The increasing use of e-commerce websites and social networks is continually generating an immense amount of data in various forms, such as text, images or sounds, videos, etc. Sentiment analysis (SA) in online product reviews is a method of identifying the overall sentiment of customers about a specific product or service. This study used Natural Language Processing (NLP) and Machine Learning (ML) algorithms to identify and extract opinions and emotions expressed in text. Online reviews are often written in informal language, slang, and dialects, making it difficult for ML models to accurately classify sentiments. In addition, the use of misspelled words or incorrect grammar can further complicate the analysis. The recent developments of Deep Learning (DL) models can be used for the accurate classification of sentiments. This paper presents an Adaptive Particle Grey Wolf Optimizer with Deep Learning Based Sentiment Analysis (APGWO-DLSA) method to accurately classify sentiments in product reviews. Initially, data pre-processing was performed to improve the quality of the product reviews using the word2vec embedding process. For sentiment classification, the proposed method used a Deep Belief Network (DBN) model. Finally, the hyperparameter tuning of the DBN was performed using the APGWO algorithm. An extensive experimental analysis demonstrated the improved results of APGWO-DLSA over other methods, showing a maximum accuracy of 94.77% and 85.31% on the Cell Phones And Accessories (CPAA) and Amazon Products (AP) datasets.