一种求解代数方程组的混合遗传算法及工程应用

针对用遗传算法求解代数方程组时解的精度问题，提出了一种混合遗传算法，这种算法采用实数编码方法，在遗传算法的基础上，引入一种用适应度函数值构成动态变化的搜索步长的随机搜索算子，当遗传算法求解达到某一精度时，应用该搜索算子在最优个体附近进行随机搜索，使算法解较快地逼近到所要求的精度，实验表明用这种算法求解代数方程组，可以达到较高的求解精度，在工程中用于求解关节型机器人速度逆解，避免了矩阵求逆，取得了满意的效果。

A Hybrid Genetic Algorithm for Solving Algebraic Equations Set and Its Application in Engineering

Aiming at the precision of the solution of algebraic equations set which has been solved by genetic algorithm, a new hybrid genetic algorithm(HGA) is presented in this paper. This HGA has employed a floating-point gene encoding method and a random searching operator with dynamic variational searching step obtained from the fitness function value. When the solutions of GA get at a certain precision, the operator was employed to search the required solution randomly near the best individual of GA population, which made the required solution precision quickly obtained. Experimental results indicate that higher precision solutions can be obtained by using this new HGA to solve algebraic equations set. A typical engineering application of it was to solve inverse velocity solutions of joint-type robot, by which a satisfactory effect was achieved and the complex process of inverse matrix computation was avoided.