Accurate prediction of drug-target interactions (DTIs) plays a central role in computational drug discovery and drug repositioning. Although deep learning models have substantially improved DTI prediction performance, most existing approaches rely exclusively on gradient-based optimization, which may suffer from unstable convergence or suboptimal solutions in sparse and high-dimensional biological datasets. In this study, we propose PSO-DTI, a swarm intelligence-enhanced neural framework that integrates similarity-based relational feature transformation with Particle Swarm Optimization (PSO) for adaptive neural weight refinement. Drugs and proteins are transformed into similarity-profile representations using Jaccard and cosine similarity measures, respectively. A neural classifier is then optimized using a validation-guided PSO-based selective weight adoption strategy. Experiments on benchmark C. elegans and Human datasets demonstrate consistent performance improvements over representative state-of-the-art models across AUROC, AUPRC, Accuracy, F1-score, and MCC metrics. Ablation studies confirm the contribution of similarity-based preprocessing and PSO-enhanced optimization. Case analyses further support the biological plausibility of top-ranked predictions. These findings suggest that integrating global search heuristics into neural training pipelines can enhance robustness and generalization in DTI prediction.