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Electromagnetic follow-up of gravitational wave detections is very resourceintensive, taking up hours of limited observation time on dozens of telescopes.Creating more efficient schedules for follow-up will lead to a commensurateincrease in counterpart location efficiency without using more telescope time.Widely used in operations research and telescope scheduling, mixed integerlinear programming (MILP) is a strong candidate to produce thesehigher-efficiency schedules, as it can make use of powerful commercial solversthat find globally optimal solutions to provided problems . We detail a newtarget of opportunity scheduling algorithm designed with Zwicky TransientFacility in mind that uses mixed integer linear programming. We compare itsperformance to \texttt{gwemopt}, the tuned heuristic scheduler used by theZwicky Transient Facility and other facilities during the third LIGO-Virgogravitational wave observing run. This new algorithm uses variable-lengthobserving blocks to enforce cadence requirements and ensure fieldobservability, along with having a secondary optimization step to minimize slewtime. \blue{We show that by employing a hybrid method utilizing both thisscheduler and \texttt{gwemopt}, the previous scheduler used, in concert, we canachieve an average improvement in detection efficiency of 3\%-11\% over\texttt{gwemopt} alone} for a simulated binary neutron star merger data setconsistent with LIGO-Virgo's third observing run, highlighting the potential ofmixed integer target of opportunity schedulers for future multimessengerfollow-up surveys.

astrophysical journal/the astrophysical journal

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