This study evaluated the influence of asphalt binder and biochar-based geopolymer composites on the permanent deformation resistance (PDR) of asphalt concrete. The influence of three design variations: asphalt binder, biochar, and geopolymer content was evaluated by employing the response surface method (RSM) based on the Box Behnken approach. The asphalt binder content ranged between 4 and 6%, whereas the biochar and geopolymer content ranged between 0 and 4%. The average rut depth of Bio-Geopolymer Asphalt concrete (BGAC) was employed as the response variable. The synergetic influence of the design variable was examined using the RSM approach, and a model was developed to determine optimum contents for improving PDR. The model has very high R² values and adequate precision, showing that there is a significant relationship between the experimental and predicted values. The study ANOVA revealed that the asphalt binder and a biochar-based geopolymer composite modifier showed a significant effect in enhancing the PDR of BGAC. Furthermore, the optimization shows that the optimal content for biochar, geopolymer, and asphalt binder are 3.22%, 1.81%, and 5.4% respectively. The generated model's percentage error was found to be 5%, showing a significant correlation between actual and predicted data. The results of this study show that using RSM to predict and optimize the PDR of BGAC is a very efficient and effective technique.