The lower bound of maximum predictable time can be formulated into a constrained nonlinear opti- mization problem, and the traditional solutions to this problem are the filtering method and the conditional nonlinear o...The lower bound of maximum predictable time can be formulated into a constrained nonlinear opti- mization problem, and the traditional solutions to this problem are the filtering method and the conditional nonlinear optimal perturbation （CNOP） method. Usually, the CNOP method is implemented with the help of a gradient descent algorithm based on the adjoint method, which is named the ADJ-CNOP. However, with the increasing improvement of actual prediction models, more and more physical processes are taken into consideration in models in the form of parameterization, thus giving rise to the on–off switch problem, which tremendously affects the effectiveness of the conventional gradient descent algorithm based on the ad- joint method. In this study, we attempted to apply a genetic algorithm （GA） to the CNOP method, named GA-CNOP, to solve the predictability problems involving on–off switches. As the precision of the filtering method depends uniquely on the division of the constraint region, its results were taken as benchmarks, and a series of comparisons between the ADJ-CNOP and the GA-CNOP were performed for the modified Lorenz equation. Results show that the GA-CNOP can always determine the accurate lower bound of maximum predictable time, even in non-smooth cases, while the ADJ-CNOP, owing to the effect of on–off switches, often yields the incorrect lower bound of maximum predictable time. Therefore, in non-smooth cases, using GAs to solve predictability problems is more effective than using the conventional optimization algorithm based on gradients, as long as genetic operators in GAs are properly configured.展开更多
There are many population-based stochastic search algorithms for solving optimization problems. However, the universality and robustness of these algorithms are still unsatisfactory. This paper proposes an enhanced se...There are many population-based stochastic search algorithms for solving optimization problems. However, the universality and robustness of these algorithms are still unsatisfactory. This paper proposes an enhanced self-adaptiveevolutionary algorithm （ESEA） to overcome the demerits above. In the ESEA, four evolutionary operators are designed to enhance the evolutionary structure. Besides, the ESEA employs four effective search strategies under the framework of the self-adaptive learning. Four groups of the experiments are done to find out the most suitable parameter values for the ESEA. In order to verify the performance of the proposed algorithm, 26 state-of-the-art test functions are solved by the ESEA and its competitors. The experimental results demonstrate that the universality and robustness of the ESEA out-perform its competitors.展开更多
In this paper, we first reformulate the max-min dispersion problem as a saddle-point problem. Specifically, we introduce an auxiliary problem whose optimum value gives an upper bound on that of the original problem. T...In this paper, we first reformulate the max-min dispersion problem as a saddle-point problem. Specifically, we introduce an auxiliary problem whose optimum value gives an upper bound on that of the original problem. Then we propose the saddle-point problem to be solved by an adaptive custom proximal point algorithm. Numerical results show that the proposed algorithm is efficient.展开更多
基金supported bythe National Natural Science Foundation of China(Grant Nos40975063 and 40830955)
文摘The lower bound of maximum predictable time can be formulated into a constrained nonlinear opti- mization problem, and the traditional solutions to this problem are the filtering method and the conditional nonlinear optimal perturbation （CNOP） method. Usually, the CNOP method is implemented with the help of a gradient descent algorithm based on the adjoint method, which is named the ADJ-CNOP. However, with the increasing improvement of actual prediction models, more and more physical processes are taken into consideration in models in the form of parameterization, thus giving rise to the on–off switch problem, which tremendously affects the effectiveness of the conventional gradient descent algorithm based on the ad- joint method. In this study, we attempted to apply a genetic algorithm （GA） to the CNOP method, named GA-CNOP, to solve the predictability problems involving on–off switches. As the precision of the filtering method depends uniquely on the division of the constraint region, its results were taken as benchmarks, and a series of comparisons between the ADJ-CNOP and the GA-CNOP were performed for the modified Lorenz equation. Results show that the GA-CNOP can always determine the accurate lower bound of maximum predictable time, even in non-smooth cases, while the ADJ-CNOP, owing to the effect of on–off switches, often yields the incorrect lower bound of maximum predictable time. Therefore, in non-smooth cases, using GAs to solve predictability problems is more effective than using the conventional optimization algorithm based on gradients, as long as genetic operators in GAs are properly configured.
基金supported by the Aviation Science Funds of China(2010ZC13012)the Fund of Jiangsu Innovation Program for Graduate Education (CXLX11 0203)
文摘There are many population-based stochastic search algorithms for solving optimization problems. However, the universality and robustness of these algorithms are still unsatisfactory. This paper proposes an enhanced self-adaptiveevolutionary algorithm （ESEA） to overcome the demerits above. In the ESEA, four evolutionary operators are designed to enhance the evolutionary structure. Besides, the ESEA employs four effective search strategies under the framework of the self-adaptive learning. Four groups of the experiments are done to find out the most suitable parameter values for the ESEA. In order to verify the performance of the proposed algorithm, 26 state-of-the-art test functions are solved by the ESEA and its competitors. The experimental results demonstrate that the universality and robustness of the ESEA out-perform its competitors.
文摘In this paper, we first reformulate the max-min dispersion problem as a saddle-point problem. Specifically, we introduce an auxiliary problem whose optimum value gives an upper bound on that of the original problem. Then we propose the saddle-point problem to be solved by an adaptive custom proximal point algorithm. Numerical results show that the proposed algorithm is efficient.
文摘生产规划过程需要同时考虑装配序列规划(Assembly Sequence Planning,ASP)和装配线平衡(Assembly Line Balancing,ALB)。针对ASP和ALB的多项式复杂程度的非确定性问题(Non-Deterministic Polynomial Hard,NP难题)及二者耦合问题,以产品结构图为基础,结合物料清单(Bill of Material,BOM)层次图构建装配约束矩阵,分析产品内部各子装配体独立装配可行性,并对子装配体分拆以获得可行的装配序列矩阵。其次,以工作站最大装配时间、装配方向和工具切换次数、站间平衡为目标,构建综合ASP和ALB的联合规划模型。提出基于Pareto解集的混合人工鱼群算法(Hybrid Artificial Fish Swarm Algorithm,HAFSA),采用自适应视野串行觅食,减少并行觅食重复搜索。对人工鱼群算法得到的装配序列进行粒子群优化(Particle Swarm Optimization,PSO)操作,提高跳出局部最优的可能。将所提算法应用于某装配实例,与基本AFSA、PSO算法对比,验证算法有效性。
