Energy consumption is a fundamental concern in mobile application development, bearing substantial significance for both developers and end-users. Main objective of this research is to propose a novel neural network-based framework, enhanced by a metaheuristic approach, to achieve robust energy prediction in the context of mobile app development. The metaheuristic approach here aims to achieve two goals: 1) identifying suitable learning algorithms and their corresponding hyperparameters, and 2) determining the optimal number of layers and neurons within each layer. Moreover, due to limitations in accessing certain aspects of a mobile phone, there might be missing data in the data set, and the proposed framework can handle this. In addition, we conducted an optimal algorithm selection strategy, employing 13 base and advanced metaheuristic algorithms, to identify the best algorithm based on accuracy and resistance to missing values. The representation in our proposed metaheuristic algorithm is variable-size, meaning that the length of the candidate solutions changes over time. We compared the algorithms based on the architecture found by each algorithm at different levels of missing values, accuracy, F-measure, and stability analysis. Additionally, we conducted a Wilcoxon signed-rank test for statistical comparison of the results. The extensive experiments show that our proposed approach significantly improves energy consumption prediction. Particularly, the JADE algorithm, a variant of Differential Evolution (DE), DE, and the Covariance Matrix Adaptation Evolution Strategy deliver superior results under various conditions and across different missing value levels.