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Network topology design (NTD) with multiple objectives has been presented by many researchers. However, no work in the literature has addressed this issue with both multiple objectives and multiple criteria. In order to suit real-world situations, this paper presents a new idea integrating genetic algorithm and goal programming to establish a model for solving the NTD problem with multiple objectives and multiple criteria taken into consideration. In addition, the proposed model can also solve both construct and extend network topology problems under shared risk link group (SRLG) constraints. Finally, illustrative examples are included to demonstrate the superiority and usefulness of the proposed method.