A Crossover Algebra for Solving Minimum Spanning Tree in Network Design with Diameter Constraints

Abstract

Abstract The minimum spanning tree problem with diameter constraint is an important problem for many applications such as network design and reliability. The diameter constraint makes it be different from the common minimum spanning tree problem, it is difficult to get the optimal solution, even the feasible solution can not be obtained by the traditional method. To address this problem, in this paper, a new crossover algebra is designed to ensure that the crossover tree still satisfies the diameter constraint. During the crossover process, structure of the subtree will be retained, thus avoiding the problem that the new generated tree is not a feasible solution. Experimental results show the effectiveness of the improved algorithm.