This study investigates the characteristics of existing flexible job shop scheduling problems and examines relevant algorithms, proposing a scheduling method based on an improved Non-dominated Sorting Genetic Algorithm (NSGA-II) to address these challenges. To mitigate the limitations of NSGA-II, such as low population diversity and slow computational speed, this research introduces an adaptive crossover operator based on crowding distance and incorporates a competitive selection mechanism inspired by bidding principles to enhance solution quality. Experimental simulations are conducted to verify the feasibility and effectiveness of the proposed algorithm.