Internet of Things (IoT) includes numerous sensing nodes that constitute a large scale-free network. Optimizing the network topology for increased resistance against malicious attacks is an NP-hard problem. Heuristic algorithms, particularly genetic algorithms, can effectively cope with such problems. However, conventional genetic algorithms are prone to falling into premature convergence owing to the lack of global search ability caused by the loss of population diversity during evolution. Although this can be alleviated by increasing population size, additional computational overhead will be incurred. Moreover, after crossover and mutation operations, individual changes in the population are mixed, and loss of optimal individuals may occur, which will slow down the evolution of the population. Therefore, we combine the population state with the evolutionary process and propose an Adaptive Robustness Evolution Algorithm (AREA) with self-competition for scale-free IoT topologies. In AREA, the crossover and mutation operations are dynamically adjusted according to population diversity to ensure global search ability. Moreover, a self-competitive mechanism is used to ensure convergence. The simulation results demonstrate that AREA is more effective in improving the robustness of scale-free IoT networks than several existing methods.