One of the leading causes of cancer-related deaths among women is cervical cancer. Early diagnosis and treatment can minimize the complications of this cancer. Recently, researchers have designed and implemented many deep learning-based automated cervical cancer diagnosis models. However, the majority of these models suffer from over-fitting, parameter tuning, and gradient vanishing problems. To overcome these problems, in this paper a metaheuristics-based lightweight deep learning network (MLNet) is proposed. Initially, the hyper-parameters tuning problem of convolutional neural network (CNN) is defined as a multi-objective problem. Particle swarm optimization (PSO) is used to optimally define the CNN architecture. Thereafter, Dynamically hybrid niching differential evolution (DHDE) is utilized to optimize the hyper-parameters of CNN layers. Each particle of PSO and solution of DHDE together represent the possible CNN configuration. F-score is used as a fitness function. The proposed MLNet is trained and validated on three benchmark cervical cancer datasets. On the Herlev dataset, MLNet outperforms the existing models in terms of accuracy, f-measure, sensitivity, specificity, and precision by 1.6254%, 1.5178%, 1.5780%, 1.7145%, and 1.4890%, respectively. Also, on the SIPaKMeD dataset, MLNet achieves better performance than the existing models in terms of accuracy, f-measure, sensitivity, specificity, and precision by 2.1250%, 2.2455%, 1.9074%, 1.9258%, and 1.8975%, respectively. Finally, on the Mendeley LBC dataset, MLNet achieves better performance than the competitive models in terms of accuracy, f-measure, sensitivity, specificity, and precision by 1.4680%, 1.5845%, 1.3582%, 1.3926%, and 1.4125%, respectively.