## 3 Utilized Design Optimization Algorithms
### Grey Wolf Optimizer (GWO)
while GA and SQP did not do well compared to GWO and produced a transmitted load of 285.58 lb. (the worst) and 38.7002 lb., respectively. When considering combined loads, GWO outperformed GA and SQP as can be seen in Figure 18. GWO minimized the shaking and road loads and transmitted about 92.94 lbs. to the motorcycle frame compared to GA (transmitted 288 lbs.) and SQP, which was the worst in this loading case (transmitted 434 lbs.). It can be concluded that GWO did very well for both models by minimizing and isolating mechanical vibrations. Finally, GO surpassed the competition in terms of PMS design optimization, as well as being more resilient and less costly in terms of CPU costs. The results of GWO were positive, highlighting the importance of swarm intelligence algorithms in MPS design and optimization. On the other hand, different optimization techniques such as GA and SQP may perform well in other technological applications. As a result, the engineering problem determines the optimization algorithm. In MPS applications, GWO was better than MPS; however, it may not be as effective in other engineering applications. ## 6 Conclusions

This paper investigated and optimized two 12-DOF PMS models. The first model considers only shaking loads, while the second model considers both shaking loads and road loads. The purpose of this work was to determine optimal PMS design parameters that minimize the loads induced by shaking forces, which eventually isolate mechanical vibrations. Stiffness, position, and orientation of the engine mounts were considered to be design parameters. The optimal design parameters that minimize the selected objective function of both models were determined using low-cost swarm intelligence and evolutionary optimization approaches. The implemented optimization approaches were successful in capturing vibration isolation qualities and producing appropriate PMS design parameters. Based on the findings of this study, swarm intelligence optimization approaches such as GWO have been shown to be promising in sophisticated and extensive computation engineering applications such as PMS. The transmitted force from the engine to the framework was minimized for model 1 (including only shaking loads) and found to be 1.5981 lb., 285.5898 lb., and 38.7022 lb. using GWO, GA, and SQP, respectively. Comparedto GA's and SQP's high values, GWO had the ideal and least transmitted force value of 1.5981 lb. For the other model, model 2 (combined loading), the transmitted force obtained by GWO was 92.9407 lb., which was the smallest (optimal) when compared to 288.0116 lb. and 434.3781 lb. using GA and SQP, respectively. A comparison of the optimization algorithms utilized in this work revealed GWO's superior performance. In comparison to GA and SQP, GWO successfully decoupled vibration modes at high frequencies with less computational cost. GWO demonstrated improved performance in terms of reducing the transmitted force values from the engine to the frame and decoupling vibration modes at a reduced computational cost. Based on the simulation and computational findings for this particular application PMS, GWO was the best in terms of convergence speed, accuracy, and computing cost. Conceptualization, A.Y., F.A. and Z.D. ; methodology, A.Y. ; software, A.Y. ; validation, A.Y., F.A. and Z.D. ; formal analysis, A.Y. ; investigation, A.Y. ; resources, A.Y., F.A. and Z.D. ; data curation, A.Y. and F.A. ; writing--original draft preparation, A.Y. ; writing--review and editing, Z.D. ; visualization, A.Y. ; supervision, Z.D. ; project administration, A.Y. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The authors declare no conflict of interest. ## References

* (1) [PERSON]; [PERSON] _Investigation of Structural Motorcycle Vibrations Due to Engine_; Omniscriptum Gmbh & Co., Kg. : Saarbrucken, Germany, 2015; ISBN 978-3639659429.