RL-SBRP Methodology and Türkiye Transport Market Analysis

Türkiye Student and Personnel Transport Market Data

The number of students transported from pre-school through secondary education in Türkiye, and the size of the vehicle fleet serving them, illustrates the critical importance of transport infrastructure. Personnel transport carries separate economic weight, particularly in industrial zones around major cities.

SBRP: Mathematical Definition

The School Bus Routing Problem (SBRP) is a combinatorial optimization problem that simultaneously optimizes stop locations, student-stop assignments, and vehicle routes for student transport.

Formal definition: On undirected graph G = (V, E), with stop set S ⊂ V, student set P, and vehicle set K; each student p ∈ P is assigned to the nearest stop s ∈ S satisfying walking distance d_walk(p, s) ≤ d_max, and vehicles K determine routes over stops S to minimize the total cost function.

SBRP is NP-hard. The solution space for n stops is O(n!); for n=50 this exceeds 3 × 10⁶⁴.

• Objective: min Σ(vehicle costs) + Σ(route distances) + λ·Σ(violation penalties)
• Capacity constraint: For each vehicle k, load q_k ≤ Q_k (vehicle capacity)
• Walking constraint: d_walk(p, s_p) ≤ d_max (500 m or 1,000 m per MEB)
• Time constraint: School arrival t_arrival ≤ t_school (school start time)
• District constraint: Route must remain within relevant district boundaries

RL-SBRP: Solving SBRP with Reinforcement Learning

vitaRoute's RL-SBRP framework is built on a Markov Decision Process (MDP) formulation. The agent learns the next optimal decision (stop selection, passenger assignment, vehicle transition) at each step.

MDP components: State space S = {current route, unassigned passengers, vehicle positions, remaining capacity}; Action space A = {select next stop, close route, switch vehicle}; Reward R = -Δdistance - λ_cap·capacity_violation - λ_walk·walk_violation + μ·occupancy_bonus.

• Architecture: Transformer-based Policy Network + Value Network
• Training environment: 50,000+ virtual scenarios on Türkiye OSM data
• Training algorithm: Proximal Policy Optimization (PPO)
• Local search: 2-opt and Or-opt improvement post-processing
• Average optimization time: <10s for 1,000 passengers (CPU), <2s (GPU)

Performance Comparison

RL-SBRP performance versus classical methods on standard benchmarks and real Türkiye datasets:

Türkiye-Specific Adaptations

Standard SBRP formulations do not fully model Türkiye's unique operational and legal constraints. vitaRoute's RL-SBRP framework includes these proprietary components:

• OSM-Türkiye map layer: Monthly-updated OSRM server optimized for Turkish road topology
• District constraint module: Polygon-based boundary enforcement for Türkiye's 973 districts
• MEB parameter pack: Primary (500 m) and secondary (1,000 m) walking distance profiles
• Dynamic re-optimization: Adapts to instant list updates in Δt < 3 seconds
• Two-way route synchronization: Morning and evening routes use consistent stop sets
• Multi-school support: A single vehicle can serve multiple schools (split route)

TÜBİTAK R&D Support

The research and development process for vitaRoute's RL-SBRP framework was supported by TÜBİTAK (The Scientific and Technological Research Council of Türkiye) through an R&D grant. This support enabled the algorithm's academic foundation, independent validation processes, and operational validation against Türkiye's real conditions.

Citation

Suggested citation format for those who wish to reference this page or vitaRoute's RL-SBRP technology in academic work:

vitaRND (2025). RL-SBRP: Reinforcement Learning-Based School Bus Routing Problem Framework for Turkish Student and Personnel Transport. vitaRoute Research Summary. Retrieved from https://vitaroute.ai/en/methodology