Hybrid GA-GWO with Dual-Vector Encoding for Indonesian School Timetabling

Abstract

School timetabling is a complex combinatorial optimization problem that involves assigning subjects, teachers, and classes to predefined time slots while satisfying numerous institutional constraints. In many Indonesian junior high schools, scheduling is still performed using manual approaches, which are often time-consuming and prone to conflicts. Compared with university timetabling, school timetabling presents additional challenges due to fixed class groups, rigid subject allocations, teacher availability constraints, and institutional regulations. To address these challenges, this study proposes a hybrid optimization framework that combines a Guided Genetic Algorithm (GA) and Grey Wolf Optimizer (GWO) for the school timetable. The proposed framework incorporates dual-vector solution encoding to provide a structured representation of scheduling components and support efficient constraint handling during the optimization process. In addition, a majority-voting and guided mutation strategy is employed to enhance the balance between exploration and exploitation. The proposed method was evaluated using real-world scheduling data from an Indonesian junior high school consisting of 27 classes, 54 teachers, 13 subjects, and 36 time slots. Experimental results show that the proposed hybrid GA-GWO achieved a fitness improvement of 95.84%, reducing the fitness value from 16,120 to 670, compared with improvements of 89.83% and 94.31% obtained by Traditional GA and Guided GA, respectively. Although the proposed method required approximately 28 minutes of execution time, it produced the highest overall timetable quality among the evaluated approaches. These findings demonstrate that the integration of dual-vector encoding, majority voting, and guided mutation within a hybrid GA-GWO framework can effectively improve timetable optimization for real-world Indonesian school scheduling environments.