Detecting and solving aircraft conflicts using bilevel programming

Martina Cerulli; Claudia D’Ambrosio; Leo Liberti; Mercedes Pelegrín

doi:10.1007/s10898-021-00997-1

Detecting and solving aircraft conflicts using bilevel programming

Martina Cerulli
, Claudia D’Ambrosio
, Leo Liberti
, Mercedes Pelegrín

Research output: Contribution to journal › Article › peer-review

Abstract

We present two bilevel programming formulations for the aircraft deconfliction problem: one based on speed regulation in k dimensions, the other on heading angle changes in 2 dimensions. We propose three reformulations of each problem based on KKT conditions and on two different duals of the lower-level subproblems. We also propose a cut generation algorithm to solve the bilevel formulations. Finally, we present computational results on a variety of instances.

Original language	English
Pages (from-to)	529-557
Number of pages	29
Journal	Journal of Global Optimization
Volume	81
Issue number	2
DOIs	https://doi.org/10.1007/s10898-021-00997-1
Publication status	Published - 1 Oct 2021

Keywords

Air traffic management
Bilevel programming
Cutting plane
Deconfliction
Mathematical programming

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10.1007/s10898-021-00997-1

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title = "Detecting and solving aircraft conflicts using bilevel programming",

abstract = "We present two bilevel programming formulations for the aircraft deconfliction problem: one based on speed regulation in k dimensions, the other on heading angle changes in 2 dimensions. We propose three reformulations of each problem based on KKT conditions and on two different duals of the lower-level subproblems. We also propose a cut generation algorithm to solve the bilevel formulations. Finally, we present computational results on a variety of instances.",

keywords = "Air traffic management, Bilevel programming, Cutting plane, Deconfliction, Mathematical programming",

author = "Martina Cerulli and Claudia D{\textquoteright}Ambrosio and Leo Liberti and Mercedes Pelegr{\'i}n",

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N2 - We present two bilevel programming formulations for the aircraft deconfliction problem: one based on speed regulation in k dimensions, the other on heading angle changes in 2 dimensions. We propose three reformulations of each problem based on KKT conditions and on two different duals of the lower-level subproblems. We also propose a cut generation algorithm to solve the bilevel formulations. Finally, we present computational results on a variety of instances.

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KW - Air traffic management

KW - Bilevel programming

KW - Cutting plane

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KW - Mathematical programming

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Detecting and solving aircraft conflicts using bilevel programming

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