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
Solving constrained multi-objective optimization problems(CMOPs)is a challenging task due to the presence of multiple conflicting objectives and intricate constraints.In order to better address CMOPs and achieve a bal...Solving constrained multi-objective optimization problems(CMOPs)is a challenging task due to the presence of multiple conflicting objectives and intricate constraints.In order to better address CMOPs and achieve a balance between objectives and constraints,existing constrained multi-objective evolutionary algorithms(CMOEAs)predominantly focus on devising various strategies by leveraging the relationships between objectives and constraints,and the designed strategies usually are effective for the problems with simple constraints.However,these methods most ignore the relationship between decision variables and constraints.In fact,the essence of optimization is to find appropriate decision variables to meet various complex constraints.Therefore,it is hoped that the problem can be analyzed from the perspective of decision variables,so as to obtain more excellent results.Based on the above motivation,this paper proposes a decision variables classification approach,according to the relationship between decision variables and constraints,variables are divided into constraint-related(CR)variables and constraintindependent(CI)variables.Consequently,by optimizing these two types of variables independently,the population can sustain a favorable balance between feasibility and diversity.Furthermore,specific offspring generation strategies are proposed for the two categories of decision variables in order to achieve rapid convergence while maintaining population diversity.Experimental results on 31 test problems as well as 20 real-world problems demonstrate that the proposed algorithm is competitive compared to some state-of-the-art constrained multi-objective optimization algorithms.展开更多
Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-obj...Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-objective evolutionary algorithms(CMOEAs) have been developed. However, most of them tend to converge into local areas due to the loss of diversity. Evolutionary multitasking(EMT) is new model of solving complex optimization problems, through the knowledge transfer between the source task and other related tasks. Inspired by EMT, this paper develops a new EMT-based CMOEA to solve CMOPs, in which the main task, a global auxiliary task, and a local auxiliary task are created and optimized by one specific population respectively. The main task focuses on finding the feasible Pareto front(PF), and global and local auxiliary tasks are used to respectively enhance global and local diversity. Moreover, the global auxiliary task is used to implement the global search by ignoring constraints, so as to help the population of the main task pass through infeasible obstacles. The local auxiliary task is used to provide local diversity around the population of the main task, so as to exploit promising regions. Through the knowledge transfer among the three tasks, the search ability of the population of the main task will be significantly improved. Compared with other state-of-the-art CMOEAs, the experimental results on three benchmark test suites demonstrate the superior or competitive performance of the proposed CMOEA.展开更多
In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However,...In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.展开更多
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
Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been dev...Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been developed with the use of different algorithmic strategies,evolutionary operators,and constraint-handling techniques.The performance of CMOEAs may be heavily dependent on the operators used,however,it is usually difficult to select suitable operators for the problem at hand.Hence,improving operator selection is promising and necessary for CMOEAs.This work proposes an online operator selection framework assisted by Deep Reinforcement Learning.The dynamics of the population,including convergence,diversity,and feasibility,are regarded as the state;the candidate operators are considered as actions;and the improvement of the population state is treated as the reward.By using a Q-network to learn a policy to estimate the Q-values of all actions,the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance.The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems.The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.展开更多
A constrained multi-objective biogeography-based optimization algorithm （CMBOA） was proposed to solve robot path planning （RPP）. For RPP, the length and smoothness of path were taken as the optimization objectives...A constrained multi-objective biogeography-based optimization algorithm （CMBOA） was proposed to solve robot path planning （RPP）. For RPP, the length and smoothness of path were taken as the optimization objectives, and the distance from the obstacles was constraint. In CMBOA, a new migration operator with disturbance factor was designed and applied to the feasible population to generate many more non-dominated feasible individuals; meanwhile, some infeasible individuals nearby feasible region were recombined with the nearest feasible ones to approach the feasibility. Compared with classical multi-objective evolutionary algorithms, the current study indicates that CM- BOA has better performance for RPP.展开更多
In recent years, sinmlated annealing algo-rithms have been extensively developed and uti-lized to solve nmlti-objective optimization problems. In order to obtain better optimization perfonmnce, this paper proposes a N...In recent years, sinmlated annealing algo-rithms have been extensively developed and uti-lized to solve nmlti-objective optimization problems. In order to obtain better optimization perfonmnce, this paper proposes a Novel Adaptive Simulated Annealing （NASA） algorithm for constrained multi-objective optimization based on Archived Multi-objective Simulated Annealing （AMOSA）. For han-dling multi-objective, NASA makes improverrents in three aspects： sub-iteration search, sub-archive and adaptive search, which effectively strengthen the stability and efficiency of the algorithnm For handling constraints, NASA introduces corresponding solution acceptance criterion. Furtherrrore, NASA has also been applied to optimize TD-LTE network perform-ance by adjusting antenna paranleters; it can achieve better extension and convergence than AMOSA, NS-GAII and MOPSO. Analytical studies and simulations indicate that the proposed NASA algorithm can play an important role in improving multi-objective optimi-zation performance.展开更多
This work investigates one immune optimization approach for dynamic constrained multi-objective multimodal optimization in terms of biological immune inspirations and the concept of constraint dominance. Such approach...This work investigates one immune optimization approach for dynamic constrained multi-objective multimodal optimization in terms of biological immune inspirations and the concept of constraint dominance. Such approach includes mainly three functional modules, environmental detection, population initialization and immune evolution. The first, inspired by the function of immune surveillance, is designed to detect the change of such kind of problem and to decide the type of a new environment;the second generates an initial population for the current environment, relying upon the result of detection;the last evolves two sub-populations along multiple directions and searches those excellent and diverse candidates. Experimental results show that the proposed approach can adaptively track the environmental change and effectively find the global Pareto-optimal front in each environment.展开更多
Dear Editor,This letter proposes a novel Nash bargaining solution-based multiobjective model predictive control(MPC)scheme to deal with the interaction force control and the path-following problem of the constrained i...Dear Editor,This letter proposes a novel Nash bargaining solution-based multiobjective model predictive control(MPC)scheme to deal with the interaction force control and the path-following problem of the constrained interactive robot.Considering the elastic interaction force model,a mechanical trade-off always exists between the interaction force and position,which means that neither force nor path following can satisfy their desired demands completely.Based on this consideration,two irreconcilable control specifications,the force object function and the position track object function,are proposed,and a new multi-objective MPC scheme is then designed.展开更多
Financial market has systemic complexity and uncertainty.For investors,return and risk often coexist.How to rationally allocate funds into different assets and achieve excess returns with effectively controlling risk ...Financial market has systemic complexity and uncertainty.For investors,return and risk often coexist.How to rationally allocate funds into different assets and achieve excess returns with effectively controlling risk are main problems to be solved in the field of portfolio optimization(PO).At present,due to the influence of modeling and algorithm solving,the PO models established by many researchers are still mainly focused on single-stage single-objective models or single-stage multiobjective models.PO is actually considered as a multi-stage multi-objective optimization problem in real investment scenarios.It is more difficult than the previous single-stage PO model for meeting the realistic requirements.In this paper,the authors proposed a mean-improved stable tail adjusted return ratio-maximum drawdown rate(M-ISTARR-MD)PO model which effectively characterizes the real investment scenario.In order to solve the multi-stage multi-objective PO model with complex multi-constraints,the authors designed a multi-stage constrained multi-objective evolutionary algorithm with orthogonal learning(MSCMOEA-OL).Comparing with four well-known intelligence algorithms,the MSCMOEA-OL algorithm has competitive advantages in solving the M-ISTARR-MD model on the proposed constructed carbon neutral stock dataset.This paper provides a new way to construct and solve the complex PO model.展开更多
In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the op...In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the optimality conditions of the problem,we introduce appropriate affine matrix and construct an affine scaling ARC subproblem with linearized constraints.Composite step methods and reduced Hessian methods are applied to tackle the linearized constraints.As a result,a standard unconstrained ARC subproblem is deduced and its solution can supply sufficient decrease.The fraction to the boundary rule maintains the strict feasibility(for nonnegative constraints on variables)of every iteration point.Reflection techniques are employed to prevent the iterations from approaching zero too early.Under mild assumptions,global convergence of the algorithm is analysed.Preliminary numerical results are reported.展开更多
Autonomous connected vehicles(ACV)involve advanced control strategies to effectively balance safety,efficiency,energy consumption,and passenger comfort.This research introduces a deep reinforcement learning(DRL)-based...Autonomous connected vehicles(ACV)involve advanced control strategies to effectively balance safety,efficiency,energy consumption,and passenger comfort.This research introduces a deep reinforcement learning(DRL)-based car-following(CF)framework employing the Deep Deterministic Policy Gradient(DDPG)algorithm,which integrates a multi-objective reward function that balances the four goals while maintaining safe policy learning.Utilizing real-world driving data from the highD dataset,the proposed model learns adaptive speed control policies suitable for dynamic traffic scenarios.The performance of the DRL-based model is evaluated against a traditional model predictive control-adaptive cruise control(MPC-ACC)controller.Results show that theDRLmodel significantly enhances safety,achieving zero collisions and a higher average time-to-collision(TTC)of 8.45 s,compared to 5.67 s for MPC and 6.12 s for human drivers.For efficiency,the model demonstrates 89.2% headway compliance and maintains speed tracking errors below 1.2 m/s in 90% of cases.In terms of energy optimization,the proposed approach reduces fuel consumption by 5.4% relative to MPC.Additionally,it enhances passenger comfort by lowering jerk values by 65%,achieving 0.12 m/s3 vs.0.34 m/s3 for human drivers.A multi-objective reward function is integrated to ensure stable policy convergence while simultaneously balancing the four key performance metrics.Moreover,the findings underscore the potential of DRL in advancing autonomous vehicle control,offering a robust and sustainable solution for safer,more efficient,and more comfortable transportation systems.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
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
Community detection is one of the most fundamental applications in understanding the structure of complicated networks.Furthermore,it is an important approach to identifying closely linked clusters of nodes that may r...Community detection is one of the most fundamental applications in understanding the structure of complicated networks.Furthermore,it is an important approach to identifying closely linked clusters of nodes that may represent underlying patterns and relationships.Networking structures are highly sensitive in social networks,requiring advanced techniques to accurately identify the structure of these communities.Most conventional algorithms for detecting communities perform inadequately with complicated networks.In addition,they miss out on accurately identifying clusters.Since single-objective optimization cannot always generate accurate and comprehensive results,as multi-objective optimization can.Therefore,we utilized two objective functions that enable strong connections between communities and weak connections between them.In this study,we utilized the intra function,which has proven effective in state-of-the-art research studies.We proposed a new inter-function that has demonstrated its effectiveness by making the objective of detecting external connections between communities is to make them more distinct and sparse.Furthermore,we proposed a Multi-Objective community strength enhancement algorithm(MOCSE).The proposed algorithm is based on the framework of the Multi-Objective Evolutionary Algorithm with Decomposition(MOEA/D),integrated with a new heuristic mutation strategy,community strength enhancement(CSE).The results demonstrate that the model is effective in accurately identifying community structures while also being computationally efficient.The performance measures used to evaluate the MOEA/D algorithm in our work are normalized mutual information(NMI)and modularity(Q).It was tested using five state-of-the-art algorithms on social networks,comprising real datasets(Zachary,Dolphin,Football,Krebs,SFI,Jazz,and Netscience),as well as twenty synthetic datasets.These results provide the robustness and practical value of the proposed algorithm in multi-objective community identification.展开更多
Vehicle Edge Computing(VEC)and Cloud Computing(CC)significantly enhance the processing efficiency of delay-sensitive and computation-intensive applications by offloading compute-intensive tasks from resource-constrain...Vehicle Edge Computing(VEC)and Cloud Computing(CC)significantly enhance the processing efficiency of delay-sensitive and computation-intensive applications by offloading compute-intensive tasks from resource-constrained onboard devices to nearby Roadside Unit(RSU),thereby achieving lower delay and energy consumption.However,due to the limited storage capacity and energy budget of RSUs,it is challenging to meet the demands of the highly dynamic Internet of Vehicles(IoV)environment.Therefore,determining reasonable service caching and computation offloading strategies is crucial.To address this,this paper proposes a joint service caching scheme for cloud-edge collaborative IoV computation offloading.By modeling the dynamic optimization problem using Markov Decision Processes(MDP),the scheme jointly optimizes task delay,energy consumption,load balancing,and privacy entropy to achieve better quality of service.Additionally,a dynamic adaptive multi-objective deep reinforcement learning algorithm is proposed.Each Double Deep Q-Network(DDQN)agent obtains rewards for different objectives based on distinct reward functions and dynamically updates the objective weights by learning the value changes between objectives using Radial Basis Function Networks(RBFN),thereby efficiently approximating the Pareto-optimal decisions for multiple objectives.Extensive experiments demonstrate that the proposed algorithm can better coordinate the three-tier computing resources of cloud,edge,and vehicles.Compared to existing algorithms,the proposed method reduces task delay and energy consumption by 10.64%and 5.1%,respectively.展开更多
Spaceborne antennas are essential for remote sensing,deep-space communication,and Earth observation,yet their trajectory planning is complicated by nonlinear base-manipulator coupling and antenna flexibility.To addres...Spaceborne antennas are essential for remote sensing,deep-space communication,and Earth observation,yet their trajectory planning is complicated by nonlinear base-manipulator coupling and antenna flexibility.To address these challenges,this paper proposes a multi-objective trajectory optimization framework.The system dynamics capture both nonlinear rigid-flexible coupling and antenna deformation through a reduced-order formulation.To enhance discretization efficiency,a predictive-terminal hp-adaptive pseudospectral method is employed,assigning collocation density based on task-phase characteristics:finer resolution is applied to dynamic segments requiring higher accuracy,especially near the terminal phase.This enables efficient transcription of the continuous-time problem into a Nonlinear Programming Problem(NLP).The resulting NLP is then solved using a multi-objective optimization strategy based on the nondominated sorting genetic algorithm II,which explores trade-offs among antenna pointing accuracy,energy consumption,and structural vibration.Numerical results demonstrate that the proposed method achieves a reduction of approximately 14.0% in control energy and 41.8%in peak actuation compared to a GPOPS-II baseline,while significantly enhancing vibration suppression.The resulting Pareto front reveals structured trade-offs and clustered solutions,offering robust and diverse options for precision,low-disturbance mission planning.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 investigates a distributed heterogeneous hybrid blocking flow-shop scheduling problem(DHHBFSP)designed to minimize the total tardiness and total energy consumption simultaneously,and proposes an improved pr...This paper investigates a distributed heterogeneous hybrid blocking flow-shop scheduling problem(DHHBFSP)designed to minimize the total tardiness and total energy consumption simultaneously,and proposes an improved proximal policy optimization(IPPO)method to make real-time decisions for the DHHBFSP.A multi-objective Markov decision process is modeled for the DHHBFSP,where the reward function is represented by a vector with dynamic weights instead of the common objectiverelated scalar value.A factory agent(FA)is formulated for each factory to select unscheduled jobs and is trained by the proposed IPPO to improve the decision quality.Multiple FAs work asynchronously to allocate jobs that arrive randomly at the shop.A two-stage training strategy is introduced in the IPPO,which learns from both single-and dual-policy data for better data utilization.The proposed IPPO is tested on randomly generated instances and compared with variants of the basic proximal policy optimization(PPO),dispatch rules,multi-objective metaheuristics,and multi-agent reinforcement learning methods.Extensive experimental results suggest that the proposed strategies offer significant improvements to the basic PPO,and the proposed IPPO outperforms the state-of-the-art scheduling methods in both convergence and solution quality.展开更多
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 in part by the National Natural Science Foundation of China(U23A20340,62176238,62476254,62106230)the Key Research and Development Projects of the Ministry of Science and Technology of China(2022YFD2001200)+3 种基金the Natural Science Foundation Project of Henan Province(242300420277)the Key Research and Development Program of Henan(251111113900)the Frontier Exploration Projects of Longmen Laboratory(LMQYTSKT031)Chongqing University of Posts and Telecommunications Key Laboratory of Big Data Open Fund Project(BDIC-2023-B-005).
文摘Solving constrained multi-objective optimization problems(CMOPs)is a challenging task due to the presence of multiple conflicting objectives and intricate constraints.In order to better address CMOPs and achieve a balance between objectives and constraints,existing constrained multi-objective evolutionary algorithms(CMOEAs)predominantly focus on devising various strategies by leveraging the relationships between objectives and constraints,and the designed strategies usually are effective for the problems with simple constraints.However,these methods most ignore the relationship between decision variables and constraints.In fact,the essence of optimization is to find appropriate decision variables to meet various complex constraints.Therefore,it is hoped that the problem can be analyzed from the perspective of decision variables,so as to obtain more excellent results.Based on the above motivation,this paper proposes a decision variables classification approach,according to the relationship between decision variables and constraints,variables are divided into constraint-related(CR)variables and constraintindependent(CI)variables.Consequently,by optimizing these two types of variables independently,the population can sustain a favorable balance between feasibility and diversity.Furthermore,specific offspring generation strategies are proposed for the two categories of decision variables in order to achieve rapid convergence while maintaining population diversity.Experimental results on 31 test problems as well as 20 real-world problems demonstrate that the proposed algorithm is competitive compared to some state-of-the-art constrained multi-objective optimization algorithms.
基金supported in part by the National Natural Science Fund for Outstanding Young Scholars of China (61922072)the National Natural Science Foundation of China (62176238, 61806179, 61876169, 61976237)+2 种基金China Postdoctoral Science Foundation (2020M682347)the Training Program of Young Backbone Teachers in Colleges and Universities in Henan Province (2020GGJS006)Henan Provincial Young Talents Lifting Project (2021HYTP007)。
文摘Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-objective evolutionary algorithms(CMOEAs) have been developed. However, most of them tend to converge into local areas due to the loss of diversity. Evolutionary multitasking(EMT) is new model of solving complex optimization problems, through the knowledge transfer between the source task and other related tasks. Inspired by EMT, this paper develops a new EMT-based CMOEA to solve CMOPs, in which the main task, a global auxiliary task, and a local auxiliary task are created and optimized by one specific population respectively. The main task focuses on finding the feasible Pareto front(PF), and global and local auxiliary tasks are used to respectively enhance global and local diversity. Moreover, the global auxiliary task is used to implement the global search by ignoring constraints, so as to help the population of the main task pass through infeasible obstacles. The local auxiliary task is used to provide local diversity around the population of the main task, so as to exploit promising regions. Through the knowledge transfer among the three tasks, the search ability of the population of the main task will be significantly improved. Compared with other state-of-the-art CMOEAs, the experimental results on three benchmark test suites demonstrate the superior or competitive performance of the proposed CMOEA.
基金partly supported by the National Natural Science Foundation of China(62076225)。
文摘In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.
基金supported in part by the National Key Research and Development Program of China(2022YFD2001200)the National Natural Science Foundation of China(62176238,61976237,62206251,62106230)+3 种基金China Postdoctoral Science Foundation(2021T140616,2021M692920)the Natural Science Foundation of Henan Province(222300420088)the Program for Science&Technology Innovation Talents in Universities of Henan Province(23HASTIT023)the Program for Science&Technology Innovation Teams in Universities of Henan Province(23IRTSTHN010).
文摘Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.
基金the National Natural Science Foundation of China(62076225,62073300)the Natural Science Foundation for Distinguished Young Scholars of Hubei(2019CFA081)。
文摘Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been developed with the use of different algorithmic strategies,evolutionary operators,and constraint-handling techniques.The performance of CMOEAs may be heavily dependent on the operators used,however,it is usually difficult to select suitable operators for the problem at hand.Hence,improving operator selection is promising and necessary for CMOEAs.This work proposes an online operator selection framework assisted by Deep Reinforcement Learning.The dynamics of the population,including convergence,diversity,and feasibility,are regarded as the state;the candidate operators are considered as actions;and the improvement of the population state is treated as the reward.By using a Q-network to learn a policy to estimate the Q-values of all actions,the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance.The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems.The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.
基金Supported by the National Natural Science Foundation of Chi- na（61075113） the Excellent Young Teacher Foundation of Heilongjiang Province of China （1155G18） the Fundamental Research Funds for the Central Universities （HEUCFZl209）
文摘A constrained multi-objective biogeography-based optimization algorithm （CMBOA） was proposed to solve robot path planning （RPP）. For RPP, the length and smoothness of path were taken as the optimization objectives, and the distance from the obstacles was constraint. In CMBOA, a new migration operator with disturbance factor was designed and applied to the feasible population to generate many more non-dominated feasible individuals; meanwhile, some infeasible individuals nearby feasible region were recombined with the nearest feasible ones to approach the feasibility. Compared with classical multi-objective evolutionary algorithms, the current study indicates that CM- BOA has better performance for RPP.
基金supported by the Major National Science & Technology Specific Project of China under Grants No.2010ZX03002-007-02,No.2009ZX03002-002,No.2010ZX03002-002-03
文摘In recent years, sinmlated annealing algo-rithms have been extensively developed and uti-lized to solve nmlti-objective optimization problems. In order to obtain better optimization perfonmnce, this paper proposes a Novel Adaptive Simulated Annealing （NASA） algorithm for constrained multi-objective optimization based on Archived Multi-objective Simulated Annealing （AMOSA）. For han-dling multi-objective, NASA makes improverrents in three aspects： sub-iteration search, sub-archive and adaptive search, which effectively strengthen the stability and efficiency of the algorithnm For handling constraints, NASA introduces corresponding solution acceptance criterion. Furtherrrore, NASA has also been applied to optimize TD-LTE network perform-ance by adjusting antenna paranleters; it can achieve better extension and convergence than AMOSA, NS-GAII and MOPSO. Analytical studies and simulations indicate that the proposed NASA algorithm can play an important role in improving multi-objective optimi-zation performance.
文摘This work investigates one immune optimization approach for dynamic constrained multi-objective multimodal optimization in terms of biological immune inspirations and the concept of constraint dominance. Such approach includes mainly three functional modules, environmental detection, population initialization and immune evolution. The first, inspired by the function of immune surveillance, is designed to detect the change of such kind of problem and to decide the type of a new environment;the second generates an initial population for the current environment, relying upon the result of detection;the last evolves two sub-populations along multiple directions and searches those excellent and diverse candidates. Experimental results show that the proposed approach can adaptively track the environmental change and effectively find the global Pareto-optimal front in each environment.
基金supported by the National Natural Science Foundation of China(62303095)the Natural Science Foundation of Sichuan Province(2023NSFSC0872).
文摘Dear Editor,This letter proposes a novel Nash bargaining solution-based multiobjective model predictive control(MPC)scheme to deal with the interaction force control and the path-following problem of the constrained interactive robot.Considering the elastic interaction force model,a mechanical trade-off always exists between the interaction force and position,which means that neither force nor path following can satisfy their desired demands completely.Based on this consideration,two irreconcilable control specifications,the force object function and the position track object function,are proposed,and a new multi-objective MPC scheme is then designed.
基金supported by the National Natural Science Foundation of China under Grant No.61973042Beijing Natural Science Foundation under Grant No.1202020。
文摘Financial market has systemic complexity and uncertainty.For investors,return and risk often coexist.How to rationally allocate funds into different assets and achieve excess returns with effectively controlling risk are main problems to be solved in the field of portfolio optimization(PO).At present,due to the influence of modeling and algorithm solving,the PO models established by many researchers are still mainly focused on single-stage single-objective models or single-stage multiobjective models.PO is actually considered as a multi-stage multi-objective optimization problem in real investment scenarios.It is more difficult than the previous single-stage PO model for meeting the realistic requirements.In this paper,the authors proposed a mean-improved stable tail adjusted return ratio-maximum drawdown rate(M-ISTARR-MD)PO model which effectively characterizes the real investment scenario.In order to solve the multi-stage multi-objective PO model with complex multi-constraints,the authors designed a multi-stage constrained multi-objective evolutionary algorithm with orthogonal learning(MSCMOEA-OL).Comparing with four well-known intelligence algorithms,the MSCMOEA-OL algorithm has competitive advantages in solving the M-ISTARR-MD model on the proposed constructed carbon neutral stock dataset.This paper provides a new way to construct and solve the complex PO model.
基金Supported by the National Natural Science Foundation of China(12071133)Natural Science Foundation of Henan Province(252300421993)Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110005)。
文摘In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the optimality conditions of the problem,we introduce appropriate affine matrix and construct an affine scaling ARC subproblem with linearized constraints.Composite step methods and reduced Hessian methods are applied to tackle the linearized constraints.As a result,a standard unconstrained ARC subproblem is deduced and its solution can supply sufficient decrease.The fraction to the boundary rule maintains the strict feasibility(for nonnegative constraints on variables)of every iteration point.Reflection techniques are employed to prevent the iterations from approaching zero too early.Under mild assumptions,global convergence of the algorithm is analysed.Preliminary numerical results are reported.
基金the Hebei Province Science and Technology Plan Project(19221909D)rincess Nourah bint Abdulrahman University Researchers Supporting Project number(PNURSP2025R308),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘Autonomous connected vehicles(ACV)involve advanced control strategies to effectively balance safety,efficiency,energy consumption,and passenger comfort.This research introduces a deep reinforcement learning(DRL)-based car-following(CF)framework employing the Deep Deterministic Policy Gradient(DDPG)algorithm,which integrates a multi-objective reward function that balances the four goals while maintaining safe policy learning.Utilizing real-world driving data from the highD dataset,the proposed model learns adaptive speed control policies suitable for dynamic traffic scenarios.The performance of the DRL-based model is evaluated against a traditional model predictive control-adaptive cruise control(MPC-ACC)controller.Results show that theDRLmodel significantly enhances safety,achieving zero collisions and a higher average time-to-collision(TTC)of 8.45 s,compared to 5.67 s for MPC and 6.12 s for human drivers.For efficiency,the model demonstrates 89.2% headway compliance and maintains speed tracking errors below 1.2 m/s in 90% of cases.In terms of energy optimization,the proposed approach reduces fuel consumption by 5.4% relative to MPC.Additionally,it enhances passenger comfort by lowering jerk values by 65%,achieving 0.12 m/s3 vs.0.34 m/s3 for human drivers.A multi-objective reward function is integrated to ensure stable policy convergence while simultaneously balancing the four key performance metrics.Moreover,the findings underscore the potential of DRL in advancing autonomous vehicle control,offering a robust and sustainable solution for safer,more efficient,and more comfortable transportation systems.
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(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Community detection is one of the most fundamental applications in understanding the structure of complicated networks.Furthermore,it is an important approach to identifying closely linked clusters of nodes that may represent underlying patterns and relationships.Networking structures are highly sensitive in social networks,requiring advanced techniques to accurately identify the structure of these communities.Most conventional algorithms for detecting communities perform inadequately with complicated networks.In addition,they miss out on accurately identifying clusters.Since single-objective optimization cannot always generate accurate and comprehensive results,as multi-objective optimization can.Therefore,we utilized two objective functions that enable strong connections between communities and weak connections between them.In this study,we utilized the intra function,which has proven effective in state-of-the-art research studies.We proposed a new inter-function that has demonstrated its effectiveness by making the objective of detecting external connections between communities is to make them more distinct and sparse.Furthermore,we proposed a Multi-Objective community strength enhancement algorithm(MOCSE).The proposed algorithm is based on the framework of the Multi-Objective Evolutionary Algorithm with Decomposition(MOEA/D),integrated with a new heuristic mutation strategy,community strength enhancement(CSE).The results demonstrate that the model is effective in accurately identifying community structures while also being computationally efficient.The performance measures used to evaluate the MOEA/D algorithm in our work are normalized mutual information(NMI)and modularity(Q).It was tested using five state-of-the-art algorithms on social networks,comprising real datasets(Zachary,Dolphin,Football,Krebs,SFI,Jazz,and Netscience),as well as twenty synthetic datasets.These results provide the robustness and practical value of the proposed algorithm in multi-objective community identification.
基金supported by Key Science and Technology Program of Henan Province,China(Grant Nos.242102210147,242102210027)Fujian Province Young and Middle aged Teacher Education Research Project(Science and Technology Category)(No.JZ240101)(Corresponding author:Dong Yuan).
文摘Vehicle Edge Computing(VEC)and Cloud Computing(CC)significantly enhance the processing efficiency of delay-sensitive and computation-intensive applications by offloading compute-intensive tasks from resource-constrained onboard devices to nearby Roadside Unit(RSU),thereby achieving lower delay and energy consumption.However,due to the limited storage capacity and energy budget of RSUs,it is challenging to meet the demands of the highly dynamic Internet of Vehicles(IoV)environment.Therefore,determining reasonable service caching and computation offloading strategies is crucial.To address this,this paper proposes a joint service caching scheme for cloud-edge collaborative IoV computation offloading.By modeling the dynamic optimization problem using Markov Decision Processes(MDP),the scheme jointly optimizes task delay,energy consumption,load balancing,and privacy entropy to achieve better quality of service.Additionally,a dynamic adaptive multi-objective deep reinforcement learning algorithm is proposed.Each Double Deep Q-Network(DDQN)agent obtains rewards for different objectives based on distinct reward functions and dynamically updates the objective weights by learning the value changes between objectives using Radial Basis Function Networks(RBFN),thereby efficiently approximating the Pareto-optimal decisions for multiple objectives.Extensive experiments demonstrate that the proposed algorithm can better coordinate the three-tier computing resources of cloud,edge,and vehicles.Compared to existing algorithms,the proposed method reduces task delay and energy consumption by 10.64%and 5.1%,respectively.
基金supported by the National Natural Science Foundation of China(No.62173107).
文摘Spaceborne antennas are essential for remote sensing,deep-space communication,and Earth observation,yet their trajectory planning is complicated by nonlinear base-manipulator coupling and antenna flexibility.To address these challenges,this paper proposes a multi-objective trajectory optimization framework.The system dynamics capture both nonlinear rigid-flexible coupling and antenna deformation through a reduced-order formulation.To enhance discretization efficiency,a predictive-terminal hp-adaptive pseudospectral method is employed,assigning collocation density based on task-phase characteristics:finer resolution is applied to dynamic segments requiring higher accuracy,especially near the terminal phase.This enables efficient transcription of the continuous-time problem into a Nonlinear Programming Problem(NLP).The resulting NLP is then solved using a multi-objective optimization strategy based on the nondominated sorting genetic algorithm II,which explores trade-offs among antenna pointing accuracy,energy consumption,and structural vibration.Numerical results demonstrate that the proposed method achieves a reduction of approximately 14.0% in control energy and 41.8%in peak actuation compared to a GPOPS-II baseline,while significantly enhancing vibration suppression.The resulting Pareto front reveals structured trade-offs and clustered solutions,offering robust and diverse options for precision,low-disturbance mission planning.
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partially supported by the National Key Research and Development Program of the Ministry of Science and Technology of China(2022YFE0114200)the National Natural Science Foundation of China(U20A6004).
文摘This paper investigates a distributed heterogeneous hybrid blocking flow-shop scheduling problem(DHHBFSP)designed to minimize the total tardiness and total energy consumption simultaneously,and proposes an improved proximal policy optimization(IPPO)method to make real-time decisions for the DHHBFSP.A multi-objective Markov decision process is modeled for the DHHBFSP,where the reward function is represented by a vector with dynamic weights instead of the common objectiverelated scalar value.A factory agent(FA)is formulated for each factory to select unscheduled jobs and is trained by the proposed IPPO to improve the decision quality.Multiple FAs work asynchronously to allocate jobs that arrive randomly at the shop.A two-stage training strategy is introduced in the IPPO,which learns from both single-and dual-policy data for better data utilization.The proposed IPPO is tested on randomly generated instances and compared with variants of the basic proximal policy optimization(PPO),dispatch rules,multi-objective metaheuristics,and multi-agent reinforcement learning methods.Extensive experimental results suggest that the proposed strategies offer significant improvements to the basic PPO,and the proposed IPPO outperforms the state-of-the-art scheduling methods in both convergence and solution quality.
