Hoch B, Liers F (2022)
Publication Language: English
Publication Status: Submitted
Publication Type: Journal article
Future Publication Type: Journal article
Publication year: 2022
DOI: 10.1007/s11081-022-09719-2
Open Access Link: https://link.springer.com/article/10.1007/s11081-022-09719-2#citeas
Planning of trajectories, i.e. paths over time, is a challenging task. Thereby, the trajectories
for involved commodities often have to be considered jointly as separation constraints have to be
respected. This is for example the case in robot motion or air traffic management. Involving
these discrete separation constraints in the planning of best possible continuous trajectories
makes the task even more complex. Hence, in current practice, the resulting optimization
problems are solved sequentially or with restricted planning space. This leads to potential
losses in the usage of sparse resources.
To overcome these drawbacks, we develop a graph based model for disjoint trajectories
optimization. Further, we present a discretization technique to depict the full available space,
while respecting potentially non-convex restricted areas. As a result, an integer linear opti-
mization program needs to be solved whose size scales with the number of discretization points.
Thereby, even for moderately sized instances a sufficiently detailed representation of space and
time leads to models too large for state of the art hard- and software. To tackle this, we develop
an adaptive-refinement algorithm that works as follows: Starting from an optimal solution to
the integer program in a coarse discretization the algorithm re-optimizes trajectories in an
adaptively refined discretized neighborhood of the current solution. This is further integrated
into a rolling horizon approach. We apply our approach to the integrated trajectory optimiza-
tion and runway scheduling in the surrounding of airports. Computational experiments with
realistic instances show efficiency of the method.
APA:
Hoch, B., & Liers, F. (2022). An Integrated Rolling Horizon and Adaptive-Refinement Approach for Disjoint Trajectories Optimization. Optimization and Engineering. https://dx.doi.org/10.1007/s11081-022-09719-2
MLA:
Hoch, Benno, and Frauke Liers. "An Integrated Rolling Horizon and Adaptive-Refinement Approach for Disjoint Trajectories Optimization." Optimization and Engineering (2022).
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