We propose a novel neural architecture search (NAS) approach for the challenge of designing convolutional neural networks (CNNs) that achieve a good tradeoff between complexity and accuracy. We rely on Cartesian genetic programming (CGP) and integrated real-based and block-chained CNN representation, for optimization using multi-objective evolutionary algorithms (MOEAs) in the continuous domain. We introduce two variants, CGP-NASV1 and CGP-NASV2, which differ in the granularity of their respective search spaces. To evaluate the proposed algorithms, we utilized the non-dominated sorting genetic algorithm II (NSGA-II) on the CIFAR-10, CIFAR-100,and SVHN datasets. Additionally, we extended the empirical analysis while maintaining the same solution representation to assess other searching techniques such as differential evolution (DE), the multi-objective evolutionary algorithm based on decomposition (MOEA/D), and the S metric selection evolutionary multi-objective algorithm (SMS-EMOA). The experimental results demonstrate that our approach exhibits competitive classification performance and model complexity compared to state-of-the-art methods.