A dynamic integer programming approach for free flight air traffic management (ATM) scenario with 4D-trajectories and energy efficiency aspects


The growth in demand for air transport has generated new challenges for capacity and safety. In response, manufacturers develop new types of aircraft while airlines open new routes and adapt their fleet. This excessive demand for air transport also leads to the need for further investments in airport expansion and ATM modernization. The current work was focused on the ATM problem with respect to new procedures, such as free flight, for addressing the air capacity issues in an environmental approach. The study was triggered by and aligned with the following performance objectives set by EUROCONTROL and the European Commission: (1) to improve ATM safety whilst accommodating air traffic growth; (2) to increase the ATM network efficiency; (3) to strengthen ATM’s contribution to aviation security and to environmental objectives; (4) to match capacity and air transport growth. The proposed mathematical model covers the aforementioned objectives by focusing on energy losses and costs of flights under the scenario of a controlled free flight and a unified airspace. The factors enhanced in the model were chosen based on their impact on the ATM energy efficiency, such as the airborne delays and flight duration, the delays due to ground holding, the flight cancellation, the flight speed deviations and the flight level alterations. Therefore, the presented mathematical model minimizes the energy costs due to the above terms under certain assumptions and constraints. Finally, simulation case studies, used as proof tests, have been conducted under different ATM scenarios to examine the complexity and the efficiency of the developed model.

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We thank the Papakyriakopoulos Institution for granting Dr. Charis Ntakolia and supporting her Ph.D. work from June 2015 to June 2017.

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Correspondence to Charis Ntakolia.

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Ntakolia, C., Caceres, H. & Coletsos, J. A dynamic integer programming approach for free flight air traffic management (ATM) scenario with 4D-trajectories and energy efficiency aspects. Optim Lett 14, 1659–1680 (2020). https://doi.org/10.1007/s11590-019-01458-1

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  • Operations research
  • Integer linear programming
  • Dynamic programming
  • Air traffic management
  • Energy efficiency