This paper presents a comparison of a graph-based genetic algorithm (GB-GA) and machine learning (ML) results for the optimisation of logP values with a constraint for synthetic accessibility and shows that GA is as good or better than the ML approaches for this particular property. The molecules found by 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, while the GB-GM-based method is 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 more traditional, and often simpler, approaches such a GA.