To evaluate and improve the efficiency of photovoltaic solar modules connected with linear pipes for water supply, a three-dimensional numerical simulation is created and simulated via commercial software (Ansys-Fluent). The optimization utilizes the principles of the 1st and 2nd laws of thermodynamics by employing the Response Surface Method (RSM). Various design parameters, including the coolant inlet velocity, tube diameter, panel dimensions, and solar radiation intensity, are systematically varied to investigate their impacts on energetic and exergitic efficiencies and destroyed exergy. The relationship between the design parameters and the system responses is validated through the development of a predictive model. Both single and multi-objective optimizations are performed using the predictive model to optimize the thermal and electrical productivity under different scenarios. The findings indicate the significance of the thermal exergy effectiveness, as evidenced by its low P-value for all solar system responses, indicating its crucial role in the predictive model. For single-objective optimization, the desirability is equal to 1 in cases where only heat transfer efficiency, whole energy effectiveness, or thermal exergy efficiency is maximized or only destroyed exergy is minimized. The improvements in energy and exergy efficiencies range from 3.55% to 69.13%, with the amount of destroyed exergy reduced by 81.47% compared to the base case. For multi-objective optimization, desirability values exceeding 0.829 and 0.655 are obtained for single and multi-objective scenarios, respectively, indicating that the expected performance is within desirable limits. The findings provide valuable insights for designing high-efficiency photovoltaic/thermal systems and addressing their challenges and limitations.