This paper presents a comparison of a graph-based genetic algorithm (GB-GA) and machine learning (ML) results for the optimization of log P values with a constraint for synthetic accessibility and shows that the GA is as good as or better than the ML approaches for this particular property. The molecules found by the GB-GA bear little resemblance to the molecules used to construct the initial mating pool, indicating that the GB-GA approach can traverse a relatively large distance in chemical space using relatively few (50) generations. The paper also introduces a new non-ML graph-based generative model (GB-GM) that can be parameterized using very small data sets and combined with a Monte Carlo tree search (MCTS) algorithm. The results are comparable to previously published results (Sci. Technol. Adv. Mater., 2017, 18, 972-976) using a recurrent neural network (RNN) generative model, and the GB-GM-based method is several orders of magnitude faster. The MCTS results seem more dependent on the composition of the training set than the GA approach for this particular property. Our results suggest that the performance of new ML-based generative models should be compared to that of more traditional, and often simpler, approaches such a GA.