Abstract: Encoding is one of difficult problems of research on Genetic Algorithm（GA）.Float Code（FC） is super to other codes in function and restriction optimization.But it is ignored by researchers how FC is denoised in running environment of GA for enhancing the performance of GA.In this paper，it is proved by the wavelet theory that odd-length and even-length of chromosome encoded can all be mutated with wavelet denoising.The Float Code GA（FCGA） with orthonormal multi-Wavelet Denoising Mutation（FGAWDM） is presented based on the above result.The experiments are done.The result of the research and the experiment indicates that the method is credible in theory，is feasible in technique.It is of active significance to extend application space of FCGA.

Key words: orthonormal multiwavelet, denoising mutation, float code, genetic algorithm

摘要： 编码是遗传算法研究的难点问题之一。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。但消除浮点数编码在遗传算法运行环境中产生的噪音，以提高遗传算法性能的理论和方法尚不被人们所认识。在用正交多小波对浮点数编码遗传算法消噪变异的基础上，针对染色体编码长度的奇偶数问题，从理论上证明了正交多小波既能对偶数长度染色体编码消噪变异，也能对奇数长度染色体编码消噪变异，基于这一结论提出了基于正交多小波消噪变异的浮点数编码遗传算法（FGAWDM），并进行了实验。研究和实验的结果表明，该方法理论上是可靠的，方法上是可行的，对于拓展浮点数编码遗传算法的应用空间具有积极的意义。

关键词: 正交多小波, 消噪变异, 浮点数编码, 遗传算法