Fixed-structure neural network lacks flexibility when tackling different classification tasks, prompting a growing interest in developing automated neural architecture search (NAS) methods. Approaches so far mainly consider the classification accuracy of the searching results for NAS, yet another important factor, the computation cost, is ignored. In this paper, a feasibility problem is modeled subject to specific constraints in terms of both the classification accuracy and computation cost, which can greatly enhance the flexibility against the fixed “balanced function” proposed in recent work in identifying radar signals in different electromagnetic environments. Moreover, to be able to traverse the infinite feasible region formed by the constraints, we propose a simple yet effective method based on the Gaussian process regression model by fine-tuning an initialized balanced function and leveraging a data distribution that meets the constraints. Experimental results demonstrate the superiority of the proposed NAS technique in designing comparably accurate network structures against manually-designed models, with less computation cost compared to conventional NAS algorithms.