Abstract:  In response to the NP-hard nature of the multi-objective school bus routing optimization prob.lem and the shortcomings of existing solution methods, this paper proposes a novel “ stop-vehicle” two.stage encoding strategy. This strategy generates individuals through two phases: stop ordering and vehicleallocation, which reduces encoding redundancy and ensures the legality of the solutions. A new type ofdual-sequence crossover operator is designed to inherit the superior genes of the parents while increasingthe diversity of the population and accelerating the convergence speed of the algorithm. In terms of ex.periments, the paper selects three sets of benchmark test data of different sizes to evaluate the solutionquality and computational elficiency of the algorithm and compares it with classic heuristic algorithmssuch as the Standard Genetic Algorithm ($GA) and Simulated Annealing ( SA). The experimental re.sults show that the algorithm proposed in this paper is superior to other algorithms in terms of solutionquality and convergence speed, demonstrating good problem-solving performance and application prospects.

Key words: school bus routing optimization: multi-objective optimization: genetic algorithm, two-phaseencoding, dual sequence crossover