基于距离空间的遗传算法分析

通过对简单遗传算法的分析，发现每次执行复制、杂交、变异等操作均相当于对所作用的个体进行一次线性变换，这样，从函数的角度来看，引入非线性变换的遗传算子将是一个有待研究的问题，因而提出了非线性遗传算法。通过对二进制遗传算法的Hamming距离的扩充，引入了一种几何模型-距离空间，并在该空间上对杂交、变异等算子进行了系统的分析。根据分析结果，指出了改进遗传算法的途径，并提出一种改进的二进制非线性遗传算法，仿真实例证明了其有效性。以上分析从几何意义出发，提出了一种全新的分析遗传算子的方法，对遗传算法理论的完善与发展具有重要意义。

Mechanism Analysis of Genetic Algorithm Based on Distance Space

Through mechanism analysis of simple genetic algorithm (SGA), every genetic operator can be considered as a linear transform to the corresponding individuals. From the point of function, it is a desirable research aspect to give some new genetic operator using nonlinear transform. By the expansion of Hamming distance, a new geometry model-distance space is introduced. In this space, mechanism analysis of crossover and mutation operators is made. According to the analysis, some improved measure is given. The optimization computing of some examples is made to show that the BCNGA has better global search capacity and rapid convergence rate. The above work establishes a completely new mathematical analytic method of genetic operators and contributes much to perfection and development of the theory of genetic algorithm.