The deployment of convolutional neural networks (CNNs) on resource-constrained platforms, such as embedded systems and IoT devices, is hindered by their high computational and memory demands. This paper introduces a unified compression framework that synergistically combines Genetic Algorithms (GAs) with Knowledge Distillation (KD) to jointly optimize network sparsity and predictive accuracy. The search space, defined by all possible pruning configurations of m neurons, grows exponentially (2m) and renders exhaustive search intractable. To address this NP-hard problem, we encode network architectures as binary chromosomes and employ a GA to perform global exploration, guided by a multi-objective fitness function that simultaneously rewards classification accuracy and compression ratio.