Abstract: For the degree-constrained minimum spanning tree problem, a new encoding scheme was presented based on its characters. And then a genetic algorithm was proposed. Heuristics crossover operator, mutation operator and local search scheme were designed in the algorithm and its convergence to global optimal solution with probability one was proved. At last, the simulated results indicate that this method is effective than other four algorithms.

Key words: Genetic algorithm, minimum spanning tree, global convergence, combinatorial optimization

摘要： 针对度约束最小生成树问题的特征，设计了一种新的编码方式，并在此基础上提出了一个新遗传算法来求解该问题。该算法采用新的启发式杂交算子、变异算子和局部搜索算子，理论分析表明该算法以概率1收敛到全局最优解。数值实验表明该算法优于其他四个算法。

关键词: 遗传算法 最小生成树 全局收敛性 组合优化