Optimization of takeaway tableware recycling route considering order insertion

China's booming food-delivery industry produces massive disposable-tableware waste, demanding efficient and low-carbon reverse logistics. Here, we studied a dynamic tableware collection routing problem with real-time order insertion: a recycling center serves preset recycling points, while new door-to-door requests appear during route execution. The objective is to minimize total cost, including vehicle dispatch fixed cost, distance-based depreciation, cleaning cost (including incremental cleaning for inserted orders), waiting and lateness penalties under soft time windows, and fuel plus carbon-emission costs. Routes must satisfy depot start/end, single-service requirements, vehicle capacity limits, feasible service-time propagation, and a minimum satisfaction threshold derived from the soft time-window function. To solve this NP-hard problem, we designed an improved genetic algorithm with time-window-based grouped initialization, natural-number encoding with depot separators, OX crossover, two-point mutation, and a destruction-repair local search using farthest insertion for reinsertion. Experiments indicated faster and more stable convergence than a basic GA. In an order-insertion case, inserting new orders into en-route tours significantly outperforms dispatching an additional vehicle (total cost about 75.7% higher). The proposed method offers implementable decision support for platforms and municipalities to run time-sensitive, low-carbon tableware recovery.