Adjoint method for the optimum planning of industrial pollutant sources |
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| Authors: | Feng?Liu Email author" target="_blank">Fei?HuEmail author Jiang?Zhu |
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| Institution: | 1. College of Environmental Sciences, Peking University, Beijing 100871, China;LAPC, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
2. LAPC, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China |
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| Abstract: | The optimum planning of industrial pollutant sources, which optimizes the economic object without violating environmental constraints, is an important and hard task to be conquered. In this paper, an adjoint method is developed to solve the problem. The penalty function is in-troduced to deal with the environmental inequality constraints, and Lagrange function is con-structed to derive the adjoint equation and the gradient of the object function. In this means, the gradient of the object function can be calculated by solving the adjoint equation, and the infor-mation from the gradient is used to make the object function descend and approach to an optimal solution after some iterations. A two-dimensional, simplified model is used for numerical experi-ments. The theoretical derivations are verified by the results of the experiments. Furthermore, the adjoint method is shown to be of excellent convergence and efficiency, which is adaptive to the fast development of air quality numerical models and super computers. |
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| Keywords: | optimum planning industrial pollutant sources adjoint equation penalty function gradient |
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