The multi allocation p-hub median problem (MApHM), the multi allocation uncapacitated hub location problem (MAuHLP) and the multi allocation p-hub location problem (MApHLP) are common hub location problems with several practical applications. HLPs aim to construct a network for routing tasks between different locations. Specifically, a set of hubs must be chosen and each routing must be performed using one or two hubs as stopovers. The costs between two hubs are discounted by a parameter α. The objective is to minimize the total transportation cost in the MApHM and additionally to minimize the set-up costs for the hubs in the MAuHLP and MApHLP. In this paper, an approximation algorithm to solve these problems is developed, which improves the approximation bound for MApHM to 3.451, for MAuHLP to 2.173 and for MApHLP to 4.552 when combined with the algorithm of Benedito & Pedrosa (2019).The proposed algorithm is capable of solving much bigger instances than any exact algorithm in the literature. New benchmark instances have been created and published for evaluation, such that HLP algorithms can be tested and compared on huge instances. The proposed algorithm performs on most instances better than the algorithm of Benedito & Pedrosa (2019), which was the only known approximation algorithm for these problems by now.

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<p>Met4Airports is a research and development project funded by the German Federal Ministry for Digital and Transport (BMDV), aiming at the prediction of relevant planning and control parameters of air traffic management (ATM) by means of artificial intelligence (AI). It focusses on the effects of selected weather phenomena such as thunderstorms, significant wind events, fog, and winter weather events like snowfall, as they pose a significant disturbance for air traffic, causing capacity constraints for airports and en-route and approach sectors. The predicted quantities are mainly capacity values, delays of individual flights as well as average delay values for varying timespans with forecast lead times of up to 24 hours. Predictions of sufficient forecast qualities could be utilized to optimize decision-making processes in ATM and enhance the situational awareness of decision makers.</p><p>Throughout the development process, various machine learning models are examined, relying on both meteorological forecast products of Deutscher Wetterdienst and air traffic data of airport operators (Flughafen München GmbH and Fraport) and air traffic control (Deutsche Flugsicherung). Presently, the applied meteorological data include <em>Terminal Aerodrome Forecasts</em> (TAF) and <em>NowCastMix-Aviation</em> for short-term thunderstorm prediction. The integration of additional meteorological data types, such as forecasts from the numerical weather forecasting system <em>ICON-D2</em> is currently in progress. The applied air traffic data comprises flight lists, including estimated and target times from the <em>Airport Collaborative Decision Making</em> (A-CDM) process with an archiving period starting from 2016 as well as their historic updates. In the iterative development process, artificial neural networks with varying topologies and hyperparameters are trained on different combinations of data types in order to identify a suitable AI-model. In addition, other machine learning techniques, including gradient boosting shall be examined in the upcoming months.</p><p>A preliminary study revealed a significant enhancement of AI-model performance in predicting flight delays by integration of meteorological data. Thereafter, applicable forecasting parameters were identified by means of correlation analyses. Interim results indicate the capability of preliminary models to surpass the prediction quality of estimation timestamps (EOBT) currently used in the A-CDM process. Ultimately, delay forecasting results tend to be considerably more precise for the prediction of average values than for single flight delays, as the corresponding results are far less sensitive to short-term effects affecting individual flight operations.</p>