## 1 Introduction  
In recent years, advancements in machine learning and artificial intelligence (AI) have led to significant progress in generative models, which are used to create realistic synthetic data across various domains. Among these models, Generative Adversarial Networks (GANs) [1, 2] have emerged as a cornerstone technology, particularly in applications requiring high-quality image synthesis [3], such as medical imaging [4], autonomous driving [5], and virtual media generation [6, 7]. GANs consist of two competing neural networks--a generator that produces images and a discriminator that evaluates them. This adversarial setup has proven effective at refining the model's ability to create realistic outputs. However, despite the wide adoption of GANs, their training remains challenging. Issues such as mode collapse, unstable convergence, and sensitivity to hyperparameter selection complicate the generation of diverse, high-fidelity images. One approach to address these limitations has been the development of Deep Convolutional GANs (DCGANs) [8], which incorporate Convolutional Neural Networks (CNNs) to enhance image quality by capturing complex spatial hierarchies in visual data. DCGANs have demonstrated success in tasks like facial recognition [9, 10, 11] and image synthesis [12, 13, 14], due to their capacity to model high-dimensional image data. Nonetheless,their reliance on gradient-based learning techniques leaves DCGANs vulnerable to issues like overfitting and local minima. Researchers have thus explored methods beyond traditional optimization, with evolutionary algorithms, particularly Genetic Algorithms (GAs), showing promise for enhancing GAN performance. Genetic Algorithms utilize evolutionary principles--such as selection, crossover, and mutation--to iteratively improve solutions, offering a global search capability that complements the local search tendencies of gradient-based methods. This evolutionary approach has demonstrated its potential for improving model robustness, optimizing network hyperparameters, and introducing greater variability in generated outputs. Several approaches have been explored to address the inherent challenges in GAN training. The authors in [15] introduced Spectral Normalization to stabilize GAN training by constraining the Lipschitz constant of the discriminator, thereby reducing gradient issues that can lead to oscillatory or divergent training. Another approach, Wasserstein GAN (WGAN), introduced in [16], replaces the traditional GAN loss with the Wasserstein distance metric, offering a more stable objective function and improving convergence. While effective, these approaches do not completely resolve the problems of GAN training instability and mode collapse. Evolutionary computation, inspired by biological processes, offers another promising avenue. Genetic Algorithms (GAs) [17; 18; 19] are optimization techniques that use principles of natural selection to refine solutions over successive generations. This approach, while traditionally applied to optimization problems, has been increasingly recognized for its potential in enhancing neural network training. GAs operate through selection, crossover, and mutation of \"individuals\" within a population, which in the GAN context can be applied to optimize model weights. The application of GAs to neural networks has shown potential for improving model robustness and convergence, particularly by augmenting standard gradient-based optimization techniques with global search capabilities that prevent premature convergence to local minima [20]. More recently, hybrid models integrating GAs with GANs have been proposed. The work in [21] has demonstrated that applying evolutionary algorithms can improve the exploration of solution spaces in GAN training. These approaches enhance model diversity and stability, addressing challenges such as mode collapse and unstable convergence.