Improving numerical forecasting skill in the atmospheric and oceanic sciences by solving optimization problems is an important issue. One such method is to compute the conditional nonlinear optimal perturbation(CNOP),...Improving numerical forecasting skill in the atmospheric and oceanic sciences by solving optimization problems is an important issue. One such method is to compute the conditional nonlinear optimal perturbation(CNOP), which has been applied widely in predictability studies. In this study, the Differential Evolution(DE) algorithm, which is a derivative-free algorithm and has been applied to obtain CNOPs for exploring the uncertainty of terrestrial ecosystem processes, was employed to obtain the CNOPs for finite-dimensional optimization problems with ball constraint conditions using Burgers' equation. The aim was first to test if the CNOP calculated by the DE algorithm is similar to that computed by traditional optimization algorithms, such as the Spectral Projected Gradient(SPG2) algorithm. The second motive was to supply a possible route through which the CNOP approach can be applied in predictability studies in the atmospheric and oceanic sciences without obtaining a model adjoint system, or for optimization problems with non-differentiable cost functions. A projection skill was first explanted to the DE algorithm to calculate the CNOPs. To validate the algorithm, the SPG2 algorithm was also applied to obtain the CNOPs for the same optimization problems. The results showed that the CNOPs obtained by the DE algorithm were nearly the same as those obtained by the SPG2 algorithm in terms of their spatial distributions and nonlinear evolutions. The implication is that the DE algorithm could be employed to calculate the optimal values of optimization problems, especially for non-differentiable and nonlinear optimization problems associated with the atmospheric and oceanic sciences.展开更多
Integrating multiple systems into one has become an important trend in Process Systems Engineering research field since there is strong demand from the modern industries. In this study, a stage-wise superstructurebase...Integrating multiple systems into one has become an important trend in Process Systems Engineering research field since there is strong demand from the modern industries. In this study, a stage-wise superstructurebased method is proposed to synthesize a combined mass and heat exchange network(CM&HEN) which has two parts as the mass exchange network(MEN) and heat exchange network(HEN) involved. To express the possible heat exchange requirements resulted from mass exchange operations, a so called "indistinct HEN superstructure(IHS)", which can contain the all potential matches between streams, is constructed at first. Then, a non-linear programming(NLP) mathematical model is established for the simultaneous synthesis and optimization of networks. Therein, the interaction between mass exchange and heat exchange is modeling formulated.The NLP model has later been examined using an example from literature, and the effectiveness of the proposed method has been demonstrated with the results.展开更多
A process represented by nonlinear multi-parametric binary dynamic system is investigated in this work. This process is characterized by the pseudo Boolean objective functional. Since the transfer functions on the pro...A process represented by nonlinear multi-parametric binary dynamic system is investigated in this work. This process is characterized by the pseudo Boolean objective functional. Since the transfer functions on the process are Boolean functions, the optimal control problem related to the process can be solved by relating between the transfer functions and the objective functional. An analogue of Bellman function for the optimal control problem mentioned is defined and consequently suitable Bellman equation is constructed.展开更多
基金provided by grants from the LASG State Key Laboratory Special Fundthe National Natural Science Foundation of China (Grant Nos. 40905050, 40830955, and 41375111)
文摘Improving numerical forecasting skill in the atmospheric and oceanic sciences by solving optimization problems is an important issue. One such method is to compute the conditional nonlinear optimal perturbation(CNOP), which has been applied widely in predictability studies. In this study, the Differential Evolution(DE) algorithm, which is a derivative-free algorithm and has been applied to obtain CNOPs for exploring the uncertainty of terrestrial ecosystem processes, was employed to obtain the CNOPs for finite-dimensional optimization problems with ball constraint conditions using Burgers' equation. The aim was first to test if the CNOP calculated by the DE algorithm is similar to that computed by traditional optimization algorithms, such as the Spectral Projected Gradient(SPG2) algorithm. The second motive was to supply a possible route through which the CNOP approach can be applied in predictability studies in the atmospheric and oceanic sciences without obtaining a model adjoint system, or for optimization problems with non-differentiable cost functions. A projection skill was first explanted to the DE algorithm to calculate the CNOPs. To validate the algorithm, the SPG2 algorithm was also applied to obtain the CNOPs for the same optimization problems. The results showed that the CNOPs obtained by the DE algorithm were nearly the same as those obtained by the SPG2 algorithm in terms of their spatial distributions and nonlinear evolutions. The implication is that the DE algorithm could be employed to calculate the optimal values of optimization problems, especially for non-differentiable and nonlinear optimization problems associated with the atmospheric and oceanic sciences.
基金Supported by the Fundamental Research Funds for the Central Universities of China(DUT14RC(3)046)China Postdoctoral Science Foundation(2014M551091)the National Natural Science Foundation of China(21406026)
文摘Integrating multiple systems into one has become an important trend in Process Systems Engineering research field since there is strong demand from the modern industries. In this study, a stage-wise superstructurebased method is proposed to synthesize a combined mass and heat exchange network(CM&HEN) which has two parts as the mass exchange network(MEN) and heat exchange network(HEN) involved. To express the possible heat exchange requirements resulted from mass exchange operations, a so called "indistinct HEN superstructure(IHS)", which can contain the all potential matches between streams, is constructed at first. Then, a non-linear programming(NLP) mathematical model is established for the simultaneous synthesis and optimization of networks. Therein, the interaction between mass exchange and heat exchange is modeling formulated.The NLP model has later been examined using an example from literature, and the effectiveness of the proposed method has been demonstrated with the results.
文摘A process represented by nonlinear multi-parametric binary dynamic system is investigated in this work. This process is characterized by the pseudo Boolean objective functional. Since the transfer functions on the process are Boolean functions, the optimal control problem related to the process can be solved by relating between the transfer functions and the objective functional. An analogue of Bellman function for the optimal control problem mentioned is defined and consequently suitable Bellman equation is constructed.
