Phishing website detection relies on automated methods to spot counterfeit websites masquerading as legitimate ones, aiming to dupe users and pilfer sensitive data. These methods harness a range of cues, including suspicious Uniform Resource Locators (URLs), domain name mismatches, irregular Hypertext Markup Language (HTML) structures, expired Secure Socket Layer (SSL) certificates, and content analysis. Machine learning and deep learning models, trained on datasets containing both authentic and phishing websites, are pivotal in this endeavor. A novel approach, termed the Swarm Intelligence Binary Bat Algorithm with Convolutional Neural Network (SBBA-CNN), has been introduced for phishing website detection. SBBA optimizes CNN design to classify network URLs via a classification-driven strategy. Feature selection is pivotal, enhancing model efficiency, reducing overfitting, and emphasizing pertinent indicators to enhance accuracy and curb false positives. Thus, a newly proposed technique, Improvised Mutual information Feature Selection (IMFS), leverages minimum redundancy and maximum relevance (mRMR) principles to compute mutual information among candidate features, selecting informative ones in the dataset. Then SBBA-CNN processes these chosen features, refining model efficiency, mitigating overfitting, and diminishing false positives. Empirical results validate that IMFS-SCNN outperforms SBBA-CNN in terms of accuracy, precision, and recall for phishing website detection.