Laser marking is the latest and the most efficient permanent marking technology which can be used in a variety of materials facilitating one of the most important industrial needs of product identification and tracking for quality control and supply chain management. In the present research, laser marking on Aluminium has been performed to investigate the effect of some of the process parameters i.e. Power and Scanning speed on the process responses, i.e. Heat affected zone (HAZ) and Surface roughness (Ra). Regression analysis is done to develop a predictive model for the process responses and analysis of variance test (ANOVA) is done to check the efficacy of the model thus obtained. It is concluded that Power and Scanning speed has a significant impact on them. Finally, optimization of the process parameters is performed using the Multi-Objective Particle Swarm Optimization Technique (MOPSO) to obtain minimum heat affected zone and maximum surface roughness.