Multi-Objective Logistics Route Optimization Using a Physics- Informed Neural Network-Assisted Genetic Algorithm

Abstract

Modern logistics distribution systems require simultaneous optimization of transportation cost, delivery time, travel distance, and energy consumption under vehicle capacity and time-window constraints. Conventional genetic algorithm (GA)-based routing approaches rely on penalty-based constraint handling and static fitness evaluation, resulting in unstable convergence and reduced scalability for high- dimensional, multi-objective vehicle routing problems (VRPs). This study proposes a Physics-Informed Neural Network Assisted Genetic Algorithm for Logistics Route Optimization (PINN-GA-RouteOpt), integrating physics-regularized learning with adaptive evolutionary search. The proposed framework embeds vehicle motion dynamics, fuel–distance nonlinear relationships, and service time-window constraints into a physics-informed neural network (PINN), where the fitness function is formulated as a composite objective minimizing transportation cost, total travel time, route distance, and energy consumption. The PINN is trained using a hybrid loss function combining supervised data loss and physics residual loss derived from motion and fuel-consumption equations, thereby generating constraint- consistent fitness landscapes. An improved GA with adaptive mutation and dynamic crossover control is employed to enhance exploration–exploitation balance and accelerate convergence. Computational experiments were conducted on benchmark logistics distribution datasets with network sizes ranging from 100 to 500 nodes and fleet sizes up to 200 vehicles. Comparative evaluation against standard GA and penalty-based multi-objective GA variants demonstrates a 22% reduction in convergence iterations, 17.1% decrease in energy consumption, 12.8% reduction in total travel distance, and 15.4% improvement in average delivery time. Additionally, Pareto front dispersion variance decreased by 19.6%, indicating improved solution stability. The results confirm that PINN-GA-RouteOpt achieves computational efficiency, constraint-aware optimization, and scalability, establishing an intelligent and energy-efficient framework for large-scale logistics distribution route planning.