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Automatic network clustering is an important method for mining the meaningful communities of complex networks. Uncovered communities help to understand the potential system structure and functionality. Many algorithms that use multiple optimization criteria and optimize a population of solutions are difficult to apply to real systems because they suffer a long optimization process. In this paper, in order to accelerate the optimization process and to uncover multiple significant community structures more effectively, a multi-objective evolutionary algorithm is proposed and evaluated using problem-specific genetic mutation and group crossover, and problem-specific initialization. Since crossover operators mainly contribute to performance of genetic algorithms, more problem-specific group crossover operators are introduced and evaluated for intelligent evolution of population. The experiments on both artificial and real-world networks demonstrate that the proposed evolutionary algorithm with problem-specific genetic operations has effective performance on discovering the community structure of networks. [ABSTRACT FROM AUTHOR]