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The topological design of local area network is a process to find the network with the best performance, minimum cost and highest reliability, under the objective and engineering constraints. The problem could be considered as a multi-objective optimization problem, owing to that it requires all kinds of network performances be optimized at the same time and keeps the cost minimum, and has been proven to be a NP-hard problem by some researchers. There is no existing effective determinant algorithm that can solve it so far. In this paper, we introduce the Pareto optimization theory, Pareto ranking technique and the Pareto converging genetic algorithm based on them, and a PCGA based algorithm for solving bicriteria network topology design problems of local area network, is presented, considering the network average delay and network cost. We also adopt the PruÂ¿fer number to represent chromosomes in order to ensure the tree topology of LAN. Besides, traditional crossover approach is improved to speed up the algorithm and a new variant based halting criteria is proposed to enhance the stability of the GA results. Thought the comparison between our results and that of exhausted search, our algorithm turns out to be correct and effective, and compared with the classic NPGA, the proposed method can search faster and produce topologies closer to the real Pareto-front.