Design of Experiments (DoE) is the field of statistics concerned with helping researchers maximize the amount of information they gain from their experiments. Recently, researchers have been turning to optimal experimental designs instead of classical/catalog experimental designs. One of the most popular algorithms used today to generate optimal designs is the Coordinate Exchange (CEXCH) Algorithm. CEXCH is known to be a greedy algorithm, which means it tends to favor immediate, locally best designs instead of globally optimal designs. Previous research demonstrated that this tradeoff was efficacious in that it reduced the cost of a single run of CEXCH and allowed more independent runs of the algorithm in a reasonable time. We devote part of this thesis to implementing and validating CEXCH in the Julia programming language. Different versions of CEXCH are examined, each with a different level of greediness. We implement a large computing study on 21 distinct design scenarios and two optimality criterion to benchmark the efficacy of CEXCH under different levels of greediness. We found that less greedy implementations of CEXCH generate optimal designs with greater probability at a moderate increase to cost.