## 4 Results and Discussion
### RQ1: What NAS Approaches Are Applied to GANs in the Literature?
#### 4.1.1 Evolutionary Algorithms Approaches  
EA is a family of metaheuristic optimization algorithms, inspired by collective behaviors observed in nature [21]. These algorithms can navigate complex high-dimensional search spaces to find near-optimal solutions, making them well-suited for automatically finding answers to the many interdependent architectural decisions in deep neural networks. EAs have been increasingly applied to the field of GAN architecture search, with several notable approaches emerging in recent years. [PERSON] et al. (2019) [22] proposed E-GAN, which evolves a population of generators using different adversarial objectives as mutation operations. Specifically, they employed three different objectives: Minimax objective, Heuristic objective Least-squares objective. This method adapts to the discriminator and overcomes limitations of individual adversarial objectives, requiring 1.25 GPU Days for searching. Yet only the top-performing generator persists, which might limit diversity. [PERSON] et al. (2018) [23] introduced Lipizzaner, a coevolutionary framework that evolves the internal parameters (weights) of fixed generator and discriminator architectures. Building on this, [PERSON] et al. (2019) [24] developed Mustangs, a hybrid approach combining elements of E-GAN and Lipizzaner, incorporating multiple loss functions as mutation operators and using a spatial grid coevolution scheme. Complementing these approaches, [PERSON] et al. (2018) [25] introduced EvoGAN a neuro-evolutionary framework that evolves GAN architectures by encoding both the network topology (e.g., number of hidden layers, activation functions, weight initialization) and key training parameters such as the loss function and synchronization frequency between the generator and discriminator. Their method leverages a genetic algorithm with specialized mutation operators to navigate a flexible search space, employing Pareto set approximation and the inverted generational distance (IGD) as a benchmark for evaluating mode collapse and diversity. Notably, EvoGAN scales to 784 variables, though retaining only the top-performing architecture per generation might limit diversity. The framework was evaluated on a set of bi-objective continuous test problems for Pareto set approximation. Performance was measured using the inverted generational distance (IGD); for example, on function F1, IGD was reduced by up to two orders of magnitude in both low- (n = 10) and high-dimensional (n = 784) settings, with additional tests demonstrating transferability across functions. Similarly, [PERSON] et al. (2018) [26] propose a GA-assisted Bi-GAN framework that autonomously refines deep neural network parameters by combining discrete GA-based  
Figure 2: Distribution of NAS-GAN Methods by Search Strategy. decisions with continuous refinement via a bi-generative adversarial network. This approach optimizes parameters--including the number of neurons, filters, layers, and even the inclusion of dropout or pooling layers--thereby enabling the network to self-configure its architecture and hyper-parameters during training. By bridging exploration and exploitation, this framework overcomes the limitations of fixed discrete candidate sets typically associated with GA-only approaches. Bi-GAN was tested on the voxelized ModelNet40 dataset [27] (3D CAD models of 40 object classes). Their experiments showed that the proposed method achieved an accuracy of 85.20%, outperforming the baseline 3D Shapenet (84.17%) and two GA-only approaches (small-set GA: 82.94%; large-set GA: 36.41%). In other studies, multi-objective function and multi-stage search have been utilized. [PERSON] et al. (2020) [28], using the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) algorithm for multi-objective optimization of DCGAN structures (NSGA-II DCGAN), specifically used True Positive Rate (1-TPR) and False Positive Rate (FPR). Implementing two-stage searches, [PERSON] et al.