The interaction between a vehicle's tire and the road surface is pivotal for a driver's control over the vehicle's movements. It serves as the fundamental link between the vehicle and the road. The modeling of tires holds significant importance in contemporary vehicle design, playing a critical role in assessing aspects such as vehicle handling, ride comfort, and road load analysis. This study focuses on investigating the impact of the enveloping behavior characteristics of a pneumatic tire on the performance of a suspension system. The analysis of the vehicle's ride comfort utilizes a half-car model. Unlike a previous model with a single point of contact with the road, the presented suspension system, coupled with a four-degree-of-freedom rigid ring tire model, offers a more precise estimation of both ride comfort and road holding. The primary emphasis of this research lies in the modeling and evaluation of the proposed suspension system's performance. A comprehensive computer model of the entire system is developed using MATLAB software. This work enhances the existing framework by incorporating both a Multi-Objective Genetic Algorithm (MOGA) and a Multi-Objective Particle Swarm Optimization (MOPSO) to optimize the damping and stiffness coefficients of the passive suspension. This approach allows for a detailed comparison of the optimization capabilities and effectiveness of both algorithms in refining vehicle ride comfort. The results from MATLAB simulations highlight performance improvements, and the comparative analysis of MOGA and MOPSO provides insights into the selection of optimization techniques for suspension system design.