To address the challenges of the flexible job-shop scheduling problem (FJSP) under dynamic uncertainties and multi-objective requirements, a hybrid adaptive genetic algorithm integrated with Particle Swarm Optimization (PSO) is proposed to solve the dynamic multi-objective FJSP considering Automated Guided Vehicle (AGV) transportation delays. The algorithm aims to simultaneously minimize the makespan and optimize machine load balance. In terms of evolutionary mechanisms, a two-segment chromosome representation, load-oriented mutation, and adaptive probabilities are utilized for global exploration, while a discrete PSO is incorporated for the deep local exploitation of elite solutions. Regarding the scheduling strategy, an active insertion-based decoding mechanism utilizing real machine coordinates is introduced to accurately calculate AGV delays. Simultaneously, a gene fault-tolerant repair mechanism is designed to effectively cope with dynamic disturbances such as machine breakdowns and urgent job insertions. Experimental results demonstrate that, in static scenarios, the proposed algorithm reduces the makespan by 8.7%–15.2% on average and achieves significant advantages in metrics such as Hypervolume (HV). Furthermore, it exhibits strong convergence stability even under dynamic disturbances with probabilities up to 15%. Compared with traditional genetic algorithms and the standard NSGA-II, the proposed method achieves substantial improvements in both Pareto front diversity and system robustness, providing a highly efficient optimization framework for scheduling in smart manufacturing workshops.