دانلود رایگان مقاله بهینه سازی پیش تاکتیکی استفاده از باند فرودگاه تحت شرایط عدم اطمینان

abstract

Efficient planning of runway utilization is one of the main challenges in Air Traffic Management (ATM). It is important because runway is the combining element between airside and groundside. Furthermore, it is a bottleneck in many cases. In this paper, we develop a specific optimization approach for the pretactical planning phase that reduces complexity by omitting unnecessary information. Instead of determining arrival/departure times to the minute in this phase yet, we assign several aircraft to the same time window of a given size. The exact orders within those time windows can be decided later in tactical planning. Mathematically, we solve a generalized assignment problem on a bipartite graph. To know how many aircraft can be assigned to one time window, we consider separation requirements for consecutive aircraft types. In reality, however, uncertainty and inaccuracy almost always lead to deviations from the actual plan or schedule. Thus, we present approaches to incorporate uncertainty directly in our model in order to achieve a stabilization with respect to changes in the data. Namely, we use techniques from robust optimization and stochastic optimization. Further, we analyze real-world data from a large German airport to obtain realistic delay distributions, which turn out to be two-parametric G-distributions. Finally, we describe a simulation environment to test our new solution methods.

8. Conclusion

We have developed a mathematical optimization model for the pre-tactical optimization of assigning time windows for runway utilization. In this model, several aircraft can be assigned to the same time window which reduces the complexity of the problem. Further, we enriched the model by protection against uncertainties using techniques from robust and stochastic optimization. Our computational study showed that such an incorporation of a priori knowledge on uncertainties has a large effect on the resulting solutions. The stochastic approach optimizes the expected scenario and, therefore, is more likely to remain feasible in the face of disturbances than the nominal approach. Thus, on average it provides more stable plans and less necessary replanning. However, robust optimization methods provide even more stable solutions. Using the strict robust approach, we definitely know that a solution (if one exists) will be feasible for all scenarios within the predetermined uncertainty set. Thus, it is the approach with the highest possible stability. However, this may come at the price of increased delay. Recoverable robustness on the other hand takes into account that a time window assignment might become 8. Conclusion We have developed a mathematical optimization model for the pre-tactical optimization of assigning time windows for runway utilization. In this model, several aircraft can be assigned to the same time window which reduces the complexity of the problem. Further, we enriched the model by protection against uncertainties using techniques from robust and stochastic optimization. Our computational study showed that such an incorporation of a priori knowledge on uncertainties has a large effect on the resulting solutions. The stochastic approach optimizes the expected scenario and, therefore, is more likely to remain feasible in the face of disturbances than the nominal approach. Thus, on average it provides more stable plans and less necessary replanning. However, robust optimization methods provide even more stable solutions. Using the strict robust approach, we definitely know that a solution (if one exists) will be feasible for all scenarios within the predetermined uncertainty set. Thus, it is the approach with the highest possible stability. However, this may come at the price of increased delay. Recoverable robustness on the other hand takes into account that a time window assignment might become