## 6 Case Study
### Performance of Different Strategies
This is consistent with our theoretical expectations. The next aggregation area on the upper right contains models 1, 5, and 9, which optimize the train formation in the remaining strategies. The worst are model 4 with the strategy of optimizing the operation zone and model 8 with the strategy of optimizing the service frequency; they both have no Pareto front solutions in region III. The Pareto front of model 4 is in region IV, which shows that the strategy of optimizing the operation zone only, such as full-length and short-turn routing  
Figure 21: Comparison of Pareto fronts of line plan with different strategies. Figure 22: Categories and dominance of strategies. with a fixed service frequency, cannot obtain a better solution, but it has a lower cost with the same service level as model 8 by a smaller train service in the section with a low passenger flow. The Pareto front of model 8 is a curve passing through the real timetable, because the result is just the real timetable when the service frequency is 12. In summary, the following conclusions are drawn:  
(1) The optimization effect of model 15 is the best. We suggest conditional lines (overtaking stations and turn-back stations can be built, and vehicles can be purchased) or new lines adopting the line plan and timetable optimized by four strategies. (2) For enterprises that have difficulty in changing the number of vehicles, we suggest using a model that simultaneously optimizes the operation zone and stopping pattern, including models 6, 7, 14, and 15, which is necessary to choose the solutions that satisfy the constraint of the vehicle number. (3) When the line conditions do not support the construction of overtaking stations, we suggest using models that simultaneously optimize the service frequency and operation zone, including models 12, 13, 14, and 15, which is necessary to choose solutions without overtaking. (4) When the line conditions do not support the construction of overtaking stations and turn-back stations, we propose adopting a line plan with multiple train formations, including models 1 and 9 and their dominating models (see Figure 22), which is necessary to choose the qualified solutions. (5) When considering both system costs and passenger travel efficiency, it is not suggested to use model 4 with the strategy of optimizing the operation zone only or model 8 with the strategy of optimizing the service frequency only. From these conclusions, some line-planning strategies can be said to have combinatorial effects. The first combination is all four strategies, because the optimization effect of model 15 is significantly better than that of all other models in general, i.e., the optimization effect will be significantly reduced if any strategy is not optimized, such as models in Class B. This may be because each strategy has advantages and disadvantages for improving the imbalance of trains and station loads, and it can only achieve good results when all four strategies are combined. The second combination optimizes the operation zone and stopping pattern. Because models 6, 7, 14, and 15 gather in the second aggregation area, the optimization effect is better than that of the other models. Although models 2, 3, 11, and 10 without an optimized operation zone are also in the second aggregation area, the performance of model 6, which can achieve the effect of model 15 under some service level, allows us to speculate that models 7, 14, and 15, which dominate model 6, will obtain better solutions with a sufficient solution time. This may be because express trains can provide efficient services for long-distance passengers, while local trains can satisfy the needs of short-distance passengers. Short-turn trains can improve the equipment utilization in sections with a small flow and leave more time windows for express trains to reduce overtaking times. The third combination optimizes the service frequency and operation zone.