Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they prop...Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.展开更多
The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worke...The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.展开更多
Deep learning for topology optimization has been extensively studied to reduce the cost of calculation in recent years.However,the loss function of the above method is mainly based on pixel-wise errors from the image ...Deep learning for topology optimization has been extensively studied to reduce the cost of calculation in recent years.However,the loss function of the above method is mainly based on pixel-wise errors from the image perspective,which cannot embed the physical knowledge of topology optimization.Therefore,this paper presents an improved deep learning model to alleviate the above difficulty effectively.The feature pyramid network(FPN),a kind of deep learning model,is trained to learn the inherent physical law of topology optimization itself,of which the loss function is composed of pixel-wise errors and physical constraints.Since the calculation of physical constraints requires finite element analysis(FEA)with high calculating costs,the strategy of adjusting the time when physical constraints are added is proposed to achieve the balance between the training cost and the training effect.Then,two classical topology optimization problems are investigated to verify the effectiveness of the proposed method.The results show that the developed model using a small number of samples can quickly obtain the optimization structure without any iteration,which has not only high pixel-wise accuracy but also good physical performance.展开更多
The application of multiple UAVs in complicated tasks has been widely explored in recent years.Due to the advantages of flexibility,cheapness and consistence,the performance of heterogeneous multi-UAVs with proper coo...The application of multiple UAVs in complicated tasks has been widely explored in recent years.Due to the advantages of flexibility,cheapness and consistence,the performance of heterogeneous multi-UAVs with proper cooperative task allocation is superior to over the single UAV.Accordingly,several constraints should be satisfied to realize the efficient cooperation,such as special time-window,variant equipment,specified execution sequence.Hence,a proper task allocation in UAVs is the crucial point for the final success.The task allocation problem of the heterogeneous UAVs can be formulated as a multi-objective optimization problem coupled with the UAV dynamics.To this end,a multi-layer encoding strategy and a constraint scheduling method are designed to handle the critical logical and physical constraints.In addition,four optimization objectives:completion time,target reward,UAV damage,and total range,are introduced to evaluate various allocation plans.Subsequently,to efficiently solve the multi-objective optimization problem,an improved multi-objective quantum-behaved particle swarm optimization(IMOQPSO)algorithm is proposed.During this algorithm,a modified solution evaluation method is designed to guide algorithmic evolution;both the convergence and distribution of particles are considered comprehensively;and boundary solutions which may produce some special allocation plans are preserved.Moreover,adaptive parameter control and mixed update mechanism are also introduced in this algorithm.Finally,both the proposed model and algorithm are verified by simulation experiments.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
This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search pro...This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.展开更多
A global routing algorithm with performance optimization under multi constraints is proposed,which studies RLC coupling noise,timing performance,and routability simultaneously at global routing level.The algorithm is...A global routing algorithm with performance optimization under multi constraints is proposed,which studies RLC coupling noise,timing performance,and routability simultaneously at global routing level.The algorithm is implemented and the global router is called CEE Gr.The CEE Gr is tested on MCNC benchmarks and the experimental results are promising.展开更多
Rotor airfoil design is investigated in this paper. There are many difficulties for this highdimensional multi-objective problem when traditional multi-objective optimization methods are used. Therefore, a multi-layer...Rotor airfoil design is investigated in this paper. There are many difficulties for this highdimensional multi-objective problem when traditional multi-objective optimization methods are used. Therefore, a multi-layer hierarchical constraint method is proposed by coupling principal component analysis(PCA) dimensionality reduction and e-constraint method to translate the original high-dimensional problem into a bi-objective problem. This paper selects the main design objectives by conducting PCA to the preliminary solution of original problem with consideration of the priority of design objectives. According to the e-constraint method, the design model is established by treating the two top-ranking design goals as objective and others as variable constraints. A series of bi-objective Pareto curves will be obtained by changing the variable constraints, and the favorable solution can be obtained by analyzing Pareto curve spectrum. This method is applied to the rotor airfoil design and makes great improvement in aerodynamic performance. It is shown that the method is convenient and efficient, beyond which, it facilitates decision-making of the highdimensional multi-objective engineering problem.展开更多
To cope with the task scheduling problem under multi-task and transportation consideration in large-scale service oriented manufacturing systems(SOMS), a service allocation optimization mathematical model was establis...To cope with the task scheduling problem under multi-task and transportation consideration in large-scale service oriented manufacturing systems(SOMS), a service allocation optimization mathematical model was established, and then a hybrid discrete particle swarm optimization-genetic algorithm(HDPSOGA) was proposed. In SOMS, each resource involved in the whole life cycle of a product, whether it is provided by a piece of software or a hardware device, is encapsulated into a service. So, the transportation during production of a task should be taken into account because the hard-services selected are possibly provided by various providers in different areas. In the service allocation optimization mathematical model, multi-task and transportation were considered simultaneously. In the proposed HDPSOGA algorithm, integer coding method was applied to establish the mapping between the particle location matrix and the service allocation scheme. The position updating process was performed according to the cognition part, the social part, and the previous velocity and position while introducing the crossover and mutation idea of genetic algorithm to fit the discrete space. Finally, related simulation experiments were carried out to compare with other two previous algorithms. The results indicate the effectiveness and efficiency of the proposed hybrid algorithm.展开更多
In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the ...In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the oscillation during the homing phase for missiles with low damping.In addition,physical constraints,which can affect the performance of the missile interception,such as acceleration limit,seeker’s look angle,and look angle rate constraints are considered.The integrated guidance and control problem is formulated as a convex quadratic optimization problem with equality and inequality constraints,and the solution is obtained by a primal–dual interior point method.The performance of the proposed method is verified through several numerical examples.展开更多
This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated...This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated as a constraint multi-objective optimization problem, which is solved by a multi-objective genetic algorithm, NSGA-II. Monte Carlo Simulation (MCS) method, combined with Latin Hypercube Sampling (LHS), is applied to evaluate the stochastic system performance. The potential of the proposed method has been demonstrated by a conceptual system design. A comparative study between the proposed robust method and the deterministic method presented in literature has been conducted. The results indicate that the proposed method can find a large mount of Pareto optimal system configurations with better compromising performance than the deterministic method. The trade-off information may be derived by a systematical comparison of these configurations. The proposed robust design method should be useful for hybrid power systems that require both optimality and robustness.展开更多
The allocation of heterogeneous battlefield resources is crucial in Command and Control(C2).Balancing multiple competing objectives under complex constraints so as to provide decisionmakers with diverse feasible candi...The allocation of heterogeneous battlefield resources is crucial in Command and Control(C2).Balancing multiple competing objectives under complex constraints so as to provide decisionmakers with diverse feasible candidate decision schemes remains an urgent challenge.Based on these requirements,a constrained multi-objective multi-stage weapon-target assignment(CMOMWTA)model is established in this paper.To solve this problem,three constraint-feature-guided multi-objective evolutionary algorithms(CFG-MOEAs)are proposed under three typical multi-objective evolutionary frameworks(i.e.,NSGA-Ⅱ,NSGA-Ⅲ,and MOEA/D)to obtain various high-quality candidate decision schemes.Firstly,a constraint-feature-guided reproduction strategy incorporating crossover,mutation,and repair is developed to handle complex constraints.It extracts common row and column features from different linear constraints to generate the feasible offspring population.Then,a variable-length integer encoding method is adopted to concisely denote the decision schemes.Moreover,a hybrid initialization method incorporating both heuristic methods and random sampling is designed to better guide the population.Systemic experiments are conducted on three CFG-MOEAs to verify their effectiveness.The superior algorithm CFG-NSGA-Ⅱamong three CFG-MOEAs is compared with two state-of-the-art CMOMWTA algorithms,and extensive experimental results demonstrate the effectiveness and superiority of CFG-NSGA-Ⅱ.展开更多
Performance improvement of heat exchangers and the corresponding thermal systems benefits energy conservation, which is a multi-parameters, multi-objectives and multi-levels optimization problem. However, the optimize...Performance improvement of heat exchangers and the corresponding thermal systems benefits energy conservation, which is a multi-parameters, multi-objectives and multi-levels optimization problem. However, the optimized results of heat exchangers with improper decision parameters or objectives do not contribute and even against thermal system performance improvement. After deducing the inherent overall relations between the decision parameters and designing requirements for a typical heat exchanger network and by applying the Lagrange multiplier method, several different optimization equation sets are derived, the solutions of which offer the optimal decision parameters corresponding to different specific optimization objectives, respectively. Comparison of the optimized results clarifies that it should take the whole system, rather than individual heat exchangers, into account to optimize the fluid heat capacity rates and the heat transfer areas to minimize the total heat transfer area, the total heat capacity rate or the total entropy generation rate, while increasing the heat transfer coefficients of individual heat exchangers with different given heat capacity rates benefits the system performance. Besides, different objectives result in different optimization results due to their different intentions, and thus the optimization objectives should be chosen reasonably based on practical applications, where the inherent overall physical constraints of decision parameters are necessary and essential to be built in advance.展开更多
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supported by the Natural Science Foundation of Anhui Province(Grant Number 2208085MG181)the Science Research Project of Higher Education Institutions in Anhui Province,Philosophy and Social Sciences(Grant Number 2023AH051063)the Open Fund of Key Laboratory of Anhui Higher Education Institutes(Grant Number CS2021-ZD01).
文摘The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.
基金This work was supported in part by National Natural Science Foundation of China under Grant Nos.11725211,52005505,and 62001502Post-graduate Scientific Research Innovation Project of Hunan Province under Grant No.CX20200023.
文摘Deep learning for topology optimization has been extensively studied to reduce the cost of calculation in recent years.However,the loss function of the above method is mainly based on pixel-wise errors from the image perspective,which cannot embed the physical knowledge of topology optimization.Therefore,this paper presents an improved deep learning model to alleviate the above difficulty effectively.The feature pyramid network(FPN),a kind of deep learning model,is trained to learn the inherent physical law of topology optimization itself,of which the loss function is composed of pixel-wise errors and physical constraints.Since the calculation of physical constraints requires finite element analysis(FEA)with high calculating costs,the strategy of adjusting the time when physical constraints are added is proposed to achieve the balance between the training cost and the training effect.Then,two classical topology optimization problems are investigated to verify the effectiveness of the proposed method.The results show that the developed model using a small number of samples can quickly obtain the optimization structure without any iteration,which has not only high pixel-wise accuracy but also good physical performance.
基金Project(61801495)supported by the National Natural Science Foundation of China
文摘The application of multiple UAVs in complicated tasks has been widely explored in recent years.Due to the advantages of flexibility,cheapness and consistence,the performance of heterogeneous multi-UAVs with proper cooperative task allocation is superior to over the single UAV.Accordingly,several constraints should be satisfied to realize the efficient cooperation,such as special time-window,variant equipment,specified execution sequence.Hence,a proper task allocation in UAVs is the crucial point for the final success.The task allocation problem of the heterogeneous UAVs can be formulated as a multi-objective optimization problem coupled with the UAV dynamics.To this end,a multi-layer encoding strategy and a constraint scheduling method are designed to handle the critical logical and physical constraints.In addition,four optimization objectives:completion time,target reward,UAV damage,and total range,are introduced to evaluate various allocation plans.Subsequently,to efficiently solve the multi-objective optimization problem,an improved multi-objective quantum-behaved particle swarm optimization(IMOQPSO)algorithm is proposed.During this algorithm,a modified solution evaluation method is designed to guide algorithmic evolution;both the convergence and distribution of particles are considered comprehensively;and boundary solutions which may produce some special allocation plans are preserved.Moreover,adaptive parameter control and mixed update mechanism are also introduced in this algorithm.Finally,both the proposed model and algorithm are verified by simulation experiments.
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.
文摘This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.
文摘A global routing algorithm with performance optimization under multi constraints is proposed,which studies RLC coupling noise,timing performance,and routability simultaneously at global routing level.The algorithm is implemented and the global router is called CEE Gr.The CEE Gr is tested on MCNC benchmarks and the experimental results are promising.
基金supported by the National Natural Science Foundation of China (No. 11402288 and 11372254)the National Basic Research Program of China (No. 2014CB744804)
文摘Rotor airfoil design is investigated in this paper. There are many difficulties for this highdimensional multi-objective problem when traditional multi-objective optimization methods are used. Therefore, a multi-layer hierarchical constraint method is proposed by coupling principal component analysis(PCA) dimensionality reduction and e-constraint method to translate the original high-dimensional problem into a bi-objective problem. This paper selects the main design objectives by conducting PCA to the preliminary solution of original problem with consideration of the priority of design objectives. According to the e-constraint method, the design model is established by treating the two top-ranking design goals as objective and others as variable constraints. A series of bi-objective Pareto curves will be obtained by changing the variable constraints, and the favorable solution can be obtained by analyzing Pareto curve spectrum. This method is applied to the rotor airfoil design and makes great improvement in aerodynamic performance. It is shown that the method is convenient and efficient, beyond which, it facilitates decision-making of the highdimensional multi-objective engineering problem.
基金Project(2012B091100444)supported by the Production,Education and Research Cooperative Program of Guangdong Province and Ministry of Education,ChinaProject(2013ZM0091)supported by Fundamental Research Funds for the Central Universities of China
文摘To cope with the task scheduling problem under multi-task and transportation consideration in large-scale service oriented manufacturing systems(SOMS), a service allocation optimization mathematical model was established, and then a hybrid discrete particle swarm optimization-genetic algorithm(HDPSOGA) was proposed. In SOMS, each resource involved in the whole life cycle of a product, whether it is provided by a piece of software or a hardware device, is encapsulated into a service. So, the transportation during production of a task should be taken into account because the hard-services selected are possibly provided by various providers in different areas. In the service allocation optimization mathematical model, multi-task and transportation were considered simultaneously. In the proposed HDPSOGA algorithm, integer coding method was applied to establish the mapping between the particle location matrix and the service allocation scheme. The position updating process was performed according to the cognition part, the social part, and the previous velocity and position while introducing the crossover and mutation idea of genetic algorithm to fit the discrete space. Finally, related simulation experiments were carried out to compare with other two previous algorithms. The results indicate the effectiveness and efficiency of the proposed hybrid algorithm.
文摘In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the oscillation during the homing phase for missiles with low damping.In addition,physical constraints,which can affect the performance of the missile interception,such as acceleration limit,seeker’s look angle,and look angle rate constraints are considered.The integrated guidance and control problem is formulated as a convex quadratic optimization problem with equality and inequality constraints,and the solution is obtained by a primal–dual interior point method.The performance of the proposed method is verified through several numerical examples.
文摘This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated as a constraint multi-objective optimization problem, which is solved by a multi-objective genetic algorithm, NSGA-II. Monte Carlo Simulation (MCS) method, combined with Latin Hypercube Sampling (LHS), is applied to evaluate the stochastic system performance. The potential of the proposed method has been demonstrated by a conceptual system design. A comparative study between the proposed robust method and the deterministic method presented in literature has been conducted. The results indicate that the proposed method can find a large mount of Pareto optimal system configurations with better compromising performance than the deterministic method. The trade-off information may be derived by a systematical comparison of these configurations. The proposed robust design method should be useful for hybrid power systems that require both optimality and robustness.
基金supported by the National Science Fund of China under Grant Nos.62425304 and 62025301the Basic Science Center Programs of NSFC under Grant No.62088101+1 种基金Shanghai Municipal Science and Technology Major Project under Grant No.2021SHZDZX0100Shanghai Municipal Commission of Science and Technology Project under Grant No.19511132101。
文摘The allocation of heterogeneous battlefield resources is crucial in Command and Control(C2).Balancing multiple competing objectives under complex constraints so as to provide decisionmakers with diverse feasible candidate decision schemes remains an urgent challenge.Based on these requirements,a constrained multi-objective multi-stage weapon-target assignment(CMOMWTA)model is established in this paper.To solve this problem,three constraint-feature-guided multi-objective evolutionary algorithms(CFG-MOEAs)are proposed under three typical multi-objective evolutionary frameworks(i.e.,NSGA-Ⅱ,NSGA-Ⅲ,and MOEA/D)to obtain various high-quality candidate decision schemes.Firstly,a constraint-feature-guided reproduction strategy incorporating crossover,mutation,and repair is developed to handle complex constraints.It extracts common row and column features from different linear constraints to generate the feasible offspring population.Then,a variable-length integer encoding method is adopted to concisely denote the decision schemes.Moreover,a hybrid initialization method incorporating both heuristic methods and random sampling is designed to better guide the population.Systemic experiments are conducted on three CFG-MOEAs to verify their effectiveness.The superior algorithm CFG-NSGA-Ⅱamong three CFG-MOEAs is compared with two state-of-the-art CMOMWTA algorithms,and extensive experimental results demonstrate the effectiveness and superiority of CFG-NSGA-Ⅱ.
基金supported by the National Natural Science Foundation of China(Grant Nos.51422603,51356001&51321002)the National Basic Research Program of China("973"Project)(Grant No.2013CB228301)
文摘Performance improvement of heat exchangers and the corresponding thermal systems benefits energy conservation, which is a multi-parameters, multi-objectives and multi-levels optimization problem. However, the optimized results of heat exchangers with improper decision parameters or objectives do not contribute and even against thermal system performance improvement. After deducing the inherent overall relations between the decision parameters and designing requirements for a typical heat exchanger network and by applying the Lagrange multiplier method, several different optimization equation sets are derived, the solutions of which offer the optimal decision parameters corresponding to different specific optimization objectives, respectively. Comparison of the optimized results clarifies that it should take the whole system, rather than individual heat exchangers, into account to optimize the fluid heat capacity rates and the heat transfer areas to minimize the total heat transfer area, the total heat capacity rate or the total entropy generation rate, while increasing the heat transfer coefficients of individual heat exchangers with different given heat capacity rates benefits the system performance. Besides, different objectives result in different optimization results due to their different intentions, and thus the optimization objectives should be chosen reasonably based on practical applications, where the inherent overall physical constraints of decision parameters are necessary and essential to be built in advance.
