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REVIEW 4 major objections 5 minor 1 cited by

AstroQ: Automated Scheduling of Cadenced Astronomical Observations

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read AstroQ is an automated scheduler that formulates cadenced astronomical observation planning as an integer linear program and demonstrates proven-optimal semester-scale schedules in minutes.

desk verdict A genuinely useful autoscheduler with a solid benchmark setup and open-source code, but the written overlap constraint is off by one and the optimality claim needs a corrected model statement before it can be trusted. read the letter →

arxiv 2506.08195 v1 pith:LUZ2EZ6V submitted 2025-06-09 astro-ph.IM astro-ph.EP

Jack Lubin , Erik A. Petigura , Velibor V. Mišić , Judah Van Zandt , Luke B. Handley This is my paper · ORCID
classification astro-ph.IMastro-ph.EP
keywords schedulingoptimizationintegerlinearprogrammingradialvelocitiescadencedobservationsautoschedulertime-domainastronomyobservatoryoperationsweatherforecasting
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

AstroQ is an automated scheduler that casts the problem of planning cadenced astronomical observations as an integer linear program and solves it to proven optimality. The paper's central claim is that the method can schedule 3,680 observations of 200 targets—each with its own inter-night and intra-night cadence requirements, visit durations, and accessibility windows—over a six-month semester at five-minute resolution, producing a certificate of optimality in roughly two minutes on a modern workstation. If true, this replaces a labor-intensive manual scheduling effort of roughly one full-time person each semester with a fast, unbiased, and weather-aware process, and it makes dynamic rescheduling practical when weather or targets of opportunity intervene. The paper also shows how completion rates depend on the match between the request set and the nights allocated to a program, using a suite of simulated Doppler planet programs.

What carries the argument

The load-bearing object is the integer linear programming model built on the sparse 'yes matrix' $Y_{r,d,s}$ together with the shortfall variable $\Theta_r$. The objective $\min \sum_r \Theta_r\,t_{\mathrm{visit},r}$ minimizes the total time-weighted number of unsatisfied observation slots, and the constraints translate cadence rules into linear inequalities using the accessibility set $A_r$, which encodes instrument allocation, twilight, altitude/azimuth limits, moon avoidance, prior observations, and custom investigator constraints. The sparsity of $A_r$ and the separation of semester-level scheduling from nightly tour ordering are what make the model tractable and certifiable.

What would settle it

Run the released AstroQ code on a single request with $t_{\mathrm{visit}}=1$ and two consecutive accessible slots: the written model (Eq. 5–6) would forbid the second visit and leave one slot empty, while the reported near-full schedules imply the code places both visits. Inspecting either the generated constraint matrix or the optimal schedule on this minimal instance would settle which rule is certified.

Watch

Extended reading notes

Core claim

The paper's central claim is that semester-long scheduling of cadenced observations can be posed as a mixed-integer linear program that is small enough to solve to proven optimality at realistic scale. The formulation defines a binary 'yes matrix' $Y_{r,d,s}$ for whether request $r$ starts a visit in slot $s$ of day $d$, a day-tracking matrix $W_{r,d}$ for requests that allow multiple visits per night, and a shortfall variable $\Theta_r$ that counts the number of unscheduled visit slots. The objective minimizes the sum of $\Theta_r$ weighted by the visit duration $t_{\mathrm{visit},r}$, and linear constraints enforce that visits do not overlap, that per-request visit limits and inter-night/intra-night cadences are respected, and that per-night visit counts stay within the $[n_{\mathrm{intra,min}}, n_{\mathrm{intra,max}}]$ range. On a benchmark of 200 requests requiring 3,680 visits over a 184-night semester at five-minute resolution, the model is solved with a certificate within 1% of optimality (typically at 0% gap) in tens to hundreds of seconds, producing schedules that fill most allocated time and forecast completion under simulated weather losses.

Load-bearing premise

The load-bearing premise is that the published overlap constraint matches the enforced code; as written it forbids adjacent single-slot visits, so the reported near-full schedules require the implementation to use a slightly different inequality than the one printed.

Editorial extensions

If this is right

  • Semester-scale radial-velocity queues of a few thousand observations across a couple hundred targets can be scheduled to certified optimality in minutes, replacing roughly one full-time human scheduler and removing human bias in balancing programs.
  • The short solve time makes dynamic rescheduling practical: the schedule can be recomputed when weather losses or targets of opportunity change the accessible slots, and the weather model gives realistic completion forecasts.
  • Program completion depends critically on the match between allocated nights and target accessibility; the paper shows the same request set completes at 90% under a real allocation, 91% under random permutations, 93% under quarter-night allocations, and 79% under simulated weather loss.
  • The same formalism can be inverted to choose the optimal allocation of telescope nights to the queue, not just the optimal schedule within a fixed allocation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the framework is domain-agnostic, the open-source release could be adapted to other scheduling problems with durations, cadences, and window constraints, such as satellite downlink planning or laboratory instrument queues.
  • A natural extension is closed-loop operations: re-solve the semester ILP nightly with updated weather forecasts and actual completions, which the reported solve times make computationally feasible.
  • The gap between the 90%-ish completions in fixed-allocation tests and the fact that total requested slots slightly exceeded allocated slots suggests that co-optimizing night allocation could push completion near 100%, a hypothesis the paper's own numbers imply but do not test.
  • Because the printed overlap constraint and the executed code may differ in how single-slot adjacencies are treated, a direct comparison of the published equations against the open-source implementation on a two-slot, one-visit instance would clarify which model the optimality certificate actually covers.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper introduces AstroQ, an integer linear programming (ILP) framework for scheduling cadenced astronomical observations, with a deployment to the KPF Community Cadence program at Keck Observatory. The authors formulate a semester-level scheduling problem with inter- and intra-night cadence constraints, implement it in Python/Gurobi, and report that a realistic 200-target, 3680-observation request set can be solved to certified optimality in minutes on a modern workstation. They also describe accessibility-map construction, a weather-loss model, and benchmark results across four allocation scenarios (real Keck 2018B allocation, random permutations, quarter-night allocations, and simulated weather losses). The paper argues that AstroQ improves over manual scheduling by providing provably optimal schedules, more realistic completion projections, and a reduction in human effort and bias.

Significance. If the technical claims are correct, this is a valuable contribution to time-domain astronomy and observatory operations. The use of a certified MIP solver with a reported zero optimality gap is a genuine strength, as is the open-source implementation and the use of a realistic request set patterned on actual Keck programs. The paper also demonstrates that an ILP with ~30,000 slots per request and hundreds of thousands of decision variables can be solved in minutes, which is practically important for dynamic rescheduling. The claimed ability to produce computer-certified optimal schedules at semester scale would be a meaningful advance over heuristic schedulers. At present, however, the correctness of the constraint model is in question, and several quantitative claims in the abstract and Table 1 are not mutually consistent. The central idea is sound and the manuscript is likely salvageable, but the model statement and reported numbers need careful correction and verification before the results can be accepted.

major comments (4)
  1. [§2.4, Eq. (5)–(6)] The overlap constraint is off by one. A visit of length t_visit,r starting at slot s−δ occupies slots s−δ through s−δ+t_visit,r−1, so it overlaps a new start at slot s if and only if δ < t_visit,r. Equation (6) instead defines R'_{d,s,δ} = {r ∈ R_{d,s} | t_visit,r ≥ δ}, which for δ=1 includes all 1-slot visits. Under a literal reading, a 1-slot visit ending at slot s−1 would prohibit a new visit from starting at slot s, forcing an empty slot between every pair of adjacent 1-slot visits. This would make the near-full schedules in Figure 5 and the 90% completion in Table 1 impossible, because the maximum number of starts would be roughly half the allocated slots. If the code in fact enforces t_visit,r > δ (or t_visit,r ≥ δ+1), then the manuscript's model statement is wrong; if the code literally implements Eq. (6), the reported schedules cannot be generated by that model. In either case, the Gurobi optimality certificate applies to a model that is not fully specified, so the central claim of provable optimality is not yet established for the written formulation. Please correct the inequality and confirm that the reported results were produced by a solver using the corrected constraint.
  2. [Abstract and §4.2] The abstract claims that 'schedules of this size may be constructed in ~120 seconds on modern workstation,' but §4.2 reports model construction of 15 s, presolve of 21 s, and solve of 172 s, totaling 208 s. Section 4.6 states that all tested cases solved in ≲200 s. These numbers do not support the abstract's 120 s figure. Please either reconcile the abstract with the reported timing, or specify which configuration and hardware produce the 120 s result.
  3. [Table 1 and §4.3–§4.4] The Test 3 row is internally inconsistent with the reported completion rates. For Test 1, the 'Avg Incumbent' of 554 slots corresponds to 554/5760 ≈ 9.6% shortfall, matching the 90% completion; Tests 2 and 4 show similar consistency. For Test 3, however, an incumbent of 109±11 slots implies ~98% completion, not the reported 93±0.2%. Moreover, Program 4 alone, at 59% completion with 24 targets × 8 nights × 5 desired visits, would contribute on the order of 384 shortfall slots if the shortfall scales linearly with missing visits. Please correct the Table 1 entry or explain the units in which 'Avg Incumbent' is expressed, and verify that the completion percentages and incumbent objectives are mutually consistent.
  4. [§3.4 and §4.5] The weather-loss model is fit to 22 years of Keck data and then used in §4.5 to simulate weather losses and forecast completion rates. No independent validation or comparison with realized completion rates is presented, so the abstract's claim that AstroQ provides 'realistic projections of program completion' is not yet supported. I suggest an out-of-sample test (for example, holding out one or more years from the weather model and comparing forecasts to actual outcomes) or a comparison with operational KPF completion rates. If such validation is outside the scope of this paper, the wording should be softened to indicate that the projections are produced under an empirical weather model rather than claimed to be realistic.
minor comments (5)
  1. [§2.4] The sentence 'Note that Equation 4 is always satisfied by Equation 6' appears to be a typo: Eq. (6) defines the set R'_{d,s,δ}, so the intended statement is presumably that Eq. (4) is implied by Eq. (5). Please clarify.
  2. [§4.2] The text says 'Obj = 554, or a total shortfall of 554 slots. This is equal to 9.6% of the total requests.' Since 554/5760 ≈ 9.6%, the phrase 'total requests' should be 'total requested slots' (or 'total requested time'), because the request set comprises 3680 visits, not 5760 slots.
  3. [Table 1] The row labeled 'Avg Incumbent' should be defined explicitly: are these Gurobi objective values (slot-weighted shortfalls) or something else? The current label is ambiguous, and the Test 3 value appears to be in conflict with the completion fractions.
  4. [§2.3 and Eq. (2)–(3)] The paper states that the convex piecewise-linear objective is 'constructed using linear constraints and auxiliary variables,' but the explicit linearization of Θ_r = max{0, a_r} is not shown. Adding these constraints would improve reproducibility.
  5. [Abstract] The phrase 'provably optimal ordering of 3680 observations' may overstate the result, because the ILP optimizes the assignment of visits to slots, while the intra-night ordering of targets is later refined by a separate telescope-tour optimization (Handley et al. 2024a). I suggest phrasing such as 'provably optimal allocation of visits to slots' or clarifying that the certificate applies to the slot-assignment model.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the central optimality claim is certified by Gurobi's external LP-bound gap, the weather-based completion estimates are conditional simulations rather than fitted inputs renamed as predictions, and the paper's self-citations are not load-bearing for the main result.

full rationale

The central claim—provable optimality of semester-scale schedules—is not circular. The ILP in §2 (Eqs. 1–13) is stated in full and solved with Gurobi; the certificate is a 0% MIP gap against the relaxed LP bound, an external, machine-checked benchmark, and no constraint or objective is defined in terms of the output schedule or of any fitted value. The completion estimates in §4.5 are conditional simulations: the weather parameters (per-date loss fractions and the 14% adjacency boost, §3.4) are fitted to 22 years of Keck weather records, but the forecasted completions (Table 1, Test 4) are optimizer outputs given simulated weather draws, not parameters fitted to completion data, so no fitted input is renamed as a prediction. The paper's own limitation statement in §3.4—'we are not attempting to construct a rigorous meteorological model for Maunakea. Rather, we built a simple empirical model of past patterns'—corroborates that the weather model is an input assumption, not a derived result, and the forecasts are explicitly conditional on it. The self-citations (Handley et al. 2024b for terminology/framework; Handley et al. 2024a for the intra-night Traveling Telescope Problem) do not carry the central argument: the semester-level model is self-contained, and the cited TTP result is published, code-bearing prior work whose assumptions do not include the target semester-optimality result, so it does not raise the circularity score. One flagged issue is a correctness risk rather than circularity: Eq. (6) defines R'_{d,s,δ} with t_visit,r ≥ δ, which for δ=1 blocks already-finished 1-slot visits started at s−1 (overlap occurs only when t_visit,r ≥ δ+1); if the code enforces the strict inequality, the model statement is off by one and the exact certified feasible set is ambiguous. That ambiguity affects which integer program was certified, but the certification itself remains an external solver's bound, so the derivation does not reduce to its own inputs.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claims rest on the ILP formalization, the accessibility maps, and the weather model. The overlap constraint contains a likely off-by-one error, and the weather model's parameters are fitted to historical data without external validation. No new physical entities are introduced.

free parameters (6)
  • Daily weather loss probability p_lost(date) = empirical fractions 2002-2023 (in repo)
    Used in §3.4 and Test 4 to simulate which nights are lost; fitted from 22 years of Keck weather records.
  • Adjacent-night loss boost = 0.14
    Fit to historical data; increases probability of next night being lost by 0.14 if previous night lost.
  • Weather loss threshold = 5 hours
    Chosen by hand to classify nights as total loss or negligible loss.
  • Gurobi MIP gap tolerance = 1%
    Termination criterion; 'provably optimal' only achieved when gap reaches 0%, as in Test 1.
  • Accessibility map thresholds = Alt 18/33/85 deg, moon sep 30 deg, twilight 12 deg
    Operational choices defining the feasible set A_r; results depend on them.
  • Slot grid parameters = Ns=168, tau_slot=5 min
    Chosen balance between time resolution and computational expense; all results are tied to this discretization.
assumptions (5)
  • standard math The LP relaxation bound computed by Gurobi certifies optimality of the ILP when the gap is 0% (or within 1% tolerance).
    Relied on for 'provably optimal' claims in §4.
  • domain assumption The accessibility maps A_r correctly represent Keck's operational constraints (altitude/azimuth limits, moon separation, twilight, Nasmyth obstruction, instrument allocation).
    §3.2; if these maps are wrong, the schedule is infeasible or suboptimal in practice.
  • domain assumption Minimizing time-weighted shortfall Theta_r approximates maximizing scientific yield.
    §2.3; all programs are weighted by t_visit,r, so longer visits dominate, which may not reflect scientific priority.
  • domain assumption Weather losses can be modeled as independent Bernoulli draws with empirical probabilities and a 0.14 adjacency boost.
    §3.4; the authors admit this is not a rigorous meteorological model.
  • ad hoc to paper Constraint 1 (Eq. 5-6) as written correctly prevents overlapping visits; specifically t_visit,r >= delta is the correct overlap condition.
    This is the load-bearing constraint; if the correct condition is t_visit,r > delta, the written model is mis-stated and the optimality certificate applies to the wrong model.

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Cite this review

Pith. "Pith review of AstroQ: Automated Scheduling of Cadenced Astronomical Observations." pith.science (2026). https://pith.science/paper/LUZ2EZ6V

@misc{pith2026250608195,
  author       = {Pith},
  title        = {Pith review of: AstroQ: Automated Scheduling of Cadenced Astronomical Observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LUZ2EZ6V}},
  note         = {Machine review of arXiv:2506.08195}
}
read the original abstract

Astronomy relies heavily on time domain observations. To maximize the scientific yield of such observations, astronomers must carefully match the observational cadence to the phenomena of interest. This presents significant scheduling challenges for observatories with multiple large programs, each with different cadence needs. To address this challenge, we developed AstroQ, an automated framework for scheduling cadenced observations. We tested this on a suite of Doppler exoplanet programs at Keck Observatory, where the algorithm powers the KPF-Community Cadence project. As a point of reference, AstroQ can determine the provably optimal ordering of 3680 observations of 200 targets -- each with its own cadence needs and accessibility constraints -- over a six month period to five minute time resolution. Schedules of this size may be constructed in ~120 seconds on modern workstation, enabling dynamic rescheduling due to weather changes, target-of-opportunity interrupts, and other needs. A key advantage of AstroQ over manual scheduling is realistic projections of program completion, savings in human effort, and elimination of human bias in balancing many programs. AstroQ is open source and may be applied to other scheduling needs, both in astronomy and beyond.

Figures

Figures reproduced from arXiv: 2506.08195 by the authors.

Figure 1
Figure 1. Day-slot scheduling framework. AstroQ discretizes time in an observing semester into Nd × Ns slots of equal length, where d and s labels each day and slot. Each request is accessible for a subset of all possible (d, s) pairs, and the inaccessible slots are red. The binary decision variable Yr,d,s is 1 if a visit of request r begins in slot s on day d (shown as dark blue squares) and 0 otherwise. Here, the request sp… view at source ↗
Figure 2
Figure 2. Construction of two accessibility maps. Each panel is analogous to [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. The fraction of times each calendar date was to￾tally lost in our 22 year data set. The seasonal variations from winter to summer months are evident. A table con￾taining the information on each night’s empirical total loss probability is available at the AstroQ GitHub repository. fair weather for the upcoming night to produce a full observing plan. As we conclude this section, we note that we are not attempting to c… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Distribution of sky coordinates from the nominal request set described in §4.1. Marker colors are the same on [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Top: Bird’s eye view of the optimal semester schedule described in § [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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Reference graph

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