<p>Optimal control of Heating, Ventilation, and Air Conditioning Absorption Refrigeration (HVAC-AR) systems based on Finite-Time Thermodynamics (FTT) represents a major challenge in modern engineering application. Indeed, the solution procedure currently used to solve the thermodynamic optimization problem of static thermodynamic systems like HVAC-AR is based on the analytical-geometric technique and the variational principle. Hence, the need to explore numerical optimization methods to generate a set of optimal solutions and ultimately use them to maintain the device at its optimal operating point, through statistical machine learning methods, when operating conditions change. This manuscript therefore presents a novel approach combining FTT and Linear Programming Programing (LPP) to solve Optimal Thermal Conductance Allocation Problems (OTCAP) in R⁴ (four heat exchangers), as well as a Supervised Machine Learning (SML) for the maximum refrigeration heat load and associated coefficient of performance (COP) prediction of a practical single-effect HVAC-AR system under real operating condition. Five models of regression algorithms (Random Forest Regressor, Gradient Boosting Regressor, Decision Trees Regressor, K-Nearest Neighbors Regressor and Tweedie Regressor) were used. After the model evaluations, the nonlinear Gradient Boosting Regressor (GrBR) model was identified as suitable for predicting COP and maximum refrigeration heat load with an r2_score of 96.34% and 85.04% respectively. The obtained results demonstrate that generator fuel flow rate is a key variable that has a considerable effect on the performance parameters of the HVAC-AR system. FTT-LPP-SML has been proven to be suitable and reliable for solving optimization problems and estimating the performance of single-effect HVAC-AR system after experimental validation.</p>