Contemporary complex samples require sophisticated methods for full analysis. This work describes the development of a Bayesian optimization algorithm for the automated and unsupervised development of gradient programs. The algorithm was tailored to LC using a Gaussian process model with a novel covariance kernel. To facilitate unsupervised learning, the algorithm was designed to interface directly with the chromatographic system. Single-objective and multi-objective Bayesian optimization strategies were investigated for the separation of a complex (n>80) dye mixture. The multi-objective strategy was found to be very powerful and flexible in terms of exploring the Pareto front. The single-objective strategy was found to be slightly faster in finding a satisfactory optimum. One additional advantage of the multi-objective approach was that it allows a trade-off to be made between multiple objectives. In general, the Bayesian optimization strategy was found to be particularly suitable, but not limited to, cases where retention modelling is not possible, although its scalability might be limited in terms of the number of parameters that can be simultaneously optimized.