Some preliminary results for a new multi-objective genetic algorithm (MOGA) are presented. This new algorithm aims at obtaining the fullest possible representation of observed Pareto solutions to a multi-objective optimization problem. The algorithm, hereafter called entropy-based MOGA (or E-MOGA), is based on an application of the concepts from the statistical theory of gases to a MOGA. A few set quality metrics are introduced and used for a comparison of the E-MOGA to a previously published MOGA. Due to the stochastic nature of the MOGA, confidence intervals with a 95% confidence level are calculated for the quality metrics based on the randomness in the initial population. An engineering example, namely the design of a speed reducer is used to demonstrate the performance of E-MOGA when compared to the previous MOGA.