Leveraging optimization search methods inspired by nature has demonstrated its resilience as a valuable approach when aiming to find optimal solutions for the Traveling Salesman Problem (TSP). This problem has significant implications for delivery service companies, as routine encounters with suboptimal route issues have a direct application in affecting delivery times and, consequently, the company’s reputation. In this paper, we present a pioneering strategy referred to as Gaussian Guided Cognitive-Socio Particle Swarm Optimization (GGCSPSO), uniquely designed to tackle the intricacies of the TSP. In the framework of GGCSPSO, Gaussian random variables are integrated into the cognitive and social aspects of the PSO algorithm. This inclusion of Gaussian random variables plays a pivotal role by enhancing the search process’s efficiency while simultaneously elevating the probability of successfully identifying the global optimum solution. The evaluation of the GGCSPSO method involves a comparative analysis with ten classical TSP instances. This assessment is predominantly focused on quantifying the algorithm’s efficacy in identifying optimal solutions and assessing its computational efficiency. The computational results conclusively establish that the GGCSPSO algorithm demonstrates significant advancements in addressing TSP problems, thereby surpassing the performance of the PSO technique.