演化优化与演化建模方法及其应用研究
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摘要
演化计算是一种模仿生物进化过程的智能计算技术,它采取群体搜索策略,以求解的问题为环境压力,按照“优胜劣汰,适者生存”的规则,对群体进行迭代更新,直到求得所需解。这种搜索方式使得演化计算方法适用性强,并有自组织、自适应和自学习等特点。演化计算的这些特点使其能解决很多传统方法无法求解的复杂问题,在工程领域得到广泛的应用。
本文针对演化优化和演化建模的方法和应用进行了研究。首先介绍了演化计算的发展和主要的研究方向,重点介绍了用演化算法进行自动化程序设计和建模,数值优化,多日标优化,时间序列分析等方面的研究状况,针对这些领域中的方法和应用展开讨论,给出新的设计和改进。
首先,本文在演化多目标优化领域,针对多目标优化对算法收敛性、解的多样性的要求,给出一个新的使用子空间搜索的演化多目标优化算法。该算法使用子空间搜索技术作为杂交算子搜索Pareto前沿,提高了收敛速度,并结合了基于rank的适应值概念,以及在日标空间中采用niche的策略,在保证算法的收敛性的同时提高了解的多样性。
第二,提出来一种新的使用表达式树结构的基因表达式编程算法(Gene Expression Programming, GEP)。通过研究基因表达式编程算法和遗传程序设计算法(Genetic Programming, GP),我们认为基因表达式编程算法使用定长的线型编码作为遗传基因,使得算子设计简单,算法运行效率高；遗传程序设计算法使用语法树编码与程序结构对应,演化过程有明确的语法意义。结合两者的优点,设计了一个内嵌使用语法树结构的基因表达式编程算法,保护优良基因不被破坏。实验表明新算法与经典的GEP算法相比,既提高了解的质量,也加快了搜索速度。
第三,针对演化策略的特征,本文设计了广义预测控制演化策略算法,提出了一个新的演化策略算法的变异强度自适应技术。我们将演化策略算法进化过程中的变异步长和变异强度看做一个时间序列,对其建立受控自回归积分移动平均模型(CARIMA),使用广义预测控制技术使算法对变异强度进行自适应调整。数值实验表明这种自适应策略能使演化策略算法快速地向全局最优的方向搜索。
最后,本文给出了一个新的演化门限自回归建模算法应用在非线性时间序列数据的分析上。针对门限自回归模型的模型参数多,传统建模算法因为参数之间具有相关性而只能进行多层建模,导致计算量大的问题,我们分析了模型参数的物理意义,做出新的设计,大大地简化了参数的优化过程,将这部分参数作为一个搜索维度处理,降低了建模的层数,显著地减少了计算量。使用该模型对加拿大山猫数据的建模,演化门限自回归建模算法找到的模型能有效反映数据的物理意义并做出有效地预测。
Evolutionary Computation is a heuristic method which mimics the evolutionary process of nature biology according Darwin's theory of natural selection,"the Survival of the Fittest". It uses group search strategy. It estimates the individuals in the population and renews the population with the selection iteratively until the optimal solution appears. This method has the features of self-organization, self-adaptive, and self-learning and these features make the method capable of settling a large number of difficult problems which cannot be approached by the traditional methods. This intelligent method was used widely in many domains.
At first this thesis introduces the development of the evolutionary computation and some of its major branch. We focus on applying the evolutionary computation in the areas of auto programming and modeling, numeric optimization, multi-objective optimization and time series analysis. We mentioned some problems in these areas. We had studied these problems and designed the solutions to settle them.
In the second chapter we proposed a new evolutionary multi-objective optimization algorithm with elite-subspace strategy. We also use rank-based fitness and niche strategy to keep convergence of algorithm and diversity of the solutions.
In the third chapter we present a new gene expression programming algorithm which could use tree-based genetic operators. We noticed that the linear chromosome makes it is easy to design the genetic operators in gene expression programming algorithm and makes the algorithm speedy as well as the parse tree in genetic programming makes the operators in GP more purposive. So we discussed how to use tree-based genetic operators in GEP and designed a new GEP with these operators.
We present a new evolution strategy algorithm which using Generalized Predictive Control(GPC) to adapt the global step size in chapter4. In our method, the evolution strategy algorithm is regarded as a controlled system and modeled as a CARIMA model. We calculate the model's parameters and then the current global optimum step size is calculated by the GPC to feed back to evolution strategy algorithm. Simulation on various test functions reveals local and global search properties of the evolution strategy with GPC.
In the fifth chapter we propose a new evolutionary threshold autoregressive modeling algorithm. We analyzed the arguments of the threshold autoregressive model and designed a simple evolutionary algorithm to search the optimal value of them. We tested this method with data of Canada lynx. The model which founded by this method can reveal the real scene of the lynx number's fluctuation. It also can make a good prediction.
本文针对演化优化和演化建模的方法和应用进行了研究。首先介绍了演化计算的发展和主要的研究方向,重点介绍了用演化算法进行自动化程序设计和建模,数值优化,多日标优化,时间序列分析等方面的研究状况,针对这些领域中的方法和应用展开讨论,给出新的设计和改进。
首先,本文在演化多目标优化领域,针对多目标优化对算法收敛性、解的多样性的要求,给出一个新的使用子空间搜索的演化多目标优化算法。该算法使用子空间搜索技术作为杂交算子搜索Pareto前沿,提高了收敛速度,并结合了基于rank的适应值概念,以及在日标空间中采用niche的策略,在保证算法的收敛性的同时提高了解的多样性。
第二,提出来一种新的使用表达式树结构的基因表达式编程算法(Gene Expression Programming, GEP)。通过研究基因表达式编程算法和遗传程序设计算法(Genetic Programming, GP),我们认为基因表达式编程算法使用定长的线型编码作为遗传基因,使得算子设计简单,算法运行效率高；遗传程序设计算法使用语法树编码与程序结构对应,演化过程有明确的语法意义。结合两者的优点,设计了一个内嵌使用语法树结构的基因表达式编程算法,保护优良基因不被破坏。实验表明新算法与经典的GEP算法相比,既提高了解的质量,也加快了搜索速度。
第三,针对演化策略的特征,本文设计了广义预测控制演化策略算法,提出了一个新的演化策略算法的变异强度自适应技术。我们将演化策略算法进化过程中的变异步长和变异强度看做一个时间序列,对其建立受控自回归积分移动平均模型(CARIMA),使用广义预测控制技术使算法对变异强度进行自适应调整。数值实验表明这种自适应策略能使演化策略算法快速地向全局最优的方向搜索。
最后,本文给出了一个新的演化门限自回归建模算法应用在非线性时间序列数据的分析上。针对门限自回归模型的模型参数多,传统建模算法因为参数之间具有相关性而只能进行多层建模,导致计算量大的问题,我们分析了模型参数的物理意义,做出新的设计,大大地简化了参数的优化过程,将这部分参数作为一个搜索维度处理,降低了建模的层数,显著地减少了计算量。使用该模型对加拿大山猫数据的建模,演化门限自回归建模算法找到的模型能有效反映数据的物理意义并做出有效地预测。
Evolutionary Computation is a heuristic method which mimics the evolutionary process of nature biology according Darwin's theory of natural selection,"the Survival of the Fittest". It uses group search strategy. It estimates the individuals in the population and renews the population with the selection iteratively until the optimal solution appears. This method has the features of self-organization, self-adaptive, and self-learning and these features make the method capable of settling a large number of difficult problems which cannot be approached by the traditional methods. This intelligent method was used widely in many domains.
At first this thesis introduces the development of the evolutionary computation and some of its major branch. We focus on applying the evolutionary computation in the areas of auto programming and modeling, numeric optimization, multi-objective optimization and time series analysis. We mentioned some problems in these areas. We had studied these problems and designed the solutions to settle them.
In the second chapter we proposed a new evolutionary multi-objective optimization algorithm with elite-subspace strategy. We also use rank-based fitness and niche strategy to keep convergence of algorithm and diversity of the solutions.
In the third chapter we present a new gene expression programming algorithm which could use tree-based genetic operators. We noticed that the linear chromosome makes it is easy to design the genetic operators in gene expression programming algorithm and makes the algorithm speedy as well as the parse tree in genetic programming makes the operators in GP more purposive. So we discussed how to use tree-based genetic operators in GEP and designed a new GEP with these operators.
We present a new evolution strategy algorithm which using Generalized Predictive Control(GPC) to adapt the global step size in chapter4. In our method, the evolution strategy algorithm is regarded as a controlled system and modeled as a CARIMA model. We calculate the model's parameters and then the current global optimum step size is calculated by the GPC to feed back to evolution strategy algorithm. Simulation on various test functions reveals local and global search properties of the evolution strategy with GPC.
In the fifth chapter we propose a new evolutionary threshold autoregressive modeling algorithm. We analyzed the arguments of the threshold autoregressive model and designed a simple evolutionary algorithm to search the optimal value of them. We tested this method with data of Canada lynx. The model which founded by this method can reveal the real scene of the lynx number's fluctuation. It also can make a good prediction.
引文
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