【作者】 廖平；

【导师】 喻寿益；

【作者基本信息】 中南大学 ， 机械设计及理论， 2002， 博士

【摘要】 论文对基于遗传算法的形状误差计算进行了系统的深入研究，重点包括实数编码遗传算法理论研究；遗传算法在函数优化方面的应用研究：基于遗传算法的基本几何形体的形状误差计算：基于遗传算法的平面曲线形状误差计算；基于遗传算法的复杂几何形体的形状误差计算。论文的主要内容如下： 1．研究实数编码遗传算法的理论 对实数编码的遗传算法进行了系统的深入研究，提出了基于归一化实数编码遗传算法；讨论了其复制算子、交差算子、变异算子的选取和适应度函数的定义；对基于归一化实数编码遗传算法的模式定理进行了分析和研究；研究了一维和多维归一化实数编码长度与优化精度的关系；用马尔可夫链分析了归一化实数编码的遗传算法的收敛性；探讨了归一化实数编码的遗传算法的计算效率和性能；针对多维寻优问题，提出了基于归一化实数编码多维并行遗传算法，并对其遗传操作算子的机理进行了详细研究。 2．研究归一化实数编码遗传算法的函数优化技术 利用对实数编码遗传算法的研究成果，对函数的优化问题开展了以下研究工作： 1)应用归一化实数编码遗传算法研究一元函数优化问题，对控制参数和遗传算子的选择以及适应度函数的确定进行了探讨，对其收敛速度进行分析，并采用一系列典型的函数对其性能进行测试。 2)应用归一化实数编码多维并行遗传算法研究多元函数优化问题，对控制参数、遗传算子和适应度函数的选择进行了探讨，并对其收敛速度进行了分析，通过一系列典型函数对其性能进行测试，证明采用归一化实数编码多维并行遗传算法求解多维函数优化问题，可加快全局最优解收敛的速度。 3)应用归一化实数编码遗传算法结合惩罚函数法和模拟退火法来实现求解约束优化问题，通过一系列典型函数对其性能进行测试，证明该方法具有较好的收敛性能。 3．基于遗传算法的基本几何形状误差的计算 按照最小区域法的评定准则，基于遗传算法分别建立了描述圆度误差、平面直线度误差、空间直线度误差、平面度误差、圆柱度误差、圆锥度误差、球度误差的数学模型，解决了基于遗传算法的基本几何形体形状误差计算建模问题。采用基于归一化实数编码遗传算法的研究成果，精确计算简单几何形体的形状误差。 4.基于遗传算法的平面曲线形状误差计算的研究 建立了基于遗传算法的平面标准函数曲线形状误差数学模型，借助B样条函数建立了适合遗传算法计算的复杂平面曲线形状误差数学模型，采用归一化实数编码多维并行遗传算法进行求解，获得了满足最小区域法的平面曲线形状误差的解。 5.基于遗传算法的复杂几何形体形状误差计算 按照最小区域法评定准则，建立了基于遗传算法的标准参数曲面形状误差数学模型，借助3次B样条函数建立了复杂曲面形状误差数学模型，采用归一化实数编码多维并行遗传算法进行求解。大量的算例测试证明，所获得的结果符合最小区域法的评定原则。更多还原

【Abstract】 This dissertation mainly discussed the research on the theory of Genetic algorithms based on real encoding, the application of Genetic algorithms at function optimization, and the computation of simply form error, flat curve form error, complex surface form error. Follow are mainly study contents in this paper.1.Study and discussion of Genetic algorithms theory.This dissertation put up systemic and embedded research for genetic algorithms with real number encoding, Proposed Normalization Real number encoding, then discussed and studied the mechanism of the pattern theory, the definition of fitting function, analyzed and researched copy arithmetic, cross arithmetic and mutation arithmetic with normalization Real number encoding, studied the relation both length of normalization real number encoding and optimization precision, analyzed the convergence of genetic algorithms based on normalization real number encoding with Markov chain, discussed the calculating efficiency and performance of genetic algorithms based on normalization real number encoding. Aimed at mult-dimension optimization problem, proposed the mult-dimension combine genetic algorithms, and particularly studied its copy arithmetic, cross arithmetic and mutation arithmetic.2. Research of the function optimization technology with genetic algorithms based on normalization real number encoding.Following study works has been developed in this dissertation at function optimization problem:l)Studied the optimization problem of single dimension function with genetic algorithms based on normalization real number encoding, discussed the selection of control parameters, genetic arithmetic and fitting function, analyzed its convergence speed, at last test and analyzed the performance by use of a series of typical function.2) Studied the optimization problem of mult-dimension function with genetic algorithms based on normalization real number encoding, discussed the selection of control parameters, genetic arithmetic and fitting function, analyzed its convergence speed. With the test of a series of typical functions, The author probed that this method can accelerate convergence speed of global optimization solution.3) Discussed solved the constraint optimization problem by use of combined with genetic algorithms based on normalization real number encoding, penalty function method and simulated annealing algorithm. With The test of a series of typical functions, The author probed that this method has better convergence.3. Research of the calculating of basic form errors with genetic algorithms.This dissertation in turn set up the mathematic model of describing circularity error, flat straightness error, space straightness error, flatness error, cylindricity error, taper error and sphere error, it resolved the calculating problems of simplex form error for satisfying minimal zone law.This dissertation applied the research result of genetic algorithms based on normalization real number encoding to calculating complex form error, it can precision obtain the resolve of simplex form error and be realized easily with computer. This method inaugurated a new route for the data process of simplex form error.4. Research of calculating flat curve form error with genetic algorithms.According to minimal zone law, This dissertation set up the mathematic models of describingflat standard function curve form error, established the mathematic model of describing flat complex curve form error with B-sample function, in turn establish their fitting functions, then calculate form error with mult-dimension parallel genetic algorithms based on normalization real number encoding. The solution satisfy minimal zone law.5.Calculating of surface form error with genetic algorithms.According to minimal zone law, This dissertation set up the mathematic models of describing standard parameter surface form error, established the mathematic model of describing complex surface form error with B-sample function, in turn establish their fitting functions, then calculate更多还原