特殊变换多小波构造的浮点数编码遗传算法

浮点数编码具有精度高、便于高维大空间搜索的优点，在函数优化和约束优化领域明显有效于其他编码。浮点数编码遗传算法在操作环境中产生的噪音和对算法性能的影响尚不被人们所认识。将小波用于浮点数编码遗传算法的消噪变异是解决该问题的有效途径。单一小波对浮点数编码消噪变异泛化能力低，且对浮点数编码遗传算法性能改进有一定的局限性。研究证明了用酉变换可构造正交多小波，将正交多小波用于浮点数编码遗传算法的消噪变异，提出了FGAMW方法，并进行了实验。理论研究和实验结果表明，提出的FGAMW方法理论上是可靠的，技术上是可行的，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。

Floating point representation genetic algorithm based on construction of multiwavelets in terms of novel ;transformation

Floating Point Representation（FPR） has the advantage of higher precision and easy to search in high-dimension space. FPR is in evidence superior to other codes in fields of function optimization and restriction optimization. It is not known by researchers that noise is generated by FPR Genetic Algorithm（FPRGA） in operation environment and how it affectes on the algorithm performance. It is an available approach of solving the problem that wavelet is used to FPRGA denoising mutation. Single wavelet is of lower generalization ability in FPRGA denoising mutation. It is of a limitation of improving performance of FPRGA. The paper presents a Floating point representation Genetic Algorithm based on Multiwavelets in terms of a novel transformation（FGAMW）. It is proved that orthogonal multiwavelet is constructed by unitary transform. Orthogonal multiwavelet is used to denoise mutation in FPRGA. The experiments are done in it. The results of the theoretic research and the experiments indicate that FGAMW is reliable in theory and feasible in technique. It is of active significance to extend application of FPRGA.