提出了求解度约束最小生成树问题的单亲遗传算法.该算法首先利用Prufer数对生成树进行编码;然后精心地设计了一个随机地产生初始种群的方法,用这种方法产生的初始种群,不会含有任何不可行解;在遗传操作中只使用选择和变异操作,共设计了三种变异操作,其中两种变异操作均不会产生不可行解,只有一种变异操作可能会产生不可行解,需要作树的度的检查和修改;这样就大大的降低了不可行解产生的机会,从而提高了遗传算法的效率;而且只使用变异算子,有效的避免了早熟收敛现象的产生;通过大量的数值试验,表明该算法简单,高效,收敛率高;最后对此算法做了适当推广,并给出了用它求解TSP问题的具体步骤和实例. A single parent genetic algorithm is proposed to solve the minimum spanning tree problem with degree of constraint.The algorithm first uses the Prufer number to encode the spanning tree and then elaborately designs a method to generate the initial population at random.The initial population generated by this method is not Will contain any infeasible solution; in the genetic operation using only selection and mutation operation, a total of three kinds of mutation design operation, of which two kinds of mutation operation will not produce infeasible solution, only one mutation operation may produce infeasible solution , Need to check and modify the degree of tree; thus greatly reducing the chances of infeasible solution, thus improving the efficiency of genetic algorithm; and only using mutation operator, effectively avoid the premature convergence phenomenon; through A large number of numerical experiments show that the algorithm is simple and efficient, and has a high convergence rate. Finally, the algorithm is generalized and the specific steps and examples are given to solve the TSP problem.