The Prediction Optimization Bridge (POB): A Surrogate Assisted Random Forest–NSGA-II Framework for Energy Efficient Vehicle Routing

Urban freight transport is an essential component of urban mobility, playing a key role in supporting the economic and social development of cities. However, the growth of freight and delivery activities can intensify energy consumption and increase pressure on urban transportation systems. In this context, the Energy-Efficient Vehicle Routing Problem (EE-VRP) has emerged as an important research challenge, requiring a balance between routing complexity and non-linear operational dynamics. From this perspective, data-driven and intelligent optimization approaches can support more efficient decision-making in urban transportation systems by integrating operational efficiency with energy performance. To address this challenge, this paper proposes the Prediction-Optimization Bridge (POB) model, a hybrid Artificial Intelligence and Multi-Objective Optimization framework that seamlessly integrates supervised machine learning with multi-objective evolutionary optimization. The proposed model combines a Random Forest surrogate model with the NSGA-II evolutionary algorithm to identify efficient vehicle routes. First, we used the RF surrogate to capture complex non-linear relationships and minimize total fleet energy consumption. Then, the predicted energy values are subsequently integrated into the NSGA-II multi-objective evolutionary algorithm, which explores alternative routing solutions. To enhance operational realism, a dynamic payload updating mechanism adjusts vehicle load after each delivery, reflecting the progressive reduction in transported goods along the route. As a result, the Random Forest surrogate achieved a predictive accuracy of R2 = 0.9960. Furthermore, the proposed framework attained an average energy reduction of 12.47% ± 2.32% compared with a conventional distance-greedy routing heuristic, while achieving a normalized Hypervolume of 0.6305 ± 0.0277 over five independent experimental runs. Feature importance analysis based on Gini metrics identified vehicle load as the most influential factor affecting energy consumption (approximately 70%). Overall, the results demonstrate that integrating vectorized machine learning surrogates with evolutionary multi-objective optimization provides an efficient, robust, and reproducible approach for developing energy-efficient and sustainable fleet routing strategies.