Determining the remaining useful life (RUL) of key assets in a manufacturing company is one of the most important maintenance engineering activities to improve system reliability and reduce maintenance costs. Knowing the RUL of the equipment can help the decision-making process regarding the proper maintenance of the equipment (for example, repair or replacement). In this regard, one of the challenges is to determine the appropriate forecasting model. This includes designing a mathematical model as well as finding a model that is trained with the most similar data to the data obtained from the current state of the equipment. In this research, to design an appropriate forecasting model, a DE algorithm is proposed to optimize the LSTM deep learning model architecture. Also, to find a suitable reference forecasting model, the cross-correlation criterion has been used as a similarity index. This index takes into account time lags and can determine the most similar learning data set to the current state of the equipment data. To evaluate the proposed model, the FEMTO-ST Institute bearings data were used, which included run-to-failure vibration data of 6 learning bearings and 11 test bearings. To evaluate the proposed optimized forecasting model, competing forecasting models including optimized MLP, optimized SVR, and optimized GPR has been used. Also, the proposed similarity index (cross-correlation) has been compared with the Pearson correlation coefficient and inverse Euclidean distance. The evaluation results show that the proposed model of this research has a better performance than competing models.