinforcement learning algorithm effectively achieves the optimization goal of the train driving strategy.They also reveal that the intrinsic curiosity module prioritized experience replay dueling double deep Q-network(ICM-PER-D3QN)algorithm outperforms the deep Q-network(DQN)algorithm in optimizing the driving strategy of the leader train.The ICM-PER-D3QN algorithm enhances the leader train driving strategy by an average of 57%when compared to the DQN algorithm.Furthermore,the particle swarm optimization(PSO)-based model predictive control(MPC)algorithm has also demonstrated tracking accuracy and further improved safety during VCTS operation,with an average increase of 37.7%in tracking accuracy compared to the traditional MPC algorithm.
基金Supported by State Grid Corporation of China Science and Technology Project:Research on Key Technologies for Intelligent Carbon Metrology in Vehicle-to-Grid Interaction(Project Number:B3018524000Q).
文摘To achieve low-carbon regulation of electric vehicle(EV)charging loads under the“dual carbon”goals,this paper proposes a coordinated scheduling strategy that integrates dynamic carbon factor prediction and multiobjective optimization.First,a dual-convolution enhanced improved Crossformer prediction model is constructed,which employs parallel 1×1 global and 3×3 local convolutionmodules(Integrated Convolution Block,ICB)formultiscale feature extraction,combinedwith anAdaptive Spectral Block(ASB)to enhance time-series fluctuationmodeling.Based on high-precision predictions,a carbon-electricity cost joint optimization model is further designed to balance economic,environmental,and grid-friendly objectives.The model’s superiority was validated through a case study using real-world data from a renewable-heavy grid.Simulation results show that the proposed multi-objective strategy demonstrated a superior balance compared to baseline and benchmark models,achieving a 15.8%reduction in carbon emissions and a 5.2%reduction in economic costs,while still providing a substantial 22.2%reduction in the peak-valley difference.Its balanced performance significantly outperformed both a single-objective strategy and a state-of-the-art Model Predictive Control(MPC)benchmark,highlighting the advantage of a global optimization approach.This study provides theoretical and technical pathways for dynamic carbon factor-driven EV charging optimization.
文摘The evolutionary strategy with a dynamic weighting schedule is proposed to find all the compromised solutions of the multi-objective integrated structure and control optimization problem, where the optimal system performance and control cost are defined by H2 or H∞ norms. During this optimization process, the weights are varying with the increasing generation instead of fixed values. The proposed strategy together with the linear matrix inequality （LMI） or the Riccati controller design method can find a series of uniformly distributed nondominated solutions in a single run. Therefore, this method can greatly reduce the computation intensity of the integrated optimization problem compared with the weight-based single objective genetic algorithm. Active automotive suspension is adopted as an example to illustrate the effectiveness of the proposed method.
基金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 the National Natural Science Foundation of China(62073267,61903305)the Fundamental Research Funds for the Central Universities(HXGJXM202214).
文摘The lack of systematic and scientific top-level arrangement in the field of civil aircraft flight test leads to the problems of long duration and high cost.Based on the flight test activity,mathematical models of flight test duration and cost are established to set up the framework of flight test process.The top-level arrangement for flight test is optimized by multi-objective algorithm to reduce the duration and cost of flight test.In order to verify the necessity and validity of the mathematical models and the optimization algorithm of top-level arrangement,real flight test data is used to make an example calculation.Results show that the multi-objective optimization results of the top-level flight arrangement are better than the initial arrangement data,which can shorten the duration,reduce the cost,and improve the efficiency of flight test.
文摘Cloud computing has become an essential technology for the management and processing of large datasets,offering scalability,high availability,and fault tolerance.However,optimizing data replication across multiple data centers poses a significant challenge,especially when balancing opposing goals such as latency,storage costs,energy consumption,and network efficiency.This study introduces a novel Dynamic Optimization Algorithm called Dynamic Multi-Objective Gannet Optimization(DMGO),designed to enhance data replication efficiency in cloud environments.Unlike traditional static replication systems,DMGO adapts dynamically to variations in network conditions,system demand,and resource availability.The approach utilizes multi-objective optimization approaches to efficiently balance data access latency,storage efficiency,and operational costs.DMGO consistently evaluates data center performance and adjusts replication algorithms in real time to guarantee optimal system efficiency.Experimental evaluations conducted in a simulated cloud environment demonstrate that DMGO significantly outperforms conventional static algorithms,achieving faster data access,lower storage overhead,reduced energy consumption,and improved scalability.The proposed methodology offers a robust and adaptable solution for modern cloud systems,ensuring efficient resource consumption while maintaining high performance.
基金funded by the National Key Research and Development Program of China(2024YFE0106800)Natural Science Foundation of Shandong Province(ZR2021ME199).
文摘The intermittency and volatility of wind and photovoltaic power generation exacerbate issues such as wind and solar curtailment,hindering the efficient utilization of renewable energy and the low-carbon development of energy systems.To enhance the consumption capacity of green power,the green power system consumption optimization scheduling model(GPS-COSM)is proposed,which comprehensively integrates green power system,electric boiler,combined heat and power unit,thermal energy storage,and electrical energy storage.The optimization objectives are to minimize operating cost,minimize carbon emission,and maximize the consumption of wind and solar curtailment.The multi-objective particle swarm optimization algorithm is employed to solve the model,and a fuzzy membership function is introduced to evaluate the satisfaction level of the Pareto optimal solution set,thereby selecting the optimal compromise solution to achieve a dynamic balance among economic efficiency,environmental friendliness,and energy utilization efficiency.Three typical operating modes are designed for comparative analysis.The results demonstrate that the mode involving the coordinated operation of electric boiler,thermal energy storage,and electrical energy storage performs the best in terms of economic efficiency,environmental friendliness,and renewable energy utilization efficiency,achieving the wind and solar curtailment consumption rate of 99.58%.The application of electric boiler significantly enhances the direct accommodation capacity of the green power system.Thermal energy storage optimizes intertemporal regulation,while electrical energy storage strengthens the system’s dynamic regulation capability.The coordinated optimization of multiple devices significantly reduces reliance on fossil fuels.
文摘Impinging jet arrays are extensively used in numerous industrial operations,including the cooling of electronics,turbine blades,and other high-heat flux systems because of their superior heat transfer capabilities.Optimizing the design and operating parameters of such systems is essential to enhance cooling efficiency and achieve uniform pressure distribution,which can lead to improved system performance and energy savings.This paper presents two multi-objective optimization methodologies for a turbulent air jet impingement cooling system.The governing equations are resolved employing the commercial computational fluid dynamics(CFD)software ANSYS Fluent v17.The study focuses on four controlling parameters:Reynolds number(Re),swirl number(S),jet-to-jet separation distance(Z/D),and impingement height(H/D).The effects of these parameters on heat transfer and impingement pressure distribution are investigated.Non-dominated Sorting Genetic Algorithm(NSGA-II)and Weighted Sum Method(WSM)are employed to optimize the controlling parameters for maximum cooling performance.The aim is to identify optimal design parameters and system configurations that enhance heat transfer efficiency while achieving a uniform impingement pressure distribution.These findings have practical implications for applications requiring efficient cooling.The optimized design achieved a 12.28%increase in convective heat transfer efficiency with a local Nusselt number of 113.05 compared to 100.69 in the reference design.Enhanced convective cooling and heat flux were observed in the optimized configuration,particularly in areas of direct jet impingement.Additionally,the optimized design maintained lower wall temperatures,demonstrating more effective thermal dissipation.
基金Supported by the Natural Science Foundation of Zhejiang Province(No.LQ22F030015).
文摘This work addresses the cut order planning(COP)problem for multi-color garment production,which is the first step in the clothing industry.First,a multi-objective optimization model of multicolor COP(MCOP)is established with production error and production cost as optimization objectives,combined with constraints such as the number of equipment and the number of layers.Second,a decoupled multi-objective optimization algorithm(DMOA)is proposed based on the linear programming decoupling strategy and non-dominated sorting in genetic algorithmsⅡ(NSGAII).The size-combination matrix and the fabric-layer matrix are decoupled to improve the accuracy of the algorithm.Meanwhile,an improved NSGAII algorithm is designed to obtain the optimal Pareto solution to the MCOP problem,thereby constructing a practical intelligent production optimization algorithm.Finally,the effectiveness and superiority of the proposed DMOA are verified through practical cases and comparative experiments,which can effectively optimize the production process for garment enterprises.
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In recent years,decomposition-based evolutionary algorithms have become popular algorithms for solving multi-objective problems in real-life scenarios.In these algorithms,the reference vectors of the Penalty-Based boundary intersection(PBI)are distributed parallelly while those based on the normal boundary intersection(NBI)are distributed radially in a conical shape in the objective space.To improve the problem-solving effectiveness of multi-objective optimization algorithms in engineering applications,this paper addresses the improvement of the Collaborative Decomposition(CoD)method,a multi-objective decomposition technique that integrates PBI and NBI,and combines it with the Elephant Clan Optimization Algorithm,introducing the Collaborative Decomposition Multi-objective Improved Elephant Clan Optimization Algorithm(CoDMOIECO).Specifically,a novel subpopulation construction method with adaptive changes following the number of iterations and a novel individual merit ranking based onNBI and angle are proposed.,enabling the creation of subpopulations closely linked to weight vectors and the identification of diverse individuals within them.Additionally,new update strategies for the clan leader,male elephants,and juvenile elephants are introduced to boost individual exploitation capabilities and further enhance the algorithm’s convergence.Finally,a new CoD-based environmental selection method is proposed,introducing adaptive dynamically adjusted angle coefficients and individual angles on corresponding weight vectors,significantly improving both the convergence and distribution of the algorithm.Experimental comparisons on the ZDT,DTLZ,and WFG function sets with four benchmark multi-objective algorithms—MOEA/D,CAMOEA,VaEA,and MOEA/D-UR—demonstrate that CoDMOIECO achieves superior performance in both convergence and distribution.
