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
This research provides academic and practical contributions. From a theoretical standpoint, a hybrid harmony search(HS)algorithm, namely the oppositional global-based HS(OGHS), is proposed for solving the multi-object...This research provides academic and practical contributions. From a theoretical standpoint, a hybrid harmony search(HS)algorithm, namely the oppositional global-based HS(OGHS), is proposed for solving the multi-objective flexible job-shop scheduling problems(MOFJSPs) to minimize makespan, total machine workload and critical machine workload. An initialization program embedded in opposition-based learning(OBL) is developed for enabling the individuals to scatter in a well-distributed manner in the initial harmony memory(HM). In addition, the recursive halving technique based on opposite number is employed for shrinking the neighbourhood space in the searching phase of the OGHS. From a practice-related standpoint, a type of dual vector code technique is introduced for allowing the OGHS algorithm to adapt the discrete nature of the MOFJSP. Two practical techniques, namely Pareto optimality and technique for order preference by similarity to an ideal solution(TOPSIS), are implemented for solving the MOFJSP.Furthermore, the algorithm performance is tested by using different strategies, including OBL and recursive halving, and the OGHS is compared with existing algorithms in the latest studies.Experimental results on representative examples validate the performance of the proposed algorithm for solving the MOFJSP.展开更多
Production scheduling is one of the most important problems to be considered in the effective performance of the automatic manufacturing system.It is the typical kind of NP-complete problem. The methods commonly used ...Production scheduling is one of the most important problems to be considered in the effective performance of the automatic manufacturing system.It is the typical kind of NP-complete problem. The methods commonly used are not suitable to solve complicated problems because the calculating time rises exponentially with the increase of the problem size. In this paper, a new algorithm - immune based scheduling algorithm (IBSA) is proposed. After the description of the mathematics model and the calculating procedure of immune based scheduling,some examples are tested in the software system called HM IM& C that is developed usingVC+ +6.0. The testing results show that IBSA has high efficiency to solve scheduling problem.展开更多
One of the fundamental problems associated with scheduling workflows on virtual machines in a multi-cloud environment is how to find a near-optimum permutation.The workflow scheduling involves assigning independent co...One of the fundamental problems associated with scheduling workflows on virtual machines in a multi-cloud environment is how to find a near-optimum permutation.The workflow scheduling involves assigning independent computational jobs with conflicting objectives to a set of virtual machines.Most optimization methods for solving non-deterministic polynomial-time hardness(NP-hard)problems deploy multi-objective algorithms.As such,Pareto dominance is one of the most efficient criteria for determining the best solutions within the Pareto front.However,the main drawback of this method is that it requires a reasonably long time to provide an optimum solution.In this paper,a new multi-objective minimum weight algorithm is used to derive the Pareto front.The conflicting objectives considered are reliability,cost,resource utilization,risk probability and makespan.Because multi-objective algorithms select a number of permutations with an optimal trade-off between conflicting objectives,we propose a new decisionmaking approach named the minimum weight optimization(MWO).MWO produces alternative weight to determine the inertia weight by using an adaptive strategy to provide an appropriate alternative for all optimal solutions.This way,consumers’needs and service providers’interests are taken into account.Using standard scientific workflows with conflicting objectives,we compare our proposed multi-objective scheduling algorithm using minimum weigh optimization(MOS-MWO)with multi-objective scheduling algorithm(MOS).Results show that MOS-MWO outperforms MOS in term of QoS satisfaction rate.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
The cloud-fog computing paradigm has emerged as a novel hybrid computing model that integrates computational resources at both fog nodes and cloud servers to address the challenges posed by dynamic and heterogeneous c...The cloud-fog computing paradigm has emerged as a novel hybrid computing model that integrates computational resources at both fog nodes and cloud servers to address the challenges posed by dynamic and heterogeneous computing networks.Finding an optimal computational resource for task offloading and then executing efficiently is a critical issue to achieve a trade-off between energy consumption and transmission delay.In this network,the task processed at fog nodes reduces transmission delay.Still,it increases energy consumption,while routing tasks to the cloud server saves energy at the cost of higher communication delay.Moreover,the order in which offloaded tasks are executed affects the system’s efficiency.For instance,executing lower-priority tasks before higher-priority jobs can disturb the reliability and stability of the system.Therefore,an efficient strategy of optimal computation offloading and task scheduling is required for operational efficacy.In this paper,we introduced a multi-objective and enhanced version of Cheeta Optimizer(CO),namely(MoECO),to jointly optimize the computation offloading and task scheduling in cloud-fog networks to minimize two competing objectives,i.e.,energy consumption and communication delay.MoECO first assigns tasks to the optimal computational nodes and then the allocated tasks are scheduled for processing based on the task priority.The mathematical modelling of CO needs improvement in computation time and convergence speed.Therefore,MoECO is proposed to increase the search capability of agents by controlling the search strategy based on a leader’s location.The adaptive step length operator is adjusted to diversify the solution and thus improves the exploration phase,i.e.,global search strategy.Consequently,this prevents the algorithm from getting trapped in the local optimal solution.Moreover,the interaction factor during the exploitation phase is also adjusted based on the location of the prey instead of the adjacent Cheetah.This increases the exploitation capability of agents,i.e.,local search capability.Furthermore,MoECO employs a multi-objective Pareto-optimal front to simultaneously minimize designated objectives.Comprehensive simulations in MATLAB demonstrate that the proposed algorithm obtains multiple solutions via a Pareto-optimal front and achieves an efficient trade-off between optimization objectives compared to baseline methods.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 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
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
In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimizatio...In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimization objective functions caused by their physical dimensions.These deviations seriously affect the scheduling process.A novel standardization fusion method has been established to address this issue by analyzing the variation process of each objective function’s values.The optimal scheduling results of IEHS with HESS indicate that the economy and overall energy loss can be improved 2–3 times under different optimization methods.The proposed method better balances all optimization objective functions and reduces the impact of their dimensionality.When the cost of BESS decreases by approximately 30%,its participation deepens by about 1 time.Moreover,if the price of the electrolyzer is less than 15¥/kWh or if the cost of the fuel cell drops below 4¥/kWh,their participation will increase substantially.This study aims to provide a more reasonable approach to solving multi-objective optimization problems.展开更多
Intelligent production is an important development direction in intelligent manufacturing,with intelligent factories playing a crucial role in promoting intelligent production.Flexible job shops,as the main form of in...Intelligent production is an important development direction in intelligent manufacturing,with intelligent factories playing a crucial role in promoting intelligent production.Flexible job shops,as the main form of intelligent factories,constantly face dynamic disturbances during the production process,including machine failures and urgent orders.This paper discusses the basic models and research methods of job shop scheduling,emphasizing the important role of dynamic job shop scheduling and its response schemes in future research.A multi-objective flexible job shop dynamic scheduling mathematical model is established,highlighting its complex and multi-constraint characteristics under different interferences.A classification discussion is conducted on the dynamic response methods and optimization objectives under machine failures,emergency orders,fuzzy completion times,and mixed dynamic events.The development process of traditional scheduling rules and intelligent methods in dynamic scheduling are also analyzed.Finally,based on the current development status of job shop scheduling and the requirements of intelligent manufacturing,the future development trends of dynamic scheduling in flexible job shops are proposed.展开更多
In cloud computing, efficient multi-objective task scheduling, aiming at minimizing makespan, energy consumption,and load variance,remains a critical challenge due to the non-deterministic polynomial( NP)-completeness...In cloud computing, efficient multi-objective task scheduling, aiming at minimizing makespan, energy consumption,and load variance,remains a critical challenge due to the non-deterministic polynomial( NP)-completeness of the problem and the limitations of traditional algorithms like premature convergence. In this paper,a multi-strategy improved sparrow search algorithm( MISSA) was proposed to address these issues. MISSA integrates specular reflection learning for initial population optimization,nonlinear adaptive decay weights to balance global exploration and local exploitation,and an innovative strategy based on T-distribution mutation to enhance population diversity. Experimental results on benchmark functions and real cloud task scheduling scenarios using CloudSim demonstrate that MISSA outperforms comparative algorithms such as sparrow search algorithm( SSA),boosted sparrow search algorithm( BSSA),and genetic algorithm-grey wolf optimizer( GA-GWO),achieving significant reductions in makespan,energy consumption,and load variance. MISSA provides an effective solution for intelligent resource allocation in heterogeneous cloud environments,showcasing robust performance in complex multi-objective optimization tasks.展开更多
In the flexible job-shop scheduling problem （FJSP）, each operation has to be assigned to a machine from a set of capable machines before alocating the assigned operations on all machines. To solve the multi-objectiv...In the flexible job-shop scheduling problem （FJSP）, each operation has to be assigned to a machine from a set of capable machines before alocating the assigned operations on all machines. To solve the multi-objective FJSP, the Grantt graph oriented string representation （GOSR） and the basic manipulation of the genetic algorithm operator are presented. An integrated operator genetic algorithm （IOGA） and its process are described. Comparison between computational results and the latest research shows that the proposed algorithm is effective in reducing the total workload of all machines, the makespan and the critical machine workload.展开更多
To address the issue that hybrid flow shop production struggles to handle order disturbance events,a dynamic scheduling model was constructed.The model takes minimizing the maximum makespan,delivery time deviation,and...To address the issue that hybrid flow shop production struggles to handle order disturbance events,a dynamic scheduling model was constructed.The model takes minimizing the maximum makespan,delivery time deviation,and scheme deviation degree as the optimization objectives.An adaptive dynamic scheduling strategy based on the degree of order disturbance is proposed.An improved multi-objective Grey Wolf(IMOGWO)optimization algorithm is designed by combining the“job-machine”two-layer encoding strategy,the timing-driven two-stage decoding strategy,the opposition-based learning initialization population strategy,the POX crossover strategy,the dualoperation dynamic mutation strategy,and the variable neighborhood search strategy for problem solving.A variety of test cases with different scales were designed,and ablation experiments were conducted to verify the effectiveness of the improved strategies.The results show that each improved strategy can effectively enhance the performance of the IMOGWO.Additionally,performance analysis was conducted by comparing the proposed algorithm with three mature and classical algorithms.The results demonstrate that the proposed algorithm exhibits superior performance in solving the hybrid flow-shop scheduling problem(HFSP).Case validations were conducted for different types of order disturbance scenarios.The results demonstrate that the proposed adaptive dynamic scheduling strategy and the IMOGWO algorithm can effectively address order disturbance events.They enable rapid response to order disturbance while ensuring the stability of the production system.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
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
In response to the challenges faced by unmanned swarms in mountain obstacle-breaching missions within complex terrains,such as poor task-resource coupling,lengthy solution generation times,and poor inter-platform coll...In response to the challenges faced by unmanned swarms in mountain obstacle-breaching missions within complex terrains,such as poor task-resource coupling,lengthy solution generation times,and poor inter-platform collaboration,an unmanned swarm scheduling strategy tailored is proposed for mountain obstacle-breaching missions.Initially,by formalizing the descriptions of obstacle breaching operations,the swarm,and obstacle targets,an optimization model is constructed with the objectives of expected global benefit,timeliness,and task completion degree.A meta-task decomposition and reassembly strategy is then introduced to more precisely match the capabilities of unmanned platforms with task requirements.Additionally,a meta-task decomposition optimization model and a meta-task allocation operator are incorporated to achieve efficient allocation of swarm resources and collaborative scheduling.Simulation results demonstrate that the model can accurately generate reasonable and feasible obstacle breaching execution plans for unmanned swarms based on specific task requirements and environmental conditions.Moreover,compared to conventional strategies,the proposed strategy enhances task completion degree and expected returns while reducing the execution time of the plans.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
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
The proliferation of carrier aircraft and the integration of unmanned aerial vehicles(UAVs)on aircraft carriers present new challenges to the automation of launch and recovery operations.This paper investigates a coll...The proliferation of carrier aircraft and the integration of unmanned aerial vehicles(UAVs)on aircraft carriers present new challenges to the automation of launch and recovery operations.This paper investigates a collaborative scheduling problem inherent to the operational processes of carrier aircraft,where launch and recovery tasks are conducted concurrently on the flight deck.The objective is to minimize the cumulative weighted waiting time in the air for recovering aircraft and the cumulative weighted delay time for launching aircraft.To tackle this challenge,a multiple population self-adaptive differential evolution(MPSADE)algorithm is proposed.This method features a self-adaptive parameter updating mechanism that is contingent upon population diversity,an asynchronous updating scheme,an individual migration operator,and a global crossover mechanism.Additionally,comprehensive experiments are conducted to validate the effectiveness of the proposed model and algorithm.Ultimately,a comparative analysis with existing operation modes confirms the enhanced efficiency of the collaborative operation mode.展开更多
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.
基金supported by the National Key Research and Development Program of China(2016YFD0700605)the Fundamental Research Funds for the Central Universities(JZ2016HGBZ1035)the Anhui University Natural Science Research Project(KJ2017A891)
文摘This research provides academic and practical contributions. From a theoretical standpoint, a hybrid harmony search(HS)algorithm, namely the oppositional global-based HS(OGHS), is proposed for solving the multi-objective flexible job-shop scheduling problems(MOFJSPs) to minimize makespan, total machine workload and critical machine workload. An initialization program embedded in opposition-based learning(OBL) is developed for enabling the individuals to scatter in a well-distributed manner in the initial harmony memory(HM). In addition, the recursive halving technique based on opposite number is employed for shrinking the neighbourhood space in the searching phase of the OGHS. From a practice-related standpoint, a type of dual vector code technique is introduced for allowing the OGHS algorithm to adapt the discrete nature of the MOFJSP. Two practical techniques, namely Pareto optimality and technique for order preference by similarity to an ideal solution(TOPSIS), are implemented for solving the MOFJSP.Furthermore, the algorithm performance is tested by using different strategies, including OBL and recursive halving, and the OGHS is compared with existing algorithms in the latest studies.Experimental results on representative examples validate the performance of the proposed algorithm for solving the MOFJSP.
基金Shanghai Natural Science Foundation (01ZF14004) National Technology Innovation Project (02CJ-14 -05 -01)
文摘Production scheduling is one of the most important problems to be considered in the effective performance of the automatic manufacturing system.It is the typical kind of NP-complete problem. The methods commonly used are not suitable to solve complicated problems because the calculating time rises exponentially with the increase of the problem size. In this paper, a new algorithm - immune based scheduling algorithm (IBSA) is proposed. After the description of the mathematics model and the calculating procedure of immune based scheduling,some examples are tested in the software system called HM IM& C that is developed usingVC+ +6.0. The testing results show that IBSA has high efficiency to solve scheduling problem.
基金supported by Putra Grant,University PutraMalaysia,under Grant 95960000 and in part by the Ministry of Education(MOE)Malaysia.
文摘One of the fundamental problems associated with scheduling workflows on virtual machines in a multi-cloud environment is how to find a near-optimum permutation.The workflow scheduling involves assigning independent computational jobs with conflicting objectives to a set of virtual machines.Most optimization methods for solving non-deterministic polynomial-time hardness(NP-hard)problems deploy multi-objective algorithms.As such,Pareto dominance is one of the most efficient criteria for determining the best solutions within the Pareto front.However,the main drawback of this method is that it requires a reasonably long time to provide an optimum solution.In this paper,a new multi-objective minimum weight algorithm is used to derive the Pareto front.The conflicting objectives considered are reliability,cost,resource utilization,risk probability and makespan.Because multi-objective algorithms select a number of permutations with an optimal trade-off between conflicting objectives,we propose a new decisionmaking approach named the minimum weight optimization(MWO).MWO produces alternative weight to determine the inertia weight by using an adaptive strategy to provide an appropriate alternative for all optimal solutions.This way,consumers’needs and service providers’interests are taken into account.Using standard scientific workflows with conflicting objectives,we compare our proposed multi-objective scheduling algorithm using minimum weigh optimization(MOS-MWO)with multi-objective scheduling algorithm(MOS).Results show that MOS-MWO outperforms MOS in term of QoS satisfaction rate.
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appreciation to the Princess Nourah bint Abdulrahman University Researchers Supporting Project number(PNURSP2025R384)Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘The cloud-fog computing paradigm has emerged as a novel hybrid computing model that integrates computational resources at both fog nodes and cloud servers to address the challenges posed by dynamic and heterogeneous computing networks.Finding an optimal computational resource for task offloading and then executing efficiently is a critical issue to achieve a trade-off between energy consumption and transmission delay.In this network,the task processed at fog nodes reduces transmission delay.Still,it increases energy consumption,while routing tasks to the cloud server saves energy at the cost of higher communication delay.Moreover,the order in which offloaded tasks are executed affects the system’s efficiency.For instance,executing lower-priority tasks before higher-priority jobs can disturb the reliability and stability of the system.Therefore,an efficient strategy of optimal computation offloading and task scheduling is required for operational efficacy.In this paper,we introduced a multi-objective and enhanced version of Cheeta Optimizer(CO),namely(MoECO),to jointly optimize the computation offloading and task scheduling in cloud-fog networks to minimize two competing objectives,i.e.,energy consumption and communication delay.MoECO first assigns tasks to the optimal computational nodes and then the allocated tasks are scheduled for processing based on the task priority.The mathematical modelling of CO needs improvement in computation time and convergence speed.Therefore,MoECO is proposed to increase the search capability of agents by controlling the search strategy based on a leader’s location.The adaptive step length operator is adjusted to diversify the solution and thus improves the exploration phase,i.e.,global search strategy.Consequently,this prevents the algorithm from getting trapped in the local optimal solution.Moreover,the interaction factor during the exploitation phase is also adjusted based on the location of the prey instead of the adjacent Cheetah.This increases the exploitation capability of agents,i.e.,local search capability.Furthermore,MoECO employs a multi-objective Pareto-optimal front to simultaneously minimize designated objectives.Comprehensive simulations in MATLAB demonstrate that the proposed algorithm obtains multiple solutions via a Pareto-optimal front and achieves an efficient trade-off between optimization objectives compared to baseline methods.
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sponsored by R&D Program of Beijing Municipal Education Commission(KM202410009013).
文摘In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimization objective functions caused by their physical dimensions.These deviations seriously affect the scheduling process.A novel standardization fusion method has been established to address this issue by analyzing the variation process of each objective function’s values.The optimal scheduling results of IEHS with HESS indicate that the economy and overall energy loss can be improved 2–3 times under different optimization methods.The proposed method better balances all optimization objective functions and reduces the impact of their dimensionality.When the cost of BESS decreases by approximately 30%,its participation deepens by about 1 time.Moreover,if the price of the electrolyzer is less than 15¥/kWh or if the cost of the fuel cell drops below 4¥/kWh,their participation will increase substantially.This study aims to provide a more reasonable approach to solving multi-objective optimization problems.
基金supported by the National Key Research and Development Program Project(No.2021YFB3301300).
文摘Intelligent production is an important development direction in intelligent manufacturing,with intelligent factories playing a crucial role in promoting intelligent production.Flexible job shops,as the main form of intelligent factories,constantly face dynamic disturbances during the production process,including machine failures and urgent orders.This paper discusses the basic models and research methods of job shop scheduling,emphasizing the important role of dynamic job shop scheduling and its response schemes in future research.A multi-objective flexible job shop dynamic scheduling mathematical model is established,highlighting its complex and multi-constraint characteristics under different interferences.A classification discussion is conducted on the dynamic response methods and optimization objectives under machine failures,emergency orders,fuzzy completion times,and mixed dynamic events.The development process of traditional scheduling rules and intelligent methods in dynamic scheduling are also analyzed.Finally,based on the current development status of job shop scheduling and the requirements of intelligent manufacturing,the future development trends of dynamic scheduling in flexible job shops are proposed.
基金supported by the Key Research and Development Project of Heilongjiang Province (JD2023SJ20)。
文摘In cloud computing, efficient multi-objective task scheduling, aiming at minimizing makespan, energy consumption,and load variance,remains a critical challenge due to the non-deterministic polynomial( NP)-completeness of the problem and the limitations of traditional algorithms like premature convergence. In this paper,a multi-strategy improved sparrow search algorithm( MISSA) was proposed to address these issues. MISSA integrates specular reflection learning for initial population optimization,nonlinear adaptive decay weights to balance global exploration and local exploitation,and an innovative strategy based on T-distribution mutation to enhance population diversity. Experimental results on benchmark functions and real cloud task scheduling scenarios using CloudSim demonstrate that MISSA outperforms comparative algorithms such as sparrow search algorithm( SSA),boosted sparrow search algorithm( BSSA),and genetic algorithm-grey wolf optimizer( GA-GWO),achieving significant reductions in makespan,energy consumption,and load variance. MISSA provides an effective solution for intelligent resource allocation in heterogeneous cloud environments,showcasing robust performance in complex multi-objective optimization tasks.
文摘In the flexible job-shop scheduling problem （FJSP）, each operation has to be assigned to a machine from a set of capable machines before alocating the assigned operations on all machines. To solve the multi-objective FJSP, the Grantt graph oriented string representation （GOSR） and the basic manipulation of the genetic algorithm operator are presented. An integrated operator genetic algorithm （IOGA） and its process are described. Comparison between computational results and the latest research shows that the proposed algorithm is effective in reducing the total workload of all machines, the makespan and the critical machine workload.
基金funded by National Key Research and Development Program Projects of China under Grant No.2020YFB1713500.
文摘To address the issue that hybrid flow shop production struggles to handle order disturbance events,a dynamic scheduling model was constructed.The model takes minimizing the maximum makespan,delivery time deviation,and scheme deviation degree as the optimization objectives.An adaptive dynamic scheduling strategy based on the degree of order disturbance is proposed.An improved multi-objective Grey Wolf(IMOGWO)optimization algorithm is designed by combining the“job-machine”two-layer encoding strategy,the timing-driven two-stage decoding strategy,the opposition-based learning initialization population strategy,the POX crossover strategy,the dualoperation dynamic mutation strategy,and the variable neighborhood search strategy for problem solving.A variety of test cases with different scales were designed,and ablation experiments were conducted to verify the effectiveness of the improved strategies.The results show that each improved strategy can effectively enhance the performance of the IMOGWO.Additionally,performance analysis was conducted by comparing the proposed algorithm with three mature and classical algorithms.The results demonstrate that the proposed algorithm exhibits superior performance in solving the hybrid flow-shop scheduling problem(HFSP).Case validations were conducted for different types of order disturbance scenarios.The results demonstrate that the proposed adaptive dynamic scheduling strategy and the IMOGWO algorithm can effectively address order disturbance events.They enable rapid response to order disturbance while ensuring the stability of the production system.
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.
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 National Natural Science Foundation of China(61374186)。
文摘In response to the challenges faced by unmanned swarms in mountain obstacle-breaching missions within complex terrains,such as poor task-resource coupling,lengthy solution generation times,and poor inter-platform collaboration,an unmanned swarm scheduling strategy tailored is proposed for mountain obstacle-breaching missions.Initially,by formalizing the descriptions of obstacle breaching operations,the swarm,and obstacle targets,an optimization model is constructed with the objectives of expected global benefit,timeliness,and task completion degree.A meta-task decomposition and reassembly strategy is then introduced to more precisely match the capabilities of unmanned platforms with task requirements.Additionally,a meta-task decomposition optimization model and a meta-task allocation operator are incorporated to achieve efficient allocation of swarm resources and collaborative scheduling.Simulation results demonstrate that the model can accurately generate reasonable and feasible obstacle breaching execution plans for unmanned swarms based on specific task requirements and environmental conditions.Moreover,compared to conventional strategies,the proposed strategy enhances task completion degree and expected returns while reducing the execution time of the plans.
文摘Community detection is one of the most fundamental applications in understanding the structure of complicated networks.Furthermore,it is an important approach to identifying closely linked clusters of nodes that may represent underlying patterns and relationships.Networking structures are highly sensitive in social networks,requiring advanced techniques to accurately identify the structure of these communities.Most conventional algorithms for detecting communities perform inadequately with complicated networks.In addition,they miss out on accurately identifying clusters.Since single-objective optimization cannot always generate accurate and comprehensive results,as multi-objective optimization can.Therefore,we utilized two objective functions that enable strong connections between communities and weak connections between them.In this study,we utilized the intra function,which has proven effective in state-of-the-art research studies.We proposed a new inter-function that has demonstrated its effectiveness by making the objective of detecting external connections between communities is to make them more distinct and sparse.Furthermore,we proposed a Multi-Objective community strength enhancement algorithm(MOCSE).The proposed algorithm is based on the framework of the Multi-Objective Evolutionary Algorithm with Decomposition(MOEA/D),integrated with a new heuristic mutation strategy,community strength enhancement(CSE).The results demonstrate that the model is effective in accurately identifying community structures while also being computationally efficient.The performance measures used to evaluate the MOEA/D algorithm in our work are normalized mutual information(NMI)and modularity(Q).It was tested using five state-of-the-art algorithms on social networks,comprising real datasets(Zachary,Dolphin,Football,Krebs,SFI,Jazz,and Netscience),as well as twenty synthetic datasets.These results provide the robustness and practical value of the proposed algorithm in multi-objective community identification.
基金supported by the 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.
文摘The proliferation of carrier aircraft and the integration of unmanned aerial vehicles(UAVs)on aircraft carriers present new challenges to the automation of launch and recovery operations.This paper investigates a collaborative scheduling problem inherent to the operational processes of carrier aircraft,where launch and recovery tasks are conducted concurrently on the flight deck.The objective is to minimize the cumulative weighted waiting time in the air for recovering aircraft and the cumulative weighted delay time for launching aircraft.To tackle this challenge,a multiple population self-adaptive differential evolution(MPSADE)algorithm is proposed.This method features a self-adaptive parameter updating mechanism that is contingent upon population diversity,an asynchronous updating scheme,an individual migration operator,and a global crossover mechanism.Additionally,comprehensive experiments are conducted to validate the effectiveness of the proposed model and algorithm.Ultimately,a comparative analysis with existing operation modes confirms the enhanced efficiency of the collaborative operation mode.
