In the automotive industry, a good vehicle is one that not only provides comfort and adequate on-road performance but also ensures safety for its users. Therefore, various standards have been created to qualify and ensure that cars meet minimum requirements. Assays include frontal and side impact tests. However, physical tests end up being costly if performed frequently, and thus, increasing the correlation between these and computational simulations has been explored in recent years. Within the computational scope, given the nonlinear nature of the functions involved in such studies, the use of metaheuristics (MH) with constraint handling techniques (CHT) has been employed to obtain better results for such scenarios. In this work, three MH algorithms are used: Archimedean Optimization (AOA), Sine-Cosine Algorithm (SCA), and Dung Beetle Optimization (DBO). They are coupled with CHTs of the penalty methods (PM) type in their most basic character, such as Static Penalty Method (SPM), Dynamic Penalty Method (DPM), and Adaptive Penalty Method (APM), and variations of the latter. The coupling of these techniques (MHs+PMs) forms a total of 15 ways to solve the classic car side impact problem, with each combination tested dozens of times to ensure repeatability and consistency, as well as statistical metrics. In conclusion, the use of DPM with any of the MHs is not the most suitable for this type of problem. Furthermore, all other combinations made are capable of achieving better, equal, or close results to those in the literature, with AOA+SPM obtaining the lowest value for the objective function and also the lowest mean.