Abstract
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}~upmu text {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.
Highlights
Introduction and motivationThrough immense progress in the development of the respective solvers, today mixed-integer linear programming (MILP) has many applications in production and planning
We present a new approach for a very-long-baseline interferometry (VLBI) scheduling program which finds the schedule with the optimal sky coverage considering the geometries at the whole time period as a single decision entity using mixed-integer linear programming, i.e., we formalize the optimization problem as a linear objective function with a set of linear inequality constraints over a set of variables
To each atomic interval and each station, we assign a candidate activity whose tracking step starts within this interval; the actual selection of the activity is done by the MILP approach
Summary
Through immense progress in the development of the respective solvers, today mixed-integer linear programming (MILP) has many applications in production and planning. We present a new approach for a VLBI scheduling program which finds the schedule with the optimal sky coverage considering the geometries at the whole time period as a single decision entity using mixed-integer linear programming, i.e., we formalize the optimization problem as a linear objective function with a set of linear inequality constraints over a set of variables. A more detailed review of scheduling approaches in astronomy with a focus on scheduling networks of radio telescopes is provided by Buchner (2011), who notes that in typical applications it is ‘not a big deal to lose 15 min of observation,’ and a rather coarse discretization of time is justifiable This is very different in our application, in which a typical 24-h experiment incorporates several thousand observations.
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