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
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 maximum principle is a basic qualitative property of the solution of second-order elliptic boundary value problems.The preservation of the qualitative characteristics,such as the maximum principle,in discrete mode...The maximum principle is a basic qualitative property of the solution of second-order elliptic boundary value problems.The preservation of the qualitative characteristics,such as the maximum principle,in discrete model is one of the key requirements.It is well known that standard linear finite element solution does not satisfy maximum principle on general triangular meshes in 2D.In this paper we consider how to enforce discrete maximum principle for linear finite element solutions for the linear second-order self-adjoint elliptic equation.First approach is based on repair technique,which is a posteriori correction of the discrete solution.Second method is based on constrained optimization.Numerical tests that include anisotropic cases demonstrate how our method works for problems for which the standard finite element methods produce numerical solutions that violate the discrete maximum principle.展开更多
In this paper, we study variational discretization for the constrained optimal control problem governed by convection dominated diffusion equations, where the state equation is approximated by the edge stabilization G...In this paper, we study variational discretization for the constrained optimal control problem governed by convection dominated diffusion equations, where the state equation is approximated by the edge stabilization Galerkin method. A priori error estimates are derived for the state, the adjoint state and the control. Moreover, residual type a posteriori error estimates in the L^2-norm are obtained. Finally, two numerical experiments are presented to illustrate the theoretical results.展开更多
针对昂贵约束多目标离散优化问题,提出一种基于随机森林和自适应随机排序的昂贵多目标进化算法(a random forest and adaptive stochastic ranking based multi-objective evolutionary algorithm,RFASRMOEA).为了提高代理模型对离散问...针对昂贵约束多目标离散优化问题,提出一种基于随机森林和自适应随机排序的昂贵多目标进化算法(a random forest and adaptive stochastic ranking based multi-objective evolutionary algorithm,RFASRMOEA).为了提高代理模型对离散问题的近似精度,RFASRMOEA采用随机森林作为代理模型辅助进化算法进行搜索.同时,为提升综合性能,提出一种基于平衡适应度评估策略和自适应概率操作的自适应随机排序机制.具体地,平衡适应度评估策略利用种群迭代信息结合所设计的基于目标转移的多样性评估和基于余弦的收敛性评估,充分发掘种群个体潜力.而自适应概率操作通过动态调整随机排序机制的关注点,使得算法在前期探索更多可行域而后期迅速收敛于可行域,进而平衡约束条件的满足与目标函数优化之间的冲突.在测试问题上的实验结果表明,所提出算法在处理昂贵约束多目标离散优化问题时具有较高的竞争力.展开更多
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.
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the National Nuclear Security Administration of the U.S.Department of Energy at Los Alamos National Laboratory under Contract No.DE-AC52-06NA25396the DOE Office of Science Advanced Scientific Computing Research(ASCR)Program in Applied Mathematics Research.The first author has been supported in part by the Czech Ministry of Education projects MSM 6840770022 and LC06052(Necas Center for Mathematical Modeling).
文摘The maximum principle is a basic qualitative property of the solution of second-order elliptic boundary value problems.The preservation of the qualitative characteristics,such as the maximum principle,in discrete model is one of the key requirements.It is well known that standard linear finite element solution does not satisfy maximum principle on general triangular meshes in 2D.In this paper we consider how to enforce discrete maximum principle for linear finite element solutions for the linear second-order self-adjoint elliptic equation.First approach is based on repair technique,which is a posteriori correction of the discrete solution.Second method is based on constrained optimization.Numerical tests that include anisotropic cases demonstrate how our method works for problems for which the standard finite element methods produce numerical solutions that violate the discrete maximum principle.
基金support of the Chinese and German Research Foundations through the Sino-German Workshop on Applied Mathematics held in Hangzhou in October 2007support of the German Research Foundation through the grants DFG06-381 and DFG06-382+1 种基金support of the National Basic Research Program under the Grant 2005CB321701the National Natural Science Foundation of China under the Grant 60474027 and 10771211
文摘In this paper, we study variational discretization for the constrained optimal control problem governed by convection dominated diffusion equations, where the state equation is approximated by the edge stabilization Galerkin method. A priori error estimates are derived for the state, the adjoint state and the control. Moreover, residual type a posteriori error estimates in the L^2-norm are obtained. Finally, two numerical experiments are presented to illustrate the theoretical results.
文摘针对昂贵约束多目标离散优化问题,提出一种基于随机森林和自适应随机排序的昂贵多目标进化算法(a random forest and adaptive stochastic ranking based multi-objective evolutionary algorithm,RFASRMOEA).为了提高代理模型对离散问题的近似精度,RFASRMOEA采用随机森林作为代理模型辅助进化算法进行搜索.同时,为提升综合性能,提出一种基于平衡适应度评估策略和自适应概率操作的自适应随机排序机制.具体地,平衡适应度评估策略利用种群迭代信息结合所设计的基于目标转移的多样性评估和基于余弦的收敛性评估,充分发掘种群个体潜力.而自适应概率操作通过动态调整随机排序机制的关注点,使得算法在前期探索更多可行域而后期迅速收敛于可行域,进而平衡约束条件的满足与目标函数优化之间的冲突.在测试问题上的实验结果表明,所提出算法在处理昂贵约束多目标离散优化问题时具有较高的竞争力.
