Genetic algorithm approach on multi-criteria minimum spanning tree problem

Minimum Spanning Tree (MST) problem is of high importance in network optimization. The multi-criteria MST (mc-MST) is a more realistic representation of the practical problem in the real-world, but it is diicult for the traditional network optimization technique to deal with. In this paper, a genetic algorithm (GA) approach is developed to deal with this problem. Without neglecting its network topology, the proposed method adopts the Pr ufer number as the tree encoding and applies the Multiple Criteria Decision Making (MCDM) technique and nondominated sorting technique to make the GA search give out all Pareto optimal solutions either focused on the region near the ideal point or distributed all along the Pareto frontier. Compared with the enumeration method of Pareto optimal solution, the numerical analysis shows the eeciency and eeectiveness of the GA approach on the mc-MST problem.