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 recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However,...In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.展开更多
Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been dev...Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been developed with the use of different algorithmic strategies,evolutionary operators,and constraint-handling techniques.The performance of CMOEAs may be heavily dependent on the operators used,however,it is usually difficult to select suitable operators for the problem at hand.Hence,improving operator selection is promising and necessary for CMOEAs.This work proposes an online operator selection framework assisted by Deep Reinforcement Learning.The dynamics of the population,including convergence,diversity,and feasibility,are regarded as the state;the candidate operators are considered as actions;and the improvement of the population state is treated as the reward.By using a Q-network to learn a policy to estimate the Q-values of all actions,the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance.The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems.The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.展开更多
To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained ...To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained functions are combined to be an objective function.During the evolutionary process,the current optimal solution is found and treated as the reference point to divide the population into three sub-populations:one feasible and two infeasible ones.Different evolutionary operations of single or multi-objective optimization are respectively performed in each sub-population with elite strategy.Thirteen famous benchmark functions are selected to evaluate the performance of PEAES in comparison of other three optimization methods.The results show the proposed method is valid in efficiency,precision and probability for solving single-objective constrained optimization problems.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
Financial market has systemic complexity and uncertainty.For investors,return and risk often coexist.How to rationally allocate funds into different assets and achieve excess returns with effectively controlling risk ...Financial market has systemic complexity and uncertainty.For investors,return and risk often coexist.How to rationally allocate funds into different assets and achieve excess returns with effectively controlling risk are main problems to be solved in the field of portfolio optimization(PO).At present,due to the influence of modeling and algorithm solving,the PO models established by many researchers are still mainly focused on single-stage single-objective models or single-stage multiobjective models.PO is actually considered as a multi-stage multi-objective optimization problem in real investment scenarios.It is more difficult than the previous single-stage PO model for meeting the realistic requirements.In this paper,the authors proposed a mean-improved stable tail adjusted return ratio-maximum drawdown rate(M-ISTARR-MD)PO model which effectively characterizes the real investment scenario.In order to solve the multi-stage multi-objective PO model with complex multi-constraints,the authors designed a multi-stage constrained multi-objective evolutionary algorithm with orthogonal learning(MSCMOEA-OL).Comparing with four well-known intelligence algorithms,the MSCMOEA-OL algorithm has competitive advantages in solving the M-ISTARR-MD model on the proposed constructed carbon neutral stock dataset.This paper provides a new way to construct and solve the complex PO model.展开更多
Combined sewer networks carry wastewater and stormwater together.Capacity limitation of these sewer networks results in combined sewer overflows(CSOs)during high-intensity storms.Untreated CSOs when directly discharge...Combined sewer networks carry wastewater and stormwater together.Capacity limitation of these sewer networks results in combined sewer overflows(CSOs)during high-intensity storms.Untreated CSOs when directly discharged to the nearby natural water bodies cause many environmental problems.Controlling existing urban sewer networks is one possible way of addressing the issues in urban wastewater systems.However,it is still a challenge,when considering the receiving water quality effects.This paper presents an evolutionary constrained multi-objective optimization approach to control the existing combined sewer networks.The control of online storage tanks was taken into account when controlling the combined sewer network.The developed multi-objective approach considers two important objectives,i.e.the pollution load to the receiving water from CSOs and the cost of the wastewater treatment.The proposed optimization algorithm is applied here to a realistic interceptor sewer system to demonstrate its effectiveness.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61972040the Science and Technology Research and Development Project funded by China Railway Material Trade Group Luban Company.
文摘In a wide range of engineering applications,complex constrained multi-objective optimization problems(CMOPs)present significant challenges,as the complexity of constraints often hampers algorithmic convergence and reduces population diversity.To address these challenges,we propose a novel algorithm named Constraint IntensityDriven Evolutionary Multitasking(CIDEMT),which employs a two-stage,tri-task framework to dynamically integrates problem structure and knowledge transfer.In the first stage,three cooperative tasks are designed to explore the Constrained Pareto Front(CPF),the Unconstrained Pareto Front(UPF),and theε-relaxed constraint boundary,respectively.A CPF-UPF relationship classifier is employed to construct a problem-type-aware evolutionary strategy pool.At the end of the first stage,each task selects strategies from this strategy pool based on the specific type of problem,thereby guiding the subsequent evolutionary process.In the second stage,while each task continues to evolve,aτ-driven knowledge transfer mechanism is introduced to selectively incorporate effective solutions across tasks.enhancing the convergence and feasibility of the main task.Extensive experiments conducted on 32 benchmark problems from three test suites(LIRCMOP,DASCMOP,and DOC)demonstrate that CIDEMT achieves the best Inverted Generational Distance(IGD)values on 24 problems and the best Hypervolume values(HV)on 22 problems.Furthermore,CIDEMT significantly outperforms six state-of-the-art constrained multi-objective evolutionary algorithms(CMOEAs).These results confirm CIDEMT’s superiority in promoting convergence,diversity,and robustness in solving complex CMOPs.
基金partly supported by the National Natural Science Foundation of China(62076225)。
文摘In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.
基金the National Natural Science Foundation of China(62076225,62073300)the Natural Science Foundation for Distinguished Young Scholars of Hubei(2019CFA081)。
文摘Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been developed with the use of different algorithmic strategies,evolutionary operators,and constraint-handling techniques.The performance of CMOEAs may be heavily dependent on the operators used,however,it is usually difficult to select suitable operators for the problem at hand.Hence,improving operator selection is promising and necessary for CMOEAs.This work proposes an online operator selection framework assisted by Deep Reinforcement Learning.The dynamics of the population,including convergence,diversity,and feasibility,are regarded as the state;the candidate operators are considered as actions;and the improvement of the population state is treated as the reward.By using a Q-network to learn a policy to estimate the Q-values of all actions,the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance.The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems.The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.
文摘To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained functions are combined to be an objective function.During the evolutionary process,the current optimal solution is found and treated as the reference point to divide the population into three sub-populations:one feasible and two infeasible ones.Different evolutionary operations of single or multi-objective optimization are respectively performed in each sub-population with elite strategy.Thirteen famous benchmark functions are selected to evaluate the performance of PEAES in comparison of other three optimization methods.The results show the proposed method is valid in efficiency,precision and probability for solving single-objective constrained optimization problems.
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 under Grant No.61973042Beijing Natural Science Foundation under Grant No.1202020。
文摘Financial market has systemic complexity and uncertainty.For investors,return and risk often coexist.How to rationally allocate funds into different assets and achieve excess returns with effectively controlling risk are main problems to be solved in the field of portfolio optimization(PO).At present,due to the influence of modeling and algorithm solving,the PO models established by many researchers are still mainly focused on single-stage single-objective models or single-stage multiobjective models.PO is actually considered as a multi-stage multi-objective optimization problem in real investment scenarios.It is more difficult than the previous single-stage PO model for meeting the realistic requirements.In this paper,the authors proposed a mean-improved stable tail adjusted return ratio-maximum drawdown rate(M-ISTARR-MD)PO model which effectively characterizes the real investment scenario.In order to solve the multi-stage multi-objective PO model with complex multi-constraints,the authors designed a multi-stage constrained multi-objective evolutionary algorithm with orthogonal learning(MSCMOEA-OL).Comparing with four well-known intelligence algorithms,the MSCMOEA-OL algorithm has competitive advantages in solving the M-ISTARR-MD model on the proposed constructed carbon neutral stock dataset.This paper provides a new way to construct and solve the complex PO model.
文摘Combined sewer networks carry wastewater and stormwater together.Capacity limitation of these sewer networks results in combined sewer overflows(CSOs)during high-intensity storms.Untreated CSOs when directly discharged to the nearby natural water bodies cause many environmental problems.Controlling existing urban sewer networks is one possible way of addressing the issues in urban wastewater systems.However,it is still a challenge,when considering the receiving water quality effects.This paper presents an evolutionary constrained multi-objective optimization approach to control the existing combined sewer networks.The control of online storage tanks was taken into account when controlling the combined sewer network.The developed multi-objective approach considers two important objectives,i.e.the pollution load to the receiving water from CSOs and the cost of the wastewater treatment.The proposed optimization algorithm is applied here to a realistic interceptor sewer system to demonstrate its effectiveness.
