Abstract: Multiresolution Analysis （MRA） is an important method of constructing wavelet. Generalized Frame Multire-solution Analysis （GFMRA） can construct any orthonormal wavelet based on single mother function. Floating Point Representation （FPR） is superior to other representation in function optimization and restriction optimization. The noise which FPR brings about influences badly the performance of genetic algorithm in genetic operation environment. This paper is dependent on theoretical analysis. It presents Floating Point Repreaentation Genetic Algorithm （FPRGA） based on GFMRA （FPRGAG）. FPRGAG is a method of FPR denoising mutation by orthonormal wavelet. The experiments are made on FPRGAG. The results of the theoretical research and  the experiments indicate FPRGAG is superior to other used algorithms, in convergence efficiency and precision. The method is reliable in theory, is feasible in technique.

Key words: Generalized Frame Multiresolution Analysis（GFMRA）, orthonormal wavelet, floating point representation, denoising mutation

摘要： MRA是构造小波的重要方法，而GFMRA可以构造任何具有单一母波的正交小波。浮点数编码在函数优化和约束优化领域明显有效于其他编码，但浮点数编码在遗传操作环境中产生的“噪音”严重地影响着遗传算法的性能。在理论分析的基础上，提出基于GFMRA构造的正交小波对浮点数编码消噪变异的FPRGAG方法，并进行了实验。理论研究和实验结果表明，无论是收敛速度还是收敛精度，FPRGAG都远远优于传统算法。该方法理论上是可靠的，技术上是可行的。

关键词: 广义框架多分辨率分析（GFMRA）, 正交小波, 浮点数编码, 消噪变异