This paper is a study of computer communication backbone network. Based on the principles and multi-criterion models of computer-communication network reliability, the paper set up a multi-criterion optimization model for the all-terminal network reliability, with all-terminal reliability used as the indicator, where genetic algorithm is employed and proved to be able to generate a satisfactory result within the shortest time, and managed to solve the problem Np-hard, which is meant to be of high reliability and low cost.