Generative adversarial networks (GANs) have been successfully used for considerable computer vision tasks, especially the image-to-image translation. However, generators in these networks are of complicated architectures with large number of parameters and huge computational complexities. Existing methods are mainly designed for compressing and speeding-up deep neural networks in the classification task, and cannot be directly applied on GANs for image translation, due to their different objectives and training procedures. To this end, we develop a novel co-evolutionary approach for reducing their memory usage and FLOPs simultaneously. In practice, generators for two image domains are encoded as two populations and synergistically optimized for investigating the most important convolution filters iteratively. Fitness of each individual is calculated using the number of parameters, a discriminator-aware regularization, and the cycle consistency. Extensive experiments conducted on benchmark datasets demonstrate the effectiveness of the proposed method for obtaining compact and effective generators.