Cervical cancer is one of the most significant causes of cancer-related deaths in women. In this article, we have proposed a deep learning based automated cervical cancer classification system by analyzing pap smear cytology images. We have proposed a new metaheuristic optimization algorithm for deep feature selection named “Random Walk-Based Artificial Electric Field Algorithm” (RWAEFA). RWAEFA is a modification of the traditional Artificial Electric Field Algorithm (AEFA) using the random walk phenomenon, which effectively explores the feature space by capturing complex relationships and optimizing feature subsets for classification tasks. The features are extracted by pre-trained ResNet-18 model. Finally, these optimized deep features are employed for the cervical cytology image classification by Support Vector Machine(SVM). The method is experimented on two publicly available cervical cytology image datasets and it outperforms six metaheuristic optimization algorithms for this task. RWAEFA also outperforms AEFA on ten out of twelve standard benchmark functions, which reveals the robustness of the proposed system. The proposed model has achieved 99.48% and 93.78% on Mendeley LBC and SiPaKMed datasets respectively.