Engineering decision making involving multiple competing objectives relies on choosing a design solution from an optimal set of solutions. This optimal set of solutions, referred to as the Pareto set, represents the tradeoffs that exist between the competing objectives for different design solutions. Generation of this Pareto set is the main focus of multiple objective optimization. There are many methods to solve this type of problem. Some of these methods generate solutions that cannot be applied to problems with a combination of discrete and continuous variables. Often such solutions are obtained by an optimization technique that can only guarantee local Pareto solutions or is applied to convex problems. The main focus of this paper is to demonstrate two methods of using genetic algorithms to overcome these problems. The first method uses a genetic algorithm with some external modifications to handle multiple objective optimization, while the second method operates within the genetic algorithm with some significant internal modifications. The fact that the first method operates with the genetic algorithm and the second method within the genetic algorithm is the main difference between these two techniques. Each method has its strengths and weaknesses, and it is the objective of this paper to compare and contrast the two methods quantitatively as well as qualitatively. Two multiobjective design optimization examples are used for the purpose of this comparison.