Energy efficiency and delay time in the Internet of Things (IoT) system are becoming increasingly significant, especially for the emerging memristor-based crossbar arrays for smart edge computing. This article aims to find a solution for increasing energy efficiency and reducing the delay time, thereby improving the performance of ANNs in edge computing systems. The Number of Pulses Compression (NPC) method is proposed to optimize pulse distribution, energy consumption, and latency by compressing the number of pulses in every weight update step. The NPC method is implemented and verified in a memristor-based hardware simulator based on the MNIST and CIFAR-10 dataset under different circumstances of variations, failure rates, aging effects, architectures, and algorithms. The experimental results show that the NPC method can not only alleviate the uneven distribution of writing pulses but also save the writing energy of the crossbar array by 7.7--26.9 percent and reduce the writing latency by 30.0--50.0 percent. Additionally, the timing regularity of the system is enhanced by the NPC method.