A Three-Stage Hierarchical Framework Using Hybrid Genetic Algorithm for Logistics Optimization in Multi-Item and Multi-Vehicle Environments

This study addresses the logistics optimization problem in multi-supply, multi-demand, multi-item, and multi-vehicle environments, modeled directly on the structure and constraints of an actual logistics field operation rather than on a generic combinatorial abstraction. The research objective is to minimize logistics transportation costs by simultaneously optimizing demand allocation and vehicle assignment. This problem formulates a mathematical model that reflects the dual-structured nature of the logistics process. To solve the NP-hard problem where finding a mathematical optimum is difficult, we propose a three-stage hierarchical framework consisting of: (1) preprocessing for demand stabilization, (2) a policy-based vehicle-assignment heuristic based on volume, and (3) a specialized Hybrid Genetic Algorithm (HGA). The proposed HGA applies two types of crossover methods for effective exploration and three types of mutation methods specialized for overcoming each type of local optima. Additionally, it includes a local search strategy to confirm solution improvement, adaptive mutation rates, and a survival strategy that simultaneously preserves elite and infeasible solutions. The methodology was validated on four instances of varying type and scale, each modeled on real logistics operating conditions. Across these four instances, the proposed framework consistently achieved, relative to a conventional genetic algorithm, an average final-cost improvement of 9.77% (ranging from 4.39% to 17.37% depending on the instance), which was statistically highly significant in all four instances via the Wilcoxon signed-rank test over 40 independent repetitions (p < 0.001; Cohen’s d 5.14–14.08, mean 8.56). This result demonstrates the superiority of the framework for large-scale combinatorial optimization under realistic logistics field conditions. This research holds significant implications for the design of practical decision-support tools for large-scale, real-world logistics operations.