试验遗传算法研究及其在水资源系统问题中的应用
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摘要
随着人口与经济的持续增长,人类社会对水的需求量不断增加,水资源进行性短缺和水环境持续恶化已成为全球性问题。20世纪90年代以来,作为最大的发展中国家,我国也开始面临着日益突出的水资源短缺、水环境恶化和洪水灾害等水安全问题。今天,水资源系统已演变为一个多目标、多属性、多层次、多功能和多阶段的复杂巨系统,使得系统工程和系统分析成为当前解决水资源系统问题的主要理论基础和重要工具之一。随着所研究系统广度与深度的扩大,传统方法对于现代水资源系统的高维、非凸、非线性等复杂问题的处理已日显掣肘。近年来,随着现代应用数学和计算机技术的迅猛发展,针对复杂系统问题人们提出了人工智能计算理论与分析方法,如遗传算法、人工神经网络模型、模糊集等,这些方法的引入极大地促进了系统分析技术的发展,也为现代水资源系统问题的研究注入了新的活力。
在现代计算智能方法中,遗传算法由于自适应性强,全局优化,概率搜索,隐含并行性以及简单通用性等显著优点,在现代水资源系统问题中得到了广泛应用。然而在应用中发现,遗传算法尚存在诸多不足有待完善,如:解空间搜索策略,问题收敛性,控制参数设置等,这也是它之所以长期成为国内外计算智能研究热点的原因。交叉集成是当代科技创新的主要方式之一,也是遗传算法种群衍生的重要途径,把传统、常规或现代、智能的数学方法与遗传算法相结合以改善后者的性能是现代遗传算法研究的重要方式。本文在前人研究工作的基础上,首次对传统试验设计方法与遗传算法集成的可行性进行了较为深入地探讨,即①试验设计与遗传算法相结合的理论背景-广义试验方法。②试验设计与遗传算法相互集成的应用基础,即二者极强的优势互补性。以此为理论基础,第一次提出了二者相互双向集成的具体方式和操作方法:即基于遗传算法的试验设计方法(遗传正交设计、遗传均匀设计),基于试验设计的改进遗传算法。其中,试验设计嵌入遗传算法形成试验遗传算法的具体实施步骤包括:①按均匀设计表对遗传算法的初始群体进行均匀性分布。②利用多个均匀设计表对各变量进行不同水平组合,生成新的子代群体以提高种群的多样性。③在精英个体周围一定范围内进行确定性均匀分布搜索,称为确定性均匀调优操作。④随机性正态分布搜索,在部分优秀个体上周围叠加一个服从正态分布的随机变量产生新的子代群体。⑤摄动调优试验操作,即传统的坐标轮换法。数值实验的结果说明,试验遗传算法作为传统优化方法、计算智能算法和试验设计方法的综合集成新方法,采用随机性正态搜索和确定性均匀分布搜索,同时考虑变量的连续性与离散化,保证了算法较高的寻优性能,计算效率高,通用性强,对复杂系统中的高维、非线性、非凸及组合优化等问题的求解具有较强的适应性。
水资源系统优化问题是现代水资源系统问题的核心内容。本文在以下几个方面开展了试验遗传算法在水资源系统优化问题中的应用研究:①把灌溉渠道横断面设计转化为非线性优化问题,建立了相应的优化设计数学模型,并以梯形渠道断面和U形渠道断面为例,首次应用试验遗传算法进行渠道底宽和设计水深等参数的优化。②针对控制大田地下水位的排水沟间距问题,构造了以工程量最省为目标的无约束优化模型;针对控制稻田渗漏量的排水暗管设计问题,首次建立了以工程造价最小,同时考虑渗漏量等多种约束的系统优化问题,试验遗传算法对两个模型的求解结果令人满意。③建立了以经济性为目标、以结构安全性和技术可行性为约束的水电站压力埋管结构优化设计模型,试验遗传算法获得的优选设计方案明显好于传统设计方法。
水资源系统预测问题是一门技术性、艺术性要求很高的课题,它既要求预测者掌握多种系统预测方法与技术,又要求预测者具有灵活综合运用这些技术方法的能力。由于具有极强的非线性映射能力和容错性,人工神经网络已成为现代水资源系统工程中常用的建模方法之一。本文对BP人工神经网络(BP-ANN)在水资源系统建模及预测问题中的应用开展了如下工作:①在简要介绍BP-ANN原理方法的基础上,针对其不足研制了基于试验遗传算法的改进BP人工神经网络方法,提高了BP-ANN的全局优化能力。②应用BP-ANN进行非线性组合预测方法研究,有效避免了传统组合预测模型权重的繁琐计算。③针对组合预测中各模型权重难以科学确定的难题,首次根据“择优取用”原则将预测模型的组合问题转化为0、1异或的模式识别问题,并采用改进的BP-ANN方法进行该问题的求解,取得了令人满意的结果。这种确定变权重的方法实质上是一个模型优选过程,由于对每个样本都是取用各预测模型中的最优者,因此能在现有预测水平下保证模型“总是最好”,同时具有清晰易懂,简便易操作的优点。作为变权重组合预测方法的一个特例,在组合预测领域有较高的实用价值。
水资源系统评价问题的关键是评价模型的合理构造及其有效优化,基于常规建模和优化方法的传统方法已难以胜任复杂水资源系统中涉及多属性、多层次、多因子的综合评价问题。本文结合水资源系统评价问题中的不足做了以下两方面工作:①针对农业灌溉用水水质综合评价过程中存在的评价结果不相容性问题,提出基于数据探索和试验遗传算法求解的投影寻踪综合评价模型,较之灰色聚类法,其数学概念清晰,评价结果更精确合理。②基于线性属性测度函数的传统属性识别模型对随机抽样的评价结果存在较大误差,为此首次提出了基于非线性属性测度函数的改进属性识别模型。均匀随机和正交设计两种抽样的评价试验显示,改进属性识别模型评价结果准确度明显好于传统模型,说明指标的属性测度函数对属性识别模型的综合评价结果有重要影响。由于非线性测度函数比线性测度函数能更好地描述评价指标的实际隶属度,故基此改进的属性识别模型具有更高的评价可信度。
With the continuously rapid growth of population and economy, water demand has been substantially increasing which leads to the global problems of water resource shortage and water quality deterioration. Since 1990s, as the largest developing country, China has faced severe water problems such as lack of water resources, worsening of water circumstances and increase of flooding disasters, which were sometime called water security problem as a whole. Nowadays water resource system is a huge and complex system exhibiting multi-stage, multi-objective, multi-level, multi-attribute and multi-functioning characteristics. System engineering and system analysis has been becoming one of the most dominating tools for analysis of water resource system. However, as the extent and depth of system research grow, the conventional theories and methods are not suitable to deal with the problems of modern water resource system which are high dimensional, non-linear and non-convex. In recent years, with the fast development of applied mathematics and computer techniques, the methods of artificial computational intelligence (CI) have been proposed to treat the complex system problems. Some of the frequently used CI theories and methods include genetic algorithms (GA), artificial neural networks (ANN), fuzzy sets (FS) etc. The applications of CI have helped the development of system analysis techniques, and have proposed new solutions for the water resource problems.
Due to its self-adaptivity, global optimum, probability search, latent parallel process and easy operation, GA has been widely applied to the problems of modern water resource system. However, there are still some shortages for GA, such as searching algorithms in solution space, convergence of solutions and selection of controls parameters. Thus GA has been a hot research topic for a relatively long time. The operation of crossover and integration is one of the main technical and scientific innovation nowadays, which is also the vital kernel of GA. Consequently combining the conventional or intelligent mathematical methods with GA becomes an important way to improve the performance of the latter. In this study we briefly discuss the feasibility of integration of experiment design and GA, including:①t he theoretic foundation of the integration of experiment design with GA-the generalized experimental method;②the application foundation of integration of experiment design and GA - great complementarities between each other. As a result we propose a novel way of integrating the following two methods: GA based experiment design (GA orthogonal design, GA uniform design), experiment design based GA (immune GA, experimental GA). The experiment designs obtained by sub-GA were imbed into GAs in the following way:①u niform generation of forerunner individuals;②uniform searching in solution space;③utilizing uniform designs to make evolution experiment;④utilizing normal random distribution to make evolution experiment;⑤utilizing variable perturbation to make evolution experiment. Thus the so-called self-adaptive experimental genetic algorithms (EGA) based on the experiment design is developed. Digital test showed that, as a new hybrid intelligent method, EGA owns characters of fine optimizing efficiency and good precision adaptivity. It also has the ability to accelerate the individual variety to obtain the global solutions, and gives good values in area of complex water resource system.
System optimization is the core of modern water resources system. In this dissertation, EGA is applied to solve the water resource system optimization problems such as:①C anal transect design is transformed into a non-linear optimization problem by constructing a relevant optimizing mathematical model. The design of trapezoid transect and U-shaped transect canals are taken as examples to illustrate the procedure of using EGA to get the optimal solution.②For the interval design of drains which control the level of ground water, a non-restraint model with the objective of minimum project is proposed, and for interval design of hidden pipes which govern the seepage of rice field, a non-linear model is set up with the objective of minimum cost and restraints of seepage, the results given by EGA are very favorable.③A multi-variable-mixed non-linear optimization model is built during designing the structure of underground stiffened penstock of hydraulic power station, solutions given by EGA turns out to be superior to those based on the conventional methods.
System forecasting for water resource is a highly demanding technical issue. Forecasters are required to comprehensively master, as well as synthesize many methods or techniques. Because of its outstanding performance on fault-tolerance and nonlinear mapping, artificial neural nets (ANN) have been one of the most popular model-construction methods used in water resource system. In this dissertation, the application of BP-ANN to modeling and forecasting of water resource system contains:①after a brief introduction on the principle and method of BP-ANN, a hybrid artificial neural networks based on EGA is proposed to improve its ability to get the global solution;②the improved BP-ANN is utilized to form the method of nonlinear combination forecasting, which successfully avoids the tedious computation of the model weights;③according to the principle of best selection, the combined forecasting model is wisely transformed into a problem of 0 and 1 pattern recognition, and is solved by the method of improved BP-ANN with strong ability of non-linear mapping. The given example shows that, the so called selecting-best forecasting model (ANN-SFM) not only successfully avoids computing the weights of the combined forecasting models, but also owns the properties of clear concept, easy operation. As a special case of variable-weighting CFM, ANN-SFM has high values in practical applications.
The key point of water resource system assessment is the rational construction and effective optimization of the assessment model. Conventional methods based on general model construction and optimization are not fit for the requirements of comprehensive assessment of complex water resource system which involves problems of multi-attribute, multi-levels and multi-factors. In this dissertation, the following works are presented to improve the overall assessment on water resource system:①in order to solve the incompatible problem resulting from the comprehensive evaluation on the quality of agricultural irrigation water, a new evaluation method-projection pursuit model based on the technology of data exploring, and optimized by EGA, is proposed to evaluate the irrigation water quality. Compared with the traditional water quality evaluation methods, for example the gray association analysis, the mathematical concept of IGA-PP method is much simpler and clear. The results using IGA-PP are also more reasonable and precise;②large errors occur when the general attribute recognition model based on linear measure function(LMF-ARM) is employed to do assessment on virtual samples drawn randomly from the criterion of water quality. Therefore, an improved attribute recognition model based on non-linear measure function (NLMF-ARM) is also developed. The results given by the later model are much better than those from the former, according to the tests on virtual samples selected by the random method as well as the orthogonal design approach. It indicates that the measure function could play an important role during the process of utilizing attribute recognition model to do comprehensive assessment. Thus from the case study on a river water quality assessment, it can be concluded that the non-linear measure function, compared to the linear one, has better capability to describe the natural attribute degrees of assessment indexes. Also due to its higher reliability than that of LMF-ARM, NLMF-ARM has broad applicability in the comprehensive assessment of water quality.
在现代计算智能方法中,遗传算法由于自适应性强,全局优化,概率搜索,隐含并行性以及简单通用性等显著优点,在现代水资源系统问题中得到了广泛应用。然而在应用中发现,遗传算法尚存在诸多不足有待完善,如:解空间搜索策略,问题收敛性,控制参数设置等,这也是它之所以长期成为国内外计算智能研究热点的原因。交叉集成是当代科技创新的主要方式之一,也是遗传算法种群衍生的重要途径,把传统、常规或现代、智能的数学方法与遗传算法相结合以改善后者的性能是现代遗传算法研究的重要方式。本文在前人研究工作的基础上,首次对传统试验设计方法与遗传算法集成的可行性进行了较为深入地探讨,即①试验设计与遗传算法相结合的理论背景-广义试验方法。②试验设计与遗传算法相互集成的应用基础,即二者极强的优势互补性。以此为理论基础,第一次提出了二者相互双向集成的具体方式和操作方法:即基于遗传算法的试验设计方法(遗传正交设计、遗传均匀设计),基于试验设计的改进遗传算法。其中,试验设计嵌入遗传算法形成试验遗传算法的具体实施步骤包括:①按均匀设计表对遗传算法的初始群体进行均匀性分布。②利用多个均匀设计表对各变量进行不同水平组合,生成新的子代群体以提高种群的多样性。③在精英个体周围一定范围内进行确定性均匀分布搜索,称为确定性均匀调优操作。④随机性正态分布搜索,在部分优秀个体上周围叠加一个服从正态分布的随机变量产生新的子代群体。⑤摄动调优试验操作,即传统的坐标轮换法。数值实验的结果说明,试验遗传算法作为传统优化方法、计算智能算法和试验设计方法的综合集成新方法,采用随机性正态搜索和确定性均匀分布搜索,同时考虑变量的连续性与离散化,保证了算法较高的寻优性能,计算效率高,通用性强,对复杂系统中的高维、非线性、非凸及组合优化等问题的求解具有较强的适应性。
水资源系统优化问题是现代水资源系统问题的核心内容。本文在以下几个方面开展了试验遗传算法在水资源系统优化问题中的应用研究:①把灌溉渠道横断面设计转化为非线性优化问题,建立了相应的优化设计数学模型,并以梯形渠道断面和U形渠道断面为例,首次应用试验遗传算法进行渠道底宽和设计水深等参数的优化。②针对控制大田地下水位的排水沟间距问题,构造了以工程量最省为目标的无约束优化模型;针对控制稻田渗漏量的排水暗管设计问题,首次建立了以工程造价最小,同时考虑渗漏量等多种约束的系统优化问题,试验遗传算法对两个模型的求解结果令人满意。③建立了以经济性为目标、以结构安全性和技术可行性为约束的水电站压力埋管结构优化设计模型,试验遗传算法获得的优选设计方案明显好于传统设计方法。
水资源系统预测问题是一门技术性、艺术性要求很高的课题,它既要求预测者掌握多种系统预测方法与技术,又要求预测者具有灵活综合运用这些技术方法的能力。由于具有极强的非线性映射能力和容错性,人工神经网络已成为现代水资源系统工程中常用的建模方法之一。本文对BP人工神经网络(BP-ANN)在水资源系统建模及预测问题中的应用开展了如下工作:①在简要介绍BP-ANN原理方法的基础上,针对其不足研制了基于试验遗传算法的改进BP人工神经网络方法,提高了BP-ANN的全局优化能力。②应用BP-ANN进行非线性组合预测方法研究,有效避免了传统组合预测模型权重的繁琐计算。③针对组合预测中各模型权重难以科学确定的难题,首次根据“择优取用”原则将预测模型的组合问题转化为0、1异或的模式识别问题,并采用改进的BP-ANN方法进行该问题的求解,取得了令人满意的结果。这种确定变权重的方法实质上是一个模型优选过程,由于对每个样本都是取用各预测模型中的最优者,因此能在现有预测水平下保证模型“总是最好”,同时具有清晰易懂,简便易操作的优点。作为变权重组合预测方法的一个特例,在组合预测领域有较高的实用价值。
水资源系统评价问题的关键是评价模型的合理构造及其有效优化,基于常规建模和优化方法的传统方法已难以胜任复杂水资源系统中涉及多属性、多层次、多因子的综合评价问题。本文结合水资源系统评价问题中的不足做了以下两方面工作:①针对农业灌溉用水水质综合评价过程中存在的评价结果不相容性问题,提出基于数据探索和试验遗传算法求解的投影寻踪综合评价模型,较之灰色聚类法,其数学概念清晰,评价结果更精确合理。②基于线性属性测度函数的传统属性识别模型对随机抽样的评价结果存在较大误差,为此首次提出了基于非线性属性测度函数的改进属性识别模型。均匀随机和正交设计两种抽样的评价试验显示,改进属性识别模型评价结果准确度明显好于传统模型,说明指标的属性测度函数对属性识别模型的综合评价结果有重要影响。由于非线性测度函数比线性测度函数能更好地描述评价指标的实际隶属度,故基此改进的属性识别模型具有更高的评价可信度。
With the continuously rapid growth of population and economy, water demand has been substantially increasing which leads to the global problems of water resource shortage and water quality deterioration. Since 1990s, as the largest developing country, China has faced severe water problems such as lack of water resources, worsening of water circumstances and increase of flooding disasters, which were sometime called water security problem as a whole. Nowadays water resource system is a huge and complex system exhibiting multi-stage, multi-objective, multi-level, multi-attribute and multi-functioning characteristics. System engineering and system analysis has been becoming one of the most dominating tools for analysis of water resource system. However, as the extent and depth of system research grow, the conventional theories and methods are not suitable to deal with the problems of modern water resource system which are high dimensional, non-linear and non-convex. In recent years, with the fast development of applied mathematics and computer techniques, the methods of artificial computational intelligence (CI) have been proposed to treat the complex system problems. Some of the frequently used CI theories and methods include genetic algorithms (GA), artificial neural networks (ANN), fuzzy sets (FS) etc. The applications of CI have helped the development of system analysis techniques, and have proposed new solutions for the water resource problems.
Due to its self-adaptivity, global optimum, probability search, latent parallel process and easy operation, GA has been widely applied to the problems of modern water resource system. However, there are still some shortages for GA, such as searching algorithms in solution space, convergence of solutions and selection of controls parameters. Thus GA has been a hot research topic for a relatively long time. The operation of crossover and integration is one of the main technical and scientific innovation nowadays, which is also the vital kernel of GA. Consequently combining the conventional or intelligent mathematical methods with GA becomes an important way to improve the performance of the latter. In this study we briefly discuss the feasibility of integration of experiment design and GA, including:①t he theoretic foundation of the integration of experiment design with GA-the generalized experimental method;②the application foundation of integration of experiment design and GA - great complementarities between each other. As a result we propose a novel way of integrating the following two methods: GA based experiment design (GA orthogonal design, GA uniform design), experiment design based GA (immune GA, experimental GA). The experiment designs obtained by sub-GA were imbed into GAs in the following way:①u niform generation of forerunner individuals;②uniform searching in solution space;③utilizing uniform designs to make evolution experiment;④utilizing normal random distribution to make evolution experiment;⑤utilizing variable perturbation to make evolution experiment. Thus the so-called self-adaptive experimental genetic algorithms (EGA) based on the experiment design is developed. Digital test showed that, as a new hybrid intelligent method, EGA owns characters of fine optimizing efficiency and good precision adaptivity. It also has the ability to accelerate the individual variety to obtain the global solutions, and gives good values in area of complex water resource system.
System optimization is the core of modern water resources system. In this dissertation, EGA is applied to solve the water resource system optimization problems such as:①C anal transect design is transformed into a non-linear optimization problem by constructing a relevant optimizing mathematical model. The design of trapezoid transect and U-shaped transect canals are taken as examples to illustrate the procedure of using EGA to get the optimal solution.②For the interval design of drains which control the level of ground water, a non-restraint model with the objective of minimum project is proposed, and for interval design of hidden pipes which govern the seepage of rice field, a non-linear model is set up with the objective of minimum cost and restraints of seepage, the results given by EGA are very favorable.③A multi-variable-mixed non-linear optimization model is built during designing the structure of underground stiffened penstock of hydraulic power station, solutions given by EGA turns out to be superior to those based on the conventional methods.
System forecasting for water resource is a highly demanding technical issue. Forecasters are required to comprehensively master, as well as synthesize many methods or techniques. Because of its outstanding performance on fault-tolerance and nonlinear mapping, artificial neural nets (ANN) have been one of the most popular model-construction methods used in water resource system. In this dissertation, the application of BP-ANN to modeling and forecasting of water resource system contains:①after a brief introduction on the principle and method of BP-ANN, a hybrid artificial neural networks based on EGA is proposed to improve its ability to get the global solution;②the improved BP-ANN is utilized to form the method of nonlinear combination forecasting, which successfully avoids the tedious computation of the model weights;③according to the principle of best selection, the combined forecasting model is wisely transformed into a problem of 0 and 1 pattern recognition, and is solved by the method of improved BP-ANN with strong ability of non-linear mapping. The given example shows that, the so called selecting-best forecasting model (ANN-SFM) not only successfully avoids computing the weights of the combined forecasting models, but also owns the properties of clear concept, easy operation. As a special case of variable-weighting CFM, ANN-SFM has high values in practical applications.
The key point of water resource system assessment is the rational construction and effective optimization of the assessment model. Conventional methods based on general model construction and optimization are not fit for the requirements of comprehensive assessment of complex water resource system which involves problems of multi-attribute, multi-levels and multi-factors. In this dissertation, the following works are presented to improve the overall assessment on water resource system:①in order to solve the incompatible problem resulting from the comprehensive evaluation on the quality of agricultural irrigation water, a new evaluation method-projection pursuit model based on the technology of data exploring, and optimized by EGA, is proposed to evaluate the irrigation water quality. Compared with the traditional water quality evaluation methods, for example the gray association analysis, the mathematical concept of IGA-PP method is much simpler and clear. The results using IGA-PP are also more reasonable and precise;②large errors occur when the general attribute recognition model based on linear measure function(LMF-ARM) is employed to do assessment on virtual samples drawn randomly from the criterion of water quality. Therefore, an improved attribute recognition model based on non-linear measure function (NLMF-ARM) is also developed. The results given by the later model are much better than those from the former, according to the tests on virtual samples selected by the random method as well as the orthogonal design approach. It indicates that the measure function could play an important role during the process of utilizing attribute recognition model to do comprehensive assessment. Thus from the case study on a river water quality assessment, it can be concluded that the non-linear measure function, compared to the linear one, has better capability to describe the natural attribute degrees of assessment indexes. Also due to its higher reliability than that of LMF-ARM, NLMF-ARM has broad applicability in the comprehensive assessment of water quality.
引文
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