In the software testing phase, software reliability growth models (SRGMs) are commonly used to evaluate the reliability of software systems. Traditional SRGMs are restricted by their assumption of a continuous growth pattern for the failure detection rate (FDR) throughout the testing phase. However, the assumption is compromised by Change-Point phenomena, where FDR fluctuations stem from variations in testing personnel or procedural modifications, leading to reduced prediction accuracy and compromised software reliability assessments. Therefore, the objective of this study is to improve software reliability prediction using a novel approach that combines genetic algorithm (GA) and deep learning-based SRGMs to account for the Change-point phenomenon. The proposed approach uses a GA to dynamically combine activation functions from various deep learning-based SRGMs into a new mutated SRGM called MuSRGM. The MuSRGM captures the advantages of both concave and S-shaped SRGMs and is better suited to capture the change-point phenomenon during testing and more accurately reflect actual testing situations. Additionally, failure data is treated as a time series and analyzed using a combination of Long Short-Term Memory (LSTM) and Attention mechanisms. To assess the performance of MuSRGM, we conducted experiments on three distinct failure datasets. The results indicate that MuSRGM outperformed the baseline method, exhibiting low prediction error (MSE) on all three datasets. Furthermore, MuSRGM demonstrated remarkable generalization ability on these datasets, remaining unaffected by uneven data distribution. Therefore, MuSRGM represents a highly promising advanced solution that can provide increased accuracy and applicability for software reliability assessment during the testing phase.