## 3 Method
### Overall Framework of ICSO
The CelebA is a large dataset of face attributes containing more than 200,000 64 \(\times\) 64 RGB images. The CelebA dataset has been leveraged for a range of face-related computer vision tasks, including facial attribute recognition, facial expression analysis, and face generation. The CelebA-64 is a variant of CelebA in which the face of each image is centrally located and labeled with 40 attributes. The ImageNet is a large image dataset containing more than 14 million images, covering more than 20,000 categories. This dataset is usually used for classification, localization, and detection. It is extensively employed in research in the field of computer vision and related industrial applications. Figure 3: Procedure of VC. In the figure, \(D_{i}\) represents the dimension of an individual. The diagram illustrates the process of generating new dimensions for an individual across two different dimensions according to Equation (15). ### Parameter Setting

The hyperparameters involved in ICSO can be divided into search strategy and GAN: For search strategies, the population size is 10, the maximum number of iterations is 10, and the dimension of the individual (i.e., the Gaussian noise) is 100. The horizontal probability is 1. For GAN, since the latent space focused on in this paper is completely independent from the other components of GAN, the model and parameter setting of GAN remain consistent with [18]. The testing environment is described as follows: PyTorch (version 1.13.1) and Nvidia GeForce GTX 4090 (Nvidia, Santa Clara, CA, USA). ### Evaluation Metrics

In this study, we evaluate the performance of the generative models using the following metrics: Inception Scores (IS) [19], Frechet Inception Distance (FID) [20], Density [21], and Coverage [21]. The IS measures the quality and diversity of generated images, with higher values indicating better performance. The FID quantifies the similarity between the distributions of real and generated images, where lower values correspond to higher generation quality. Density evaluates how well the model covers the data manifold without generating unrealistic samples, while Coverage assesses the proportion of the test data manifold that is captured by the generated samples. Additionally, we report the computational efficiency in terms of GPU training days required to reach convergence, expressed in GPU/days. ### Generative Performance

As shown in Table 1, the experiments systematically evaluate the outstanding performance of ICSO in optimizing the latent space through comprehensive comparisons with random Gaussian noise (Baseline) and AdvLatGAN [18] (iterative fast gradient sign method: 1-FGSM), revealing the significant advantages of ICSO across various classic GAN architectures, including DCGAN [22], WGAN [23], WGAN-GP [16], SNGAN [24], LSGAN [25], WGAN-div [26], and ACGAN [27]. The experiments cover multiple benchmark datasets ranging from CIFAR-10 and STL-10 to LSUN-64/128, CelebA-64/128, and ImageNet, demonstrating the consistent superiority of ICSO on datasets of different scales and complexities. Specifically, on the CIFAR-10 and STL-10 datasets, ICSO achieves higher IS across multiple GANs, demonstrating the remarkable quality and diversity of the generated images. Similarly, lower FID further validates the authenticity and detail fidelity of the images generated by ICSO. When applied to more complex datasets such as LSUN-64/128, CelebA-64/128, and ImageNet, ICSO leverages its unique evolutionary strategies to deeply explore global optima and generate high-quality samples. Whether in a relatively simple generative adversarial network like DCGAN or in other classic GANs that employ more complex training mechanisms to enhance stability and the quality of generated images, such as WGAN-GP and WGAN-div, ICSO demonstrates outstanding optimization capabilities. However, when applied to SNGAN across CIFAR-10, STL-10, and CelebA-64 datasets, ICSO does not perform as well as AdvLatGAN.