基于改进遗传算法的建模和动态优化方法研究
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摘要
从20世纪60年代开始,人们开始研究进化算法,试图发展一种具有适应任意环境的理论,使其用于通用程序和机器。到1975年遗传算法(genetic algorithm,GA)的创立标志着进化算法成立的里程碑。80年代以后进化算法得到了广泛的发展,包括算法成型和理论研究。90年代以后,进化算法应用到了工程结构优化、计算数学、制造系统等等工程应用学科中。2000年以后,进化算法的框架基本成熟,众多学者对其各个应用领域做了不同的改进措施。至今,每年有关进化算法的文献数量都呈递增趋势发展。
进化算法有着全局搜索、实现方便等的优点,但也存在着效率较低、结果随机性大等的缺点。本文做的主要工作有：
(1)针对进化算法上述缺点,在前人工作的基础上做了对于遗传算法效率上的改进,提出了逐维进化的遗传算法,使得原优化问题分解为单独的每一维上的子问题进行优化,由原来整个种群进化分解为各个独立的子种群。各个子种群独立进化,而又协作求取优化目标值。由于各个子优化问题维数得到降低,子种群上的负担减少,优化的效率得到提高。本文所做的工作经仿真计算,体现出了一定的优势性。在此基础上,本文分别做了半参数模型和动态优化的研究,取得了一定的成果。经过验证,本文提出的算法较适用于动态优化问题或复杂参数估计问题。
(2)针对稳态建模和参数估计问题,提出了基于遗传算法和神经网络的半参数模型。该模型结合参数模型与非参数模型各自的优势,提高了建模精度,将非线性半参数模型引入到工业过程建模中。首先,提出了基于遗传算法和神经网络的非线性半参数模型的建模方法及结构方案,并给出了同时估计参数模型部分和非参数模型部分的交叉循环迭代的算法步骤；其次,进行了神经网络的设计和遗传算法的改进研究,重点讨论了在增加精英保留策略、增加算法的记忆功能、提出新的适应度计算方法和交叉变异策略等方面的改进措施；最后,采用聚乙烯装置的现场工业数据对本方法进行了验证。
(3)针对动态优化求解问题,本文提出了逐维交叉遗传算法(dimensionalcrossover genetic algorithm, DCGA)和逐维进化动态算法(dimensional evolution dynamic algorithm)。逐维交叉遗传算法对于求解含有局部最优和不可微分系统更有优势,但计算量较大。逐维进化动态算法使算法性能得到较大提高。采用逐维进化策略克服了遗传算法进化缓慢的缺点,实现了保证精确性下的效率的提高。同时采用等级交叉和精英保留策略改进了遗传算法中种群的多样性。成功的将逐维进化动态算法用于求解CSTR模型、非连续动态模型和Lee-Ramirez生物反应器模型。在Lee-Ramirez模型中,较之前研究成果在取得全局最优目标的同时,优化目标值计算量减少了29%,计算时间减少了38%,体现出了该算法效率高的优点。
From 1960's, people began to study evolution algorithm, trying to develop a kind of a theory to adapt to any environment, so for common procedures and machines. In 1975 the creation of genetic algorithm marked evolutionary algorithms established milestone. In 1980's, the evolutionary algorithms has been extensive development, including forming and theoretical study of the algorithms. In 1990's, evolutionary algorithms applied to structural optimization, computational mathematics, manufacturing systems engineering disciplines, etc... After 2000, the basic framework of evolutionary algorithms matured, many scholars have made various areas of applications of different improvement measures. So far, each of the literature on evolutionary algorithms were tested increasing trend.
(1) Evolutionary algorithm has the advantages of global search, easy to realize, but there are the faults of less efficient, the large random of the results. In this paper, based on previous work the efficiency of genetic algorithm is improved in gradual dimension evolution algorithm. The original optimization problem is divided into separate sub-problems on each dimension, the whole population divided into sub-population on each dimension. Each sub-population evolved independently but strike a cooperative optimization target. The dimension of each sub-problem is reduced, reducing the burden of each sub-population, so the efficiency of the algorithm is improved. This work compared with the latest improved genetic algorithms, expressed a certain advantage. On this basis, the studies of semi-parameter model and dynamic optimization is made. After verification, the proposed method is more suitable for dynamic optimization problems or complex parameter estimation.
(2) In order to combine parameter model and non-parameter model with their own advantage, impove the modeling accuracy, nonlinear semiparametric models was introduced into industrail process modeling. At first, the method and structure for modeling of nonlinear semiparametric based on genetic algorithm and neural network was described, with giving the algorithmic steps of cross-loop iteration for parametric part and nonparametric part's estimation. Then, the design of neural network and the improvement of genetic algrorithm was researched, new calculation method of fitness and improved measure of crossover and variation. At last, this method was varified by the on-site industrail data of polyethylene plant. The result shows that the modeling approach proposed in this paper can well meet the demand for industrial field applications.
(3) For the dynamic optimization problem, this paper proposes the improved genetic algorithm for dynamic optimization problems by dimensional evolution dynamic algorithm. Gradual dimension strategy overcome the shortcomings of the slow evolution of the genetic algorithm and avoid the proliferation of the dynamic programming. At the same time using cross-grade retention policy and elite genetic algorithm to improve the diversity of population. The improved genetic algorithm success solving the CSTR model, non-continuous dynamic model and Lee-Ramirez bioreactor model. In the model of Lee-Ramirez, this work obtained the global optimal goals while reducing computation 29% and computing time 38%, reflecting the advantages of high efficiency of the algorithm.
进化算法有着全局搜索、实现方便等的优点,但也存在着效率较低、结果随机性大等的缺点。本文做的主要工作有：
(1)针对进化算法上述缺点,在前人工作的基础上做了对于遗传算法效率上的改进,提出了逐维进化的遗传算法,使得原优化问题分解为单独的每一维上的子问题进行优化,由原来整个种群进化分解为各个独立的子种群。各个子种群独立进化,而又协作求取优化目标值。由于各个子优化问题维数得到降低,子种群上的负担减少,优化的效率得到提高。本文所做的工作经仿真计算,体现出了一定的优势性。在此基础上,本文分别做了半参数模型和动态优化的研究,取得了一定的成果。经过验证,本文提出的算法较适用于动态优化问题或复杂参数估计问题。
(2)针对稳态建模和参数估计问题,提出了基于遗传算法和神经网络的半参数模型。该模型结合参数模型与非参数模型各自的优势,提高了建模精度,将非线性半参数模型引入到工业过程建模中。首先,提出了基于遗传算法和神经网络的非线性半参数模型的建模方法及结构方案,并给出了同时估计参数模型部分和非参数模型部分的交叉循环迭代的算法步骤；其次,进行了神经网络的设计和遗传算法的改进研究,重点讨论了在增加精英保留策略、增加算法的记忆功能、提出新的适应度计算方法和交叉变异策略等方面的改进措施；最后,采用聚乙烯装置的现场工业数据对本方法进行了验证。
(3)针对动态优化求解问题,本文提出了逐维交叉遗传算法(dimensionalcrossover genetic algorithm, DCGA)和逐维进化动态算法(dimensional evolution dynamic algorithm)。逐维交叉遗传算法对于求解含有局部最优和不可微分系统更有优势,但计算量较大。逐维进化动态算法使算法性能得到较大提高。采用逐维进化策略克服了遗传算法进化缓慢的缺点,实现了保证精确性下的效率的提高。同时采用等级交叉和精英保留策略改进了遗传算法中种群的多样性。成功的将逐维进化动态算法用于求解CSTR模型、非连续动态模型和Lee-Ramirez生物反应器模型。在Lee-Ramirez模型中,较之前研究成果在取得全局最优目标的同时,优化目标值计算量减少了29%,计算时间减少了38%,体现出了该算法效率高的优点。
From 1960's, people began to study evolution algorithm, trying to develop a kind of a theory to adapt to any environment, so for common procedures and machines. In 1975 the creation of genetic algorithm marked evolutionary algorithms established milestone. In 1980's, the evolutionary algorithms has been extensive development, including forming and theoretical study of the algorithms. In 1990's, evolutionary algorithms applied to structural optimization, computational mathematics, manufacturing systems engineering disciplines, etc... After 2000, the basic framework of evolutionary algorithms matured, many scholars have made various areas of applications of different improvement measures. So far, each of the literature on evolutionary algorithms were tested increasing trend.
(1) Evolutionary algorithm has the advantages of global search, easy to realize, but there are the faults of less efficient, the large random of the results. In this paper, based on previous work the efficiency of genetic algorithm is improved in gradual dimension evolution algorithm. The original optimization problem is divided into separate sub-problems on each dimension, the whole population divided into sub-population on each dimension. Each sub-population evolved independently but strike a cooperative optimization target. The dimension of each sub-problem is reduced, reducing the burden of each sub-population, so the efficiency of the algorithm is improved. This work compared with the latest improved genetic algorithms, expressed a certain advantage. On this basis, the studies of semi-parameter model and dynamic optimization is made. After verification, the proposed method is more suitable for dynamic optimization problems or complex parameter estimation.
(2) In order to combine parameter model and non-parameter model with their own advantage, impove the modeling accuracy, nonlinear semiparametric models was introduced into industrail process modeling. At first, the method and structure for modeling of nonlinear semiparametric based on genetic algorithm and neural network was described, with giving the algorithmic steps of cross-loop iteration for parametric part and nonparametric part's estimation. Then, the design of neural network and the improvement of genetic algrorithm was researched, new calculation method of fitness and improved measure of crossover and variation. At last, this method was varified by the on-site industrail data of polyethylene plant. The result shows that the modeling approach proposed in this paper can well meet the demand for industrial field applications.
(3) For the dynamic optimization problem, this paper proposes the improved genetic algorithm for dynamic optimization problems by dimensional evolution dynamic algorithm. Gradual dimension strategy overcome the shortcomings of the slow evolution of the genetic algorithm and avoid the proliferation of the dynamic programming. At the same time using cross-grade retention policy and elite genetic algorithm to improve the diversity of population. The improved genetic algorithm success solving the CSTR model, non-continuous dynamic model and Lee-Ramirez bioreactor model. In the model of Lee-Ramirez, this work obtained the global optimal goals while reducing computation 29% and computing time 38%, reflecting the advantages of high efficiency of the algorithm.
引文
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