Solving Complex Intersection Management Problems Using Bi-level MINLPs and Piecewise Linearization Techniques

Gerdts, Matthias; Rogovs, Sergejs; Valenti, Giammarco

doi:10.1007/978-3-031-17098-0_13

Cited by 2 publications

(3 citation statements)

References 17 publications

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“…The formulation of the adaptive numerical algorithm used for the refinement of MILP relaxations is inspired by similar algorithms from [8] and [18]. The idea is outlined in Algorithm 1 and can be briefly described in the following way.…”

Section: G(t I ) T I T Imin T Imaxmentioning

confidence: 99%

“…In the next iteration step, the new refined time discretizations are examined. The whole procedure is repeated until the error bound is satisfied for all i ∈ N [8]. As to the termination condition, it was proven in [18] that the number of iteration steps is guaranteed to be finite provided that problem (6) is feasible, and all nonlinear functions are continuous.…”

Section: G(t I ) T I T Imin T Imaxmentioning

confidence: 99%

“…However, the class of coupled scheduling and optimal control problems has not been extensively researched in the literature to the best of the authors' knowledge. In a context of autonomous vehicles, [7] and [8] propose interesting methods for optimization problems with a bilevel structure. Approaches presented in [9] and [10] are designed to schedule multiple robots and provide an optimal path for each of them.…”

Section: Introductionmentioning

confidence: 99%

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Piecewise linear value function approximations in nonlinear dynamic scheduling problems with VTOLs

Nikitina¹,

Rogovs²,

Gerdts³

2023

Preprint

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Modern vertical take-off and landing vehicles (VTOLs) could significantly affect the future of mobility. The broad range of their application fields encompasses urban air mobility, transportation and logistics as well as reconnaissance and observation missions in a military context. This article presents an efficient numerical framework for dynamic scheduling of multiple VTOLs. It combines a scheduling problem with optimal trajectory planning. The whole setting is formulated as a mixedinteger bilevel optimization problem. At the upper level, VTOLs are scheduled, and their starting times are computed. The solution of the lower level problem involves the computation of a value function and yields optimal trajectories for every aerial vehicle. In order to solve the bilevel problem, it is recast into a single-level one. The resulting mixed-integer nonlinear program (MINLP) is then piecewise linearized and solved numerically by a linear solver based on the Branch-and-Bound algorithm. Numerical results prove the feasibility of the approach proposed in this work.Keywords Bilevel optimization problem • dynamic scheduling of VTOLs • mixed-integer problem • piecewise linearization • shortest path • value function.

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Section: G(t I ) T I T Imin T Imaxmentioning

confidence: 99%

Section: G(t I ) T I T Imin T Imaxmentioning

confidence: 99%