Combinatorial optimization applied to VLBI scheduling

• Published in: Journal of geodesy Vol. 94; no. 2
• Main Authors: Corbin, A., Niedermann, B., Nothnagel, A., Haas, R., Haunert, J.-H.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2020; Springer Nature B.V
• Subjects: Combinatorial optimization; Computers; Earth and Environmental Science; Earth Sciences; Geodetic VLBI; Geodetics; Geophysics/Geodesy; Interferometry; Linear programming; Local sky coverage; Mixed-integer linear programming; Optimization; Original Article; Scheduling; Telescopes; VGOS; Geodetic VLBI; Local sky coverage; Scheduling; Combinatorial optimization; VGOS; Mixed-integer linear programming
• ISSN: 0949-7714; 1432-1394; 1432-1394
• DOI: 10.1007/s00190-020-01348-w

Due to the advent of powerful solvers, today linear programming has seen many applications in production and routing. In this publication, we present mixed-integer linear programming as applied to scheduling geodetic very-long-baseline interferometry (VLBI) observations. The approach uses combinatorial optimization and formulates the scheduling task as a mixed-integer linear program. Within this new method, the schedule is considered as an entity containing all possible observations of an observing session at the same time, leading to a global optimum. In our example, the optimum is found by maximizing the sky coverage score. The sky coverage score is computed by a hierarchical partitioning of the local sky above each telescope into a number of cells. Each cell including at least one observation adds a certain gain to the score. The method is computationally expensive and this publication may be ahead of its time for large networks and large numbers of VLBI observations. However, considering that developments of solvers for combinatorial optimization are progressing rapidly and that computers increase in performance, the usefulness of this approach may come up again in some distant future. Nevertheless, readers may be prompted to look into these optimization methods already today seeing that they are available also in the geodetic literature. The validity of the concept and the applicability of the logic are demonstrated by evaluating test schedules for five 1-h, single-baseline
Intensive
VLBI sessions. Compared to schedules that were produced with the scheduling software
sked
, the number of observations per session is increased on average by three observations and the simulated precision of UT1-UTC is improved in four out of five cases (
6
μ
s
average improvement in quadrature). Moreover, a simplified and thus much faster version of the mixed-integer linear program has been developed for modern VLBI Global Observing System telescopes.