In this paper, investigate several recent multiobjective Evolutionary Algorithms (moEAs), and propose a new moEA approach for bicriteria communication spanning tree problem (bSTP). The bSTP is to find a set of links with the two conflicting objectives of minimizing communication cost and minimizing the transfer delay. This problem can be formulated as the Multiobjective Minimum Spanning Tree (mMST) problem, and is NP-complete. This paper design a new multiobjective evolutionary approach to the two conflicting objectives of minimizing cost and minimizing delay, an interactive adaptive-weight assignment mechanism is used. In addition, we investigate the different encoding, crossover and mutation operators on the performance of GAs to design of MST problems. Based on the performance analysis of these encoding methods in GAs, we improved predecessor-based encoding, in which initialization depends on an underlying random spanning-tree algorithm. We compared with the recent approaches, and provide better results on larger instances.