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Since the advent of generative adversarial networks (GANs), various loss functions have been developed and combined to constitute the overall training objective function, in order to improve model performance or for specific learning tasks. For instance, in image enhancement or restoration, there are often several criteria to consider such as signal-noise ratio, smoothness, structures and details. However, when the optimization goal has more than one adversarial loss, balancing multiple losses in the overall function becomes a challenging, critical and time-consuming problem. In this paper, we propose to tackle the problem by means of efficient multi-objective optimization. The proposed HypervolGAN adopts an adapted version of hypervolume maximization method to effectively define the multi-objective training function for GAN. We tested our proposed method on solving single image super-resolution problem. Experiments show that the proposed HypervolGAN is efficient in saving computational time and efforts for fine-tuning weights of various losses, and can generate enhanced samples that have better quality than results given by baseline GANs. The work explores the integration of adversarial learning and optimization techniques, which can benefit not only image processing but also a wide range of applications.