In engineering optimization, multi-objective (MO) problems are frequently encountered. In this work, a real-world MO problem (resin-bonded sand mould system) is tackled using Particle Swarm Optimization (PSO) in conjunction with the weighted-sum approach. Random generators (stochastic engines) provides sufficient randomness for the algorithm during the search process. The effects of non-Gaussian stochastic engines on the performance of the PSO technique in a MO setting is explored in this work. The stochastic engines operate using the Weibull distribution, Gamma distribution, Gaussian distribution and a chaotic mechanism. The two non-Gaussian distributions are the Weibull and Gamma distributions. The Pareto frontiers obtained were benchmarked using two metrics; the hypervolume indicator (HVI) and the proposed Average Explorative Rate (AER) metric. Detail comparative analysis on the effects of non-Gaussian random generators on the PSO technique is provided. © 2016 IOS Press and the authors. All rights reserved.