Solar-power-generation forecasting tools are essential for microgrid stability, operation, and planning. The prediction of solar irradiance (SI) usually relies on the time series of SI and other meteorological data. In this study, the considered microgrid was a combined cold- and power-generation system, located in Tahiti. Point forecasts were obtained using a particle swarm optimization (PSO) algorithm combined with three stand-alone models: XGboost (PSO-XGboost), the long short-term memory neural network (PSO-LSTM), and the gradient boosting regression algorithm (PSO-GBRT). The implemented daily SI forecasts relied on an hourly time-step. The input data were composed of outputs from the numerical forecasting model AROME (Météo France) combined with historical meteorological data. Our three hybrid models were compared with other stand-alone models, namely, artificial neural network (ANN), convolutional neural network (CNN), random forest (RF), LSTM, GBRT, and XGboost. The probabilistic forecasts were obtained by mapping the quantiles of the hourly residuals, which enabled the computation of 38%, 68%, 95%, and 99% prediction intervals (PIs). The experimental results showed that PSO-LSTM had the best accuracy for day-ahead solar irradiance forecasting compared with the other benchmark models, through overall deterministic and probabilistic metrics.