{"id":"ffc8e2ba-1105-4418-9c64-659829f9153e","arxiv_id":"2411.16297","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A two-stage multi-objective decomposition method for thesis defence scheduling runs in 6-32% of the time of a monolithic method while keeping comparable solution quality.","lead":"This paper proposes a faster way to solve a university scheduling problem: assigning thesis defence committees and then finding times and rooms. It splits the problem into two stages, uses genetic algorithms first and an exact method second, and reports the method is several times faster than solving the whole problem at once.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The proxy objective z5 (Eq. 25) is weakly or even inversely related to z4, so the method's claimed quality advantage over the monolithic baseline is not robust to instances where z4 conflicts with availability spread.","rationale":"The reader's weakest-assumption analysis identifies the proxy objective z5 as the load-bearing premise, and I concur. The paper itself provides direct evidence that z5 is a poor predictor of z4 (Section 10.4) and that improving z5 can hurt final quality on Instance 96 (Section 9.2). This is precisely the condition that must hold for the method's quality claims to generalize. The efficiency gain in elapsed time is real and independent of the proxy, but the abstract's broader claim of 'significant efficiency gains' has two components; the quality component is not secured by the reported experiments. I do not propose a change to the reader's CONDITIONAL verdict because the paper is honest about this limitation, and the proposed concrete test would either confirm the concern or demonstrate that the proxy is still net beneficial. The main alternative concern—that the monolithic baseline uses a coarse ε-grid and thus may be a weak comparator—is secondary; the paper's time comparisons are against a standard implementation, and the coarse grid is a practical necessity for the monolithic method. The proxy issue is more fundamental because it questions whether the method's quality advantage is intrinsic or instance-specific.","tokens_in":27204,"tokens_out":7435,"duration_ms":73428,"concrete_test":"Re-run Instance 96 and the real-world case study with the first-stage genetic algorithm optimizing only z1 and z2 (i.e., removing z5 from the objective set), keeping all other parameters, seeds, and time limits identical, and compare (a) final hyper-volume, (b) the distribution of z4 values in the obtained non-dominated sets, and (c) total runtime. If the no-proxy variant achieves similar or better z4/hyper-volume in comparable time, then z5 is not merely weakly predictive but actively harmful, contradicting the paper's justification for proxy objectives. If the no-proxy variant is worse on z4, then z5 is partially load-bearing, but the paper still needs to quantify its predictive value and report the correlation for each objective separately.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim couples two assertions: (i) the decomposition is faster than the augmented ε-constraint method, and (ii) the resulting non-dominated sets are of comparable or better quality (hyper-volume). The speed advantage (i) follows from the problem decomposition alone and is well supported. The quality assertion (ii) rests on the first-stage proxy objective z5 (Objective 25), which counts time slots where all assigned committee members are available. Section 10.4 explicitly states that z5 predicts z3 well but z4 poorly, and Section 9.2 reports that on Instance 96 a longer first stage, which improves z5, can yield worse final hyper-volume. The mechanism is concrete: maximizing the number of available slots can favor committee members whose availability is spread over many days, which increases the number of days on which they must be scheduled, thereby worsening the committee-days objective z4. Thus the claimed 'better hyper-volume indicator values' for large instances and the case-study improvement over the monolithic method are not guaranteed by the method itself; they are contingent on the unknown correlation between z5 and z4 for the specific instance. On a different instance where availability patterns make this correlation negative, the decomposed method could be both slower-to-good-quality and biased away from z4. This is the load-bearing weak point because the paper's novelty argument (Section 8.1) explicitly justifies including proxy objectives to 'reduce the bias of the decomposition towards the initial stage objectives'; if z5 does not do that for z4, the method's quality claim rests on an unvalidated premise.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a two-stage decomposition for the multi-objective thesis defence scheduling problem. In the first stage, NSGA-II or NSGA-III generates committee configurations by optimizing workload balance, committee suitability, and a proxy objective z5 that counts time slots in which all assigned committee members are available. In the second stage, an augmented epsilon-constraint method is solved separately for each committee configuration to optimize the schedule-quality objectives z3 (time-slot preferences) and z4 (committee days). All solutions are then pooled and filtered to the non-dominated set. Experiments on four random instances (two small, two large) and one real-world case study compare this approach with a monolithic augmented epsilon-constraint method. The reported results are 8--32% of monolithic time with slightly worse hypervolume on small instances, 6--18% of monolithic time with better hypervolume on large instances, and, in the case study, 39 non-dominated solutions in 1600 seconds versus 9 in 2400 seconds.","tokens_in":27542,"tokens_out":9683,"duration_ms":95255,"significance":"If the empirical claims hold, the paper offers a practical way to obtain approximate non-dominated sets for thesis defence scheduling much faster than a monolithic epsilon-constraint approach, and the proxy-objective idea could transfer to other decomposable multi-objective problems. The manuscript has clear strengths: complete MILP formulations, detailed pseudocode for all algorithmic components, 30-seed experiments for the random instances, and a real-world case study. The main empirical claim is partially supported by the reported runtimes and hypervolume values, but the quality advantage is contingent on the validity of the proxy objective z5 as a predictor of the second-stage objective z4, a relationship that the paper itself shows to be weak. The hypervolume comparison also lacks several definitions needed for reproducibility.","major_comments":[{"comment":"The proxy objective z5 (Eq. 25) is the only first-stage representation of schedule quality, but the paper itself states that z5 predicts z3 well and z4 poorly (Section 10.4), and on Instance 96 longer first-stage runs degrade the final hypervolume (Section 9.2). Since the abstract's claim of better hypervolume on larger instances and the case-study improvement depend on this proxy, the quality advantage is not established as a property of the method; it is contingent on an instance-specific correlation between z5 and z4. The paper should provide a quantitative analysis of this correlation across instances, add a proxy that is informative for z4, or restrict the claim accordingly.","section":"Sections 5.2, 8.1, 9.2, 10.4"},{"comment":"The hypervolume comparison lacks essential definitions. The manuscript does not state which objective functions enter the hypervolume calculation (all four objectives, or only z1, z3, z4 as in the case study), what reference point is used, how negative objective values are normalized, or whether the reported times include the initialization phase described in Section 8.3. The table notes give 'Minimum hyper-volume' values, but this is not a reproducible protocol. Without these details, the claim of 'better hyper-volume indicator values' for the larger instances cannot be independently verified.","section":"Section 9, Tables 1--4"},{"comment":"The time comparison in Section 9.1 uses a monolithic baseline with 10 epsilon increments, whereas the decomposed second stage uses epsilon' = 1; the monolithic run with epsilon' = 1 takes 72,356 seconds and is not used as the baseline. This baseline choice should be stated explicitly in the abstract and results, and the comparison should either use the same epsilon grid for both methods or justify why different grids are appropriate. As written, the '8--32% of the time' statement could be read as comparing against a different method than the one actually used in the tables.","section":"Section 9.1, Tables 1--2"},{"comment":"Only two random instances are tested per size category, and only one monolithic run is reported per instance, with no variability measure for the monolithic method. The claim that the decomposition achieves better hypervolume on larger instances is therefore based on two data points. A stronger experimental design, with more instances and either multiple monolithic runs or paired statistical comparisons across seeds, is needed to support the general conclusion.","section":"Section 9"}],"minor_comments":[{"comment":"The quantification in Constraint (16) is ambiguous: the notation 'sum over {jt : (jt) in A_i} x_ijt <= 1, i=1..ni, j=1..nj' should be clarified to mean that for each member i and each defence j, the sum over roles t with (j,t) in A_i is at most 1.","section":"Eq. (16)"},{"comment":"In Eq. (9), the upper limit of the first summation appears to be C^m_i, but it should presumably be n_j; the right-hand side should sum the y_ijk variables over the number of defences j.","section":"Eq. (9)"},{"comment":"The augmentation term in Eq. (28) is typeset ambiguously; it should read z1(x) + (1/nz) * sum_{i=2}^{nz} (z_i(x) - zmin_i)/(zmax_i - zmin_i) to match the explanation in the text.","section":"Eq. (28)"},{"comment":"Eq. (30) uses z'_i(x) on both sides of the definition, which makes the initialization objective self-referential; the right-hand side should presumably use the original objective functions z_i(x).","section":"Eq. (30)"},{"comment":"The table headers for the decomposition results are difficult to read because values for ng = 100 and ng = 2000 are interleaved; a clearer layout with explicit column labels for each generation count would help.","section":"Tables 1--4"},{"comment":"The case-study figures plot negative objective values, but the text describes minimization objectives; a brief note in the caption explaining that the axes are transformed for maximization would prevent confusion.","section":"Figures 13--14"}],"recommendation":"major_revision","confidential_remarks":"The paper is generally well written and the decomposition idea is timely, but the central quality claim rests on the proxy objective's behavior, which the paper itself shows to be fragile for z4. The missing hypervolume protocol and the limited number of large instances make the empirical comparison hard to assess. The authors are transparent about the proxy limitation, which is commendable, but the manuscript needs either additional validation or a more modest claim before it is publishable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my read. The genuinely new piece is treating each stage of a decomposed scheduling model as a multi-objective problem rather than a weighted sum, and injecting a proxy objective from the first stage into the second. Applied to thesis defence scheduling, stage one runs NSGA-II/III to produce committee configurations and stage two runs augmented epsilon-constraint to schedule each one. Their literature review supports the novelty claim for this class of decomposition.\n\nWhat the paper does well: the method is specified in enough detail to reimplement; the experiments cover small and large random instances with 30 seeds plus a real case study; and the reporting is candid. The authors say directly that small instances give slightly worse hypervolume, that the proxy predicts z3 well but z4 poorly, and that Instance 96 can get worse final quality from a longer first stage because interactions are lost. The citation pattern is fine; the decomposition and timetabling literatures are represented accurately.\n\nThe main issue is the proxy. z5 counts time slots where all assigned committee members are available; it correlates with slot preferences but only weakly with committee days. The stress-test note is right that maximizing z5 can spread a member over many days and worsen z4. So the hypervolume advantage for large instances and the case study is not guaranteed by the method; it is an observed property of those instances. The paper already says this in Section 10.4, but the abstract's blanket 'better hyper-volume indicator values' overstates what is established. This is a framing problem, not a fatal flaw.\n\nSmaller issues: 30 seeds are used but there are no significance tests or dispersion measures, hypervolume details are missing, and no code or data are released. Some model equations have notational slips. None of these sink the work.\n\nWho should read it: people working on decomposition for multi-objective scheduling, and anyone looking for a template for staged multi-objective optimization with proxy objectives. It deserves a serious referee. My recommendation: send it out, and require code/data release, basic statistical reporting, and claims that condition quality on the proxy's instance-dependent fidelity.","headline":"A useful, honestly reported decomposition method for multi-objective thesis scheduling; the quality claim leans on a proxy whose weak link to one objective is acknowledged in the paper.","tokens_in":28077,"tokens_out":3683,"would_cite":true,"duration_ms":35332,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["90C29","90C11","90C59"],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that decomposing the monolithic multi-objective thesis defence scheduling problem into two sequential multi-objective submodels—genetic algorithms for committee assignment, then augmented $\\epsilon$-constraint for time…","keywords":["thesis defence scheduling","multi-objective optimisation","decomposition","augmented epsilon-constraint","genetic algorithms","proxy objective","timetabling","hypervolume"],"falsifier":"Take a real instance where most committee members' available slots are spread thinly across many different days, so many defences have many 'available' slots but on non-overlapping days, and run both the decomposed method and the monolithic augmented $\\epsilon$-constraint with a generous time limit. If the decomposed method's non-dominated front in the committee-days objective ($z_4$) is consistently dominated by the monolithic front, the proxy's predictive power for $z_4$ is falsified.","tokens_in":27032,"feed_emoji":"🎓","tokens_out":5384,"duration_ms":43858,"temperature":0.7,"pith_summary":"The paper proposes a way to make multi-objective optimisation for thesis defence scheduling practical. Instead of solving one large mixed-integer model that assigns committees and time slots simultaneously, it splits the problem into two stages: first, genetic algorithms generate a set of committee configurations; second, an augmented $\\epsilon$-constraint method schedules each configuration and collects the non-dominated solutions. The central claim is that this decomposition is dramatically faster than the monolithic augmented $\\epsilon$-constraint method—8–32% of its time on small instances and 6–18% on large ones—while producing comparable or better hypervolume values where the monolithic solver cannot reach optimality. A real case study found 39 non-dominated solutions in 1600 seconds, where the monolithic method found 9 in 2400 seconds. A sympathetic reader should care because it offers a template for attacking time-consuming multi-objective problems that have a natural two-stage structure.","feed_headline":"Two-stage decomposition finds thesis defence plans up to 16x faster","feed_subtitle":"It still matches or beats the standard solver on large instances, and found 39 trade-off schedules in a real case study.","key_machinery":"The central mechanism is the multi-stage decomposition with a proxy objective. The load-bearing object is $z_5(x)$, the number of time slots where all members assigned to a defence are simultaneously available (Equation 25 in the first submodel). It is meant to predict the two second-stage objectives, $z_3$ (time-slot preferences) and $z_4$ (committee days). The second stage applies the augmented $\\epsilon$-constraint method (Mavrotas and Florios 2013) to each committee configuration, and the overall non-dominated set is collected across all configurations. The genetic algorithms (NSGA-II and NSGA-III) supply diverse partial solutions, while the proxy objective steers that diversity toward configurations with scheduling flexibility.","core_discovery":"The discovery is a multi-objective partial optimisation decomposition strategy. The monolithic problem is broken into two sequentially solved multi-objective submodels. The first submodel uses NSGA-II or NSGA-III to find committee configurations, evaluated by workload balance ($z_1$), committee suitability ($z_2$), and a proxy objective $z_5$ that counts, for each defence, the number of time slots in which all assigned committee members are available. The second submodel takes each configuration as a partial solution and applies an augmented $\\epsilon$-constraint method to optimise time-slot preference satisfaction ($z_3$) and committee days ($z_4$). The paper claims this yields substantial efficiency gains: on small instances the decomposition takes 8–32% of the monolithic time with slightly worse hypervolume; on larger instances it takes 6–18% of the time with better hypervolume; and in the case study it found more non-dominated solutions and improved the best value in all three objectives over the comparison method. The paper argues the proxy objective is what makes the decomposition viable, by transmitting information about later-stage schedule quality into the earlier committee-assignment stage.","pith_inferences":["Editorial inference: if the proxy-objective idea transfers, other two-stage scheduling problems—course timetabling, exam scheduling, or room allocation after staff assignment—could use a similar decomposition, with one proxy objective per downstream objective to avoid the $z_4$ weakness seen here.","Editorial inference: the efficiency gain is large enough that the approach could support interactive re-optimisation: a decision-maker could re-run the second stage under new preference weights in minutes rather than hours.","Editorial inference: the paper's own results suggest a testable extension—adding a second proxy specifically targeting the number of shared days across a member's committees would likely improve $z_4$ performance, since the observed failure mode is exactly the scattering of available slots across different days.","Editorial inference: hypervolume comparisons on large instances should be read with care, because the monolithic baseline's 120-second per-iteration limit means the comparison is against a truncated solver rather than the true Pareto front; the decomposition's advantage may shrink if the baseline is given more time."],"forward_implications":["On small instances where the monolithic solver reaches optimality, the decomposition achieves the same optimisation in 8–32% of the runtime, at a small cost in hypervolume.","On large instances where the monolithic solver cannot close the gap within its time limit, the decomposition runs in 6–18% of the time and produces non-dominated sets with higher hypervolume.","First-stage objectives (e.g., workload balance) will typically perform better than second-stage objectives (e.g., committee days), because the decomposition gives them priority.","The quality of second-stage objectives depends on how strongly the proxy objective predicts them; the paper shows $z_5$ predicts $z_3$ well but $z_4$ weakly.","The method is applicable to any multi-objective problem that can be split into sequential subproblems and for which partial solutions can be scored by proxy objectives."],"supporting_citations":[{"why":"Supplies the monolithic multi-objective model, the random instance generator, and the augmented $\\epsilon$-constraint baseline that the decomposition is compared against.","marker":"Almeida et al. (2024)"},{"why":"Provides the augmented $\\epsilon$-constraint method (AUGMECON2) used in both the monolithic solver and the second stage of the decomposition.","marker":"Mavrotas and Florios (2013)"},{"why":"Defines decomposition and partial optimisation for integer programming timetabling problems, the conceptual foundation the paper extends to the multi-objective setting.","marker":"Burke et al. (2010)"},{"why":"Demonstrates a two-stage decomposition of a high school timetabling problem, supporting the claim that sequential submodels can outperform a monolithic model under time limits.","marker":"Sørensen and Dahms (2014)"},{"why":"Formulates the thesis defence timetabling problem and provides a reference point for the problem class and its constraints.","marker":"Battistutta et al. (2019)"}],"fun_headline_variants":["Two-stage decomposition speeds thesis defence scheduling up to 16x","Faster multi-objective thesis defence scheduling via proxy-guided decomposition","Decomposition finds 39 thesis defence plans in 1600s, beating baseline","Split-and-conquer scheduling: faster thesis defence plans, same or better quality"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole method leans on the proxy objective $z_5$—the count of time slots where all assigned committee members are available—being a trustworthy stand-in for how well a committee configuration will score on the later scheduling objectives, especially the number of committee days; the paper itself shows this relationship is weak for $z_4$.","fun_headline_variants_meta":{"raw":{"variants":["Two-stage decomposition speeds thesis defence scheduling up to 16x","Faster multi-objective thesis defence scheduling via proxy-guided decomposition","Decomposition finds 39 thesis defence plans in 1600s, beating baseline","Split-and-conquer scheduling: faster thesis defence plans, same or better quality"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000218,"raw_usage":{"total_tokens":1512,"prompt_tokens":1090,"completion_tokens":422,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":706,"completion_tokens_details":{"reasoning_tokens":356}},"tokens_in":706,"tokens_out":422,"duration_ms":17286,"temperature":1.0,"reasoning_tokens":356,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T13:17:00.965415+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a real instance where most committee members' available slots are spread thinly across many different days, so many defences have many 'available' slots but on non-overlapping days, and run both the decomposed method and the monolithic augmented $\\epsilon$-constraint with a generous time limit. If the decomposed method's non-dominated front in the committee-days objective ($z_4$) is consistently dominated by the monolithic front, the proxy's predictive power for $z_4$ is falsified.","supporting_citations":[{"cited_title":", author Santos, D","cited_arxiv_id":null,"evidence_quote":"Supplies the monolithic multi-objective model, the random instance generator, and the augmented $\\epsilon$-constraint baseline that the decomposition is compared against."},{"cited_title":", author Florios, K","cited_arxiv_id":null,"evidence_quote":"Provides the augmented $\\epsilon$-constraint method (AUGMECON2) used in both the monolithic solver and the second stage of the decomposition."},{"cited_title":", author Mareček, J","cited_arxiv_id":null,"evidence_quote":"Defines decomposition and partial optimisation for integer programming timetabling problems, the conceptual foundation the paper extends to the multi-objective setting."},{"cited_title":", author Ceschia, S","cited_arxiv_id":null,"evidence_quote":"Formulates the thesis defence timetabling problem and provides a reference point for the problem class and its constraints."}],"review_version":1}