There has been significant progress in the development of numerical methods for the determination of optimal trajectories for continuous dynamic systems, especially in the last 20 years. In the 1990s the principal contribution was new methods for discretizing the continuous system and converting the optimization problem into a nonlinear programming problem. This has been a successful approach that has yielded optimal trajectories for very sophisticated orbit transfer problems. In the last 10-15 years researchers have applied a qualitatively different approach, using evolutionary algorithms, to solving similar problems. Evolutionary algorithms use the principle of "survival of the fittest" applied to a population of individuals representing candidate solutions for the optimal trajectories. In this paper the advantages and disadvantages of these recently developed methods are described and an attempt is made to answer the question of what is now the best extant method.