Foraging with MUSHROOMS: A Mixed-Integer Linear Programming Scheduler for Multimessenger Target of Opportunity Searches with the Zwicky Transient Facility

Electromagnetic follow-up of gravitational wave detections is very resource intensive, taking up hours of limited observation time on dozens of telescopes. Creating more efficient schedules for follow-up will lead to a commensurate increase in counterpart location efficiency without using more telescope time. Widely used in operations research and telescope scheduling, mixed integer linear programming (MILP) is a strong candidate to produce these higher-efficiency schedules, as it can make use of powerful commercial solvers that find globally optimal solutions to provided problems . We detail a new target of opportunity scheduling algorithm designed with Zwicky Transient Facility in mind that uses mixed integer linear programming. We compare its performance to \texttt{gwemopt}, the tuned heuristic scheduler used by the Zwicky Transient Facility and other facilities during the third LIGO-Virgo gravitational wave observing run. This new algorithm uses variable-length observing blocks to enforce cadence requirements and ensure field observability, along with having a secondary optimization step to minimize slew time. \blue{We show that by employing a hybrid method utilizing both this scheduler and \texttt{gwemopt}, the previous scheduler used, in concert, we can achieve an average improvement in detection efficiency of 3\%-11\% over \texttt{gwemopt} alone} for a simulated binary neutron star merger data set consistent with LIGO-Virgo's third observing run, highlighting the potential of mixed integer target of opportunity schedulers for future multimessenger follow-up surveys.