As an epitome of deep learning, convolutional neural network (CNN) has shown its advantages in solving many real-world problems. Successful CNN applications on medical prognosis and diagnosis have been achieved in recent years. Their common goal is to recognize the insights from the subtle details from medical images by building a suitable CNN model with maximum accuracy and minimum error. The CNN performance is extremely sensitive to the parameter tuning for any given network structure. To approach this concern, a novel self-tuning CNN model is proposed with a significant characteristic of having a metaheuristic-based optimizer. The most optimal set of parameters is often found via our proposed method, namely group theory and random selection-based particle swarm optimization (GTRS-PSO). The insights of symmetric essentials of model structure and parameter correlation are extracted, followed by the hierarchical partitioning of parameter space, and four operators on those partitions are designed for moving neighborhoods and formulating the swarm topology accordingly. The parameters are updated by a random selection strategy at each interval of partitions during the search process. Preliminary experiments over two radiology image datasets: breast cancer and lung cancer, are conducted for a comprehensive comparison of GTRS-PSO versus other optimization algorithms. The results show that CNN with GTRS-PSO optimizer can achieve the best performance for cancer image classifications, especially when there are symmetric components inside the data properties and model structures.