关键词: 酉变换, 多小波, 浮点数编码, 遗传算法, 消噪变异

Abstract: 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.

Key words: unitary transform, multiwavelets, floating point representation, Genetic Algorithm（GA）, denoising mutation