高效非线性优化算法在水环境系统中的应用研究
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摘要
水环境系统是一个无序的、非稳定的、非平衡的随机系统，不同元素之间往往存在着随机性、协同现象和相干效应。加上受天文、气象、气候、人文等众多方面的影响，水环境系统中的优化问题常常表现出高维、多峰值、不连续、非凸性、带噪声等特征，复杂程度已经远远超越了传统优化方法的处理能力。近些年来，虽然国内外已有不少专家致力于水环境优化问题的研究，但其理论和方法在实际应用上仍然有很大的局限性，造成了资源、资金的巨大浪费。
因此，本文在总结了传统最优化方法的基础上，初步探讨了高效非线性优化算法存水环境系统中的应用，集中对非线性算法中较为常见的遗传算法、模拟退火算法和人工神经网络的理论、算法及模式进行了研究，并针对这些算法固有的缺点，结合模糊数学理论、单纯形法和小波分析，建立了改进的高效非线性优化方法。最后用于解决水污染控制系统规划、排放口优化、多目标综合规划、水质模型参数识别及水质预测等问题。研究结果表明：
无论是确定性的水污染规划模型还是不确定性的水污染规划模型，非线性优化算法可以大大减少计算的复杂程度，并且可以很快搜索到全局最优解。优化结果与起始点选择无关，只要优化参数选取合适，该算法完全可以有效的求出最优解；
多目标规划中，通过引入模糊数学理论，克服了传统优化算法中决策者直接给出最优权重的困难，避免对某些目标进行简单量化带来的误差和数据损失。计算结果表明，鉴于非线性算法全局寻优能力强和模糊非线性优化理论能够协调模糊变量间的关系等优点，使得求解过程更加简单，同时能够保证得到水污染控制系统多目标规划全局最优解；
在对河流水质参数进行最优估值的时候，目标函数往往是一个复杂的非线性函数，尤其是当估计的参数较多时，目标函数可能会存在许多局部极值点，用常规的最优化方法难以实现。非线性优化算法及其改进算法既考虑了新点产生的随机性，又在一定程度上保证了搜索的整体性，从而加快了全局寻优速度，优化结果具有一定可信度；
高效非线性优化算法的预测模型对于提高预测精度，合理反映历史数据的内部关系，对于指导环境决策部门制定战略或中长期环境规划目标等都具有十分重要的意义。与常规方法不同，该方法以实验数据为样本，利用网络的自学习和联想记忆能力对实验数据进行学习，具有极佳的函数逼近能力，能很好的拟合历史样本，达到识别各影响因子之间复杂的非线性映射关系，也为提高水质预测模型
何之}:学位论文
的精度和实用性J「辟了一条新的途径。
将高效非线性算法应用于水环境系统中，可以协调各要素之间的关系，实现
经济效益、环境效益和社会效益的统一，使水质规划、评价、预测建立在更加科
学的基础之卜，提出合理的规划方案，从而为水质工作者提供一定的参考依据。
可以预书}，:动效一1卜线性优化方法将在环境科学优化领域中具有极为广阔的应用前
!、卜
声J互。
Water environmental system is unordered, unstable and non-equilibrium, where usually exists the randomicity, cooperative phenomena and coherent effects. However, due to the influences of many factors, such as chronometer, weather, climate and human science, the optimization problems in water environmental system are always high-dimensional, multi-peak, discontinuous, non-convex and with noise, which is so complicated that surpasses the abilities of traditional optimization methods. In recent years, more and more scholars commit themselves to the research of optimization problems in water environment system, the theories and methods of which are of limitations in practice use and result in the enormous waste of resource and funds finally.
Therefore, the paper primarily explores the application of efficient non-linear algorithms in water environmental system and puts stress on the discussion of Genetic Algorithm (GA), Simulated Annealing (SA) and Artificial Nerve Network (ANN). Focusing on the defects of the algorithms mentioning above, the improved efficient non-linear algorithms are also proposed combining Fuzzy mathematics, Simplex algorithm and wavelet analysis. Eventually, the paper solves the programming in water pollution control system, the optimization of discharge fort, multi-objective programming, identifying of water quality models parameters and the prediction of water quality using the efficient non-linear algorithms. The results show that:
The solving processes of certain or uncertain water pollution system programming models are simplified greatly by using non-linear algorithms. And global optimums can be found quickly. The results don't depend on initial values if the optimization parameters are appropriate selected;
The difficulties of how to select the weights of each object and avoid the errors and losses by simplifying certain object ones in traditional methods can be solved by using Fuzzy mathematic theory. Combining the advantages of non-linear algorithms and Fuzzy theory, the improved algorithm corresponds the relations between each objects and gets the global optimums of multi-objective programming in water pollution controlling system;
The objective functions are frequently complex and non-linear when estimating the parameters of water quality models. Especially, when many parameters are needed estimating, there will exist many local optimums in objective function, which is
difficult to solve for traditional methods. Non-linear algorithms or improved algorithms considering the randomicity of the generation of new values and assuring the integrity of searching at some extents, will accelerate the speed of searching optimums;
Efficient non-linear algorithms estimating models can raise the estimation precision and reflect the relations between historical data, which are much valuable for environmental decision department to establish the stratagem, metaphase'or long-term programming targets. Differing from traditional methods, the algorithm uses experimentation data as swatch and studies the data using the abilities of self-studying and memories, which is approximate to the swatch, distinguish the non-linear mapping between each influence factors and is a new approach to improve the precision and practicability in water quality estimation.
The relationships between each factors can be corresponded, the unifying of economic benefits, environmental benefits and society benefits can be achieved and the water quality programming, evaluation and estimation will be more reliable by using efficient non-linear algorithms into water environmental system. Therefore, it's believed that non-linear algorithm would have its extensively applied prospect in the field of optimization in environmental science.
因此，本文在总结了传统最优化方法的基础上，初步探讨了高效非线性优化算法存水环境系统中的应用，集中对非线性算法中较为常见的遗传算法、模拟退火算法和人工神经网络的理论、算法及模式进行了研究，并针对这些算法固有的缺点，结合模糊数学理论、单纯形法和小波分析，建立了改进的高效非线性优化方法。最后用于解决水污染控制系统规划、排放口优化、多目标综合规划、水质模型参数识别及水质预测等问题。研究结果表明：
无论是确定性的水污染规划模型还是不确定性的水污染规划模型，非线性优化算法可以大大减少计算的复杂程度，并且可以很快搜索到全局最优解。优化结果与起始点选择无关，只要优化参数选取合适，该算法完全可以有效的求出最优解；
多目标规划中，通过引入模糊数学理论，克服了传统优化算法中决策者直接给出最优权重的困难，避免对某些目标进行简单量化带来的误差和数据损失。计算结果表明，鉴于非线性算法全局寻优能力强和模糊非线性优化理论能够协调模糊变量间的关系等优点，使得求解过程更加简单，同时能够保证得到水污染控制系统多目标规划全局最优解；
在对河流水质参数进行最优估值的时候，目标函数往往是一个复杂的非线性函数，尤其是当估计的参数较多时，目标函数可能会存在许多局部极值点，用常规的最优化方法难以实现。非线性优化算法及其改进算法既考虑了新点产生的随机性，又在一定程度上保证了搜索的整体性，从而加快了全局寻优速度，优化结果具有一定可信度；
高效非线性优化算法的预测模型对于提高预测精度，合理反映历史数据的内部关系，对于指导环境决策部门制定战略或中长期环境规划目标等都具有十分重要的意义。与常规方法不同，该方法以实验数据为样本，利用网络的自学习和联想记忆能力对实验数据进行学习，具有极佳的函数逼近能力，能很好的拟合历史样本，达到识别各影响因子之间复杂的非线性映射关系，也为提高水质预测模型
何之}:学位论文
的精度和实用性J「辟了一条新的途径。
将高效非线性算法应用于水环境系统中，可以协调各要素之间的关系，实现
经济效益、环境效益和社会效益的统一，使水质规划、评价、预测建立在更加科
学的基础之卜，提出合理的规划方案，从而为水质工作者提供一定的参考依据。
可以预书}，:动效一1卜线性优化方法将在环境科学优化领域中具有极为广阔的应用前
!、卜
声J互。
Water environmental system is unordered, unstable and non-equilibrium, where usually exists the randomicity, cooperative phenomena and coherent effects. However, due to the influences of many factors, such as chronometer, weather, climate and human science, the optimization problems in water environmental system are always high-dimensional, multi-peak, discontinuous, non-convex and with noise, which is so complicated that surpasses the abilities of traditional optimization methods. In recent years, more and more scholars commit themselves to the research of optimization problems in water environment system, the theories and methods of which are of limitations in practice use and result in the enormous waste of resource and funds finally.
Therefore, the paper primarily explores the application of efficient non-linear algorithms in water environmental system and puts stress on the discussion of Genetic Algorithm (GA), Simulated Annealing (SA) and Artificial Nerve Network (ANN). Focusing on the defects of the algorithms mentioning above, the improved efficient non-linear algorithms are also proposed combining Fuzzy mathematics, Simplex algorithm and wavelet analysis. Eventually, the paper solves the programming in water pollution control system, the optimization of discharge fort, multi-objective programming, identifying of water quality models parameters and the prediction of water quality using the efficient non-linear algorithms. The results show that:
The solving processes of certain or uncertain water pollution system programming models are simplified greatly by using non-linear algorithms. And global optimums can be found quickly. The results don't depend on initial values if the optimization parameters are appropriate selected;
The difficulties of how to select the weights of each object and avoid the errors and losses by simplifying certain object ones in traditional methods can be solved by using Fuzzy mathematic theory. Combining the advantages of non-linear algorithms and Fuzzy theory, the improved algorithm corresponds the relations between each objects and gets the global optimums of multi-objective programming in water pollution controlling system;
The objective functions are frequently complex and non-linear when estimating the parameters of water quality models. Especially, when many parameters are needed estimating, there will exist many local optimums in objective function, which is
difficult to solve for traditional methods. Non-linear algorithms or improved algorithms considering the randomicity of the generation of new values and assuring the integrity of searching at some extents, will accelerate the speed of searching optimums;
Efficient non-linear algorithms estimating models can raise the estimation precision and reflect the relations between historical data, which are much valuable for environmental decision department to establish the stratagem, metaphase'or long-term programming targets. Differing from traditional methods, the algorithm uses experimentation data as swatch and studies the data using the abilities of self-studying and memories, which is approximate to the swatch, distinguish the non-linear mapping between each influence factors and is a new approach to improve the precision and practicability in water quality estimation.
The relationships between each factors can be corresponded, the unifying of economic benefits, environmental benefits and society benefits can be achieved and the water quality programming, evaluation and estimation will be more reliable by using efficient non-linear algorithms into water environmental system. Therefore, it's believed that non-linear algorithm would have its extensively applied prospect in the field of optimization in environmental science.
引文
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