Numerous sensor nodes deployed in the Internet of Things (IoT) can form a large heterogeneous network. The increased energy consumption of sensor nodes and the unbalanced communication load on multiple sink nodes reduce the energy efficiency of the network. Moreover, frequent network attacks also pose severe challenges to topology robustness. Optimizing the network topology to achieve the balance between energy efficiency and robustness is a complex problem. Multi-objective heuristic algorithms based on genetic evolution are commonly used to solve joint optimization problems. However, due to the lack of global search ability caused by the loss of genetic diversity, genetic operations are prone to premature convergence during multi-objective evolution. Therefore, this paper introduces multi-population cooperation into the multi-objective evolution process and proposes a novel layered-cooperation Topology Evolution Algorithm for Multi-sink IoT (TEAM). In TEAM, information entropy is used to measure the effectiveness of load balancing on multiple sink nodes. The crossover and mutation probabilities of different populations are dynamically adjusted to ensure genetic diversity. A layered-cooperation mechanism is designed to avoid premature convergence. Extensive experiments confirm that TEAM can effectively improve the energy efficiency and robustness of network topology while balancing the communication load on multi-sink nodes.