The paper introduces a novel methodology for optimizing the operation of a centralized Air Handling Unit (AHU) in a multi-zone building served by VAV boxes with interpretable rules extracted from a Deep Reinforcement Learning (DRL) controller trained to enhance energy efficiency and indoor temperature control. To ensure practical application, a Rule Extraction (RE) framework is developed, translating the DRL complex decision-making process into actionable rules using decision trees. A multi-action approach is proposed by developing three different regression trees for adjusting the supply water temperature, the position of the chiller valve, and the position of the economizer damper of the AHU. The extracted rules are benchmarked against the original DRL controller and two conventional control sequences based on ASHRAE 2006 and ASHRAE Guideline 36 within a high-fidelity co-simulation architecture combining Spawn of EnergyPlus and Python. The co-simulation environment uses EnergyPlus for building envelope and loads while HVAC components and controls are implemented in the equation-based modeling language Modelica. Results show that the RE-based controller closely approximates the performance of the DRL policy with an electric energy consumption only 3% higher, highlighting its ability to effectively mirror a more complex control logic, representing a transparent and easily implementable alternative. The controllers based on ASHRAE 2006 and ASHRAE Guideline 36 lead to higher energy consumption (for both chiller and fan) and violations of indoor temperature compared to both RE-based control and DRL. This study underscores the potential of integrating AI-driven control methods with interpretable rule-based systems, facilitating the adoption of advanced energy management strategies in real-world building automation systems.