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LUMOS : Linear programming Utility for Multi-messenger Optical Scheduling

Yogesh P. Wagh, Michael W. Coughlin, Leo P. Singer, Varun Bhalerao

TL;DR

This work tackles the challenge of efficiently following up gravitational-wave events with wide-field optical surveys under large localization uncertainties. It introduces LUMOS, a MILP-based scheduler that first solves a maximum coverage field selection within observability constraints and then optimizes multi-visit observation timing, accounting for slewing and cadence. On 1199 LVK O4 events, LUMOS delivers a substantial gain in cumulative localization probability over gwemopt (mean improvement of 84.7%, with 99.7% of cases showing better performance and several skymaps unschedulable by gwemopt successfully scheduled by LUMOS). The approach offers a scalable framework for both ground- and space-based follow-up, with potential extensions to light-curve-informed decisions, dynamic exposure times, and lunar/sky-condition constraints to further boost the efficiency of electromagnetic counterpart searches.

Abstract

The detection of gravitational-wave events by LIGO-Virgo-KAGRA has opened new avenues for multi-messenger astrophysics; however, electromagnetic counterparts remain elusive due to large localization uncertainties. Wide-field optical surveys like the Zwicky Transient Facility (ZTF) play a crucial role in follow-up, but efficient scheduling is essential. In this work, we present LUMOS, a Mixed Integer Linear Programming (MILP) approach that selects fields via a maximum coverage problem and schedules observations to maximize cumulative probability while respecting observability constraints. Using 1199 GW events from O4, we compare the LUMOS scheduler with gwemopt, showing an 84.7 percent higher mean cumulative probability and better performance in nearly all cases. While designed for ZTF, LUMOS's framework parallels the M4OPT toolkit for space missions, highlighting the broader applicability of MILP-based scheduling to both ground- and space-based follow-up.

LUMOS : Linear programming Utility for Multi-messenger Optical Scheduling

TL;DR

This work tackles the challenge of efficiently following up gravitational-wave events with wide-field optical surveys under large localization uncertainties. It introduces LUMOS, a MILP-based scheduler that first solves a maximum coverage field selection within observability constraints and then optimizes multi-visit observation timing, accounting for slewing and cadence. On 1199 LVK O4 events, LUMOS delivers a substantial gain in cumulative localization probability over gwemopt (mean improvement of 84.7%, with 99.7% of cases showing better performance and several skymaps unschedulable by gwemopt successfully scheduled by LUMOS). The approach offers a scalable framework for both ground- and space-based follow-up, with potential extensions to light-curve-informed decisions, dynamic exposure times, and lunar/sky-condition constraints to further boost the efficiency of electromagnetic counterpart searches.

Abstract

The detection of gravitational-wave events by LIGO-Virgo-KAGRA has opened new avenues for multi-messenger astrophysics; however, electromagnetic counterparts remain elusive due to large localization uncertainties. Wide-field optical surveys like the Zwicky Transient Facility (ZTF) play a crucial role in follow-up, but efficient scheduling is essential. In this work, we present LUMOS, a Mixed Integer Linear Programming (MILP) approach that selects fields via a maximum coverage problem and schedules observations to maximize cumulative probability while respecting observability constraints. Using 1199 GW events from O4, we compare the LUMOS scheduler with gwemopt, showing an 84.7 percent higher mean cumulative probability and better performance in nearly all cases. While designed for ZTF, LUMOS's framework parallels the M4OPT toolkit for space missions, highlighting the broader applicability of MILP-based scheduling to both ground- and space-based follow-up.
Paper Structure (9 sections, 6 equations, 5 figures, 1 table)

This paper contains 9 sections, 6 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Localization Coverage Strategy
  3. Mathematical Formulation
  4. Scheduling Algorithm
  5. Variables
  6. Constraints and Objective Function
  7. Scheduling GW Events
  8. Conclusion and Future Work
  9. Acknowledgments

Figures (5)

  • Figure 1: The highlighted tiles represent the fields covering the gravitational-wave event localization, obtained from the LUMOS's MILP-based maximum coverage algorithm.
  • Figure 2: Illustration of the scheduling process for multiple visits.
  • Figure 3: Comparing scheduling performance of LUMOS (upper left panel) and gwemopt (upper right panel). LUMOS correctly schedules observations of the entire high probability region, while gwemopt ends up missing a part of it, instead recommending observations of the low-probability part of the localisation. The bottom panel shows the cumulative probability coverage as a function of number of fields observed. LUMOS observations terminate faster with a higher cumulative probability coverage.
  • Figure 4: Comparison of cumulative probability coverage achieved by LUMOS and gwemopt for 1199 gravitational-wave events from O4. Each point represents a single skymap. The dashed diagonal line indicates equal performance. Points above the line correspond to cases where LUMOS outperforms gwemopt, which occurs in 99.7% of cases. The color of each point reflects the sky area covered (in deg$^2$), providing additional context for the efficiency of coverage.
  • Figure 5: Histogram plot showing the difference of cumulative probability between LUMOS and gwemopt.