Adjoint method for the optimum planning of industrial pollutant sources

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 introduced to deal with the environmental inequality constraints, and Lagrange function is constructed 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 information 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 experiments. 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. 作 者： LIU Feng    HU Fei    ZHU Jiang   作者單位： LIU Feng(College of Environmental Sciences, Peking University, Beijing 100871, China;LAPC, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China)

HU Fei,ZHU Jiang(LAPC, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China) 

期 刊： 中國科學(xué)D輯（英文版）  SCI   Journal： SCIENCE IN CHINA SERIES D(EARTH SCIENCES)  年，卷(期)： 2005, 48(8)  分類號： X1  Keywords： optimum planning    industrial pollutant sources    adjoint equation    penalty function    gradient