As a hot subject in current scientific research, complex networks have developed tremendously in the past 20 years. A large number of complex interactive systems in reality, such as the Internet, transportation networks, and neural networks, can be abstracted as complex networks for systematic analysis and research. As an optimization tool, evolutionary algorithms are applied to various tasks in different fields of complex networks, such as the tasks of detecting network community structure, optimizing robustness in network dynamics, and searching key nodes in network propagation. This study first gives a comprehensive overview of the basic knowledge related to complex networks and evolutionary algorithms and then focuses on the research progress of objective optimization in complex networks. The optimization objectives and their specific applications are introduced in detail for different tasks. At the same time, the performance evaluation indexes of the algorithms are summarized. In addition, this study demonstrates the performance of single/multi-objective optimization algorithms on complex network optimization problems through a series of experiments and represents the correlation between some objectives. In the last part of the study, the future research trends of optimization problems in complex networks are prospected, which can provide some ideas for researchers to carry out related research on the combination of evolutionary computation and complex networks.