Platform Supply Vessels (PSVs) play an essential role in supporting oil and gas platforms, and other offshore structures by transporting crew members, personnel, provisions, and further indispensable equipment from onshore to operational sites. PSV freight rate movements are subject to a complex array of non-linear interconnected influential factors. Reviewed literature reveals an absence of forecasting studies predicting PSV freight rates. Meanwhile, Automated Machine Learning (AutoML) frameworks have never before been employed to forecast maritime freight rates. Therefore, this study investigates factors influencing PSV time charter freight rates and explores AutoML modelling in capturing non-linearities while forecasting PSV freight rates over a 1, 3 and 6-month out-of-sample forecast horizon. A total of 43 relevant factors are included in prediction modelling, the most comprehensive number of explanatory variables in the shipping forecasting literature to date. The data consists of 188 monthly observations collected from two databases: Clarksons Shipping Intelligence Network and Offshore Intelligence Network. Time-lagged variables are utilized as data of explanatory variables are not immediately available at the time of forecasting. A total of 79 complex machine learning models are tested, and the best-performing models are Eureqa Generalized Additive Model, eXtreme Gradient Boosted Trees Regressor, and Ridge Regressor with Forecast Distance Modelling, benchmarked against the proven statistical forecasting model triple exponential smoothing. The most influential factors are historical PSV time charter freight rates, newbuilding prices, number of vessel deliveries, orderbook number, total vessel sales, and the unique variable number of active drilling rigs in the market.