Deep neural networks have achieved great success in many domains. However, successful deployment of such systems is determined by proper manual selection of the neural architecture. This is a tedious and time-consuming process that requires expert knowledge. Different tasks need very different architectures to obtain satisfactory results. The group of methods called the neural architecture search (NAS) helps to find effective architecture in an automated manner. In this paper, we present the use of an architecture search framework to solve the medical task of malignant melanoma detection. Unlike many other methods tested on benchmark datasets, we tested it on practical problem, which differs greatly in terms of difficulty in distinguishing between classes, resolution of images, data balance within the classes, and the number of data available. In order to find a suitable network structure, the hill-climbing search strategy was employed along with network morphism operations to explore the search space. The network morphism operations allow for incremental increases in the network size with the use of the previously trained network. This kind of knowledge reusing allows significantly reducing the computational cost. The proposed approach produces structures that achieve similar results to those provided by manually designed structures, at the same time making use of almost 20 times fewer parameters. What is more, the search process lasts on average only 18h on single GPU.