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REVIEW 4 major objections 6 minor 35 references

New Multi-objective Partial Optimisation Decomposition Strategies for the Thesis Defence Scheduling Problem

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 2411.16297 v1 pith:HAUREN76 submitted 2024-11-25 math.OC

João Almeida , Alexandre Francisco , Daniel Santos , José Rui Figueira This is my paper · ORCID
classification math.OC MSC 90C2990C1190C59
keywords thesisdefenceschedulingmulti-objectiveoptimisationdecompositionaugmentedepsilon-constraintgeneticalgorithmsproxyobjectivetimetablinghypervolume
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

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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 $z_4$.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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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 / 6 minor

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.

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 (4)
  1. [Sections 5.2, 8.1, 9.2, 10.4] 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.
  2. [Section 9, Tables 1--4] 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.
  3. [Section 9.1, Tables 1--2] 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.
  4. [Section 9] 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.
minor comments (6)
  1. [Eq. (16)] 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.
  2. [Eq. (9)] 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.
  3. [Eq. (28)] 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.
  4. [Eq. (30)] 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).
  5. [Tables 1--4] 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.
  6. [Figures 13--14] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the decomposition efficiency gain is structural, the proxy objective is an untrained heuristic rather than a fitted or self-referential quantity, and the empirical comparisons are self-contained benchmark results.

full rationale

The paper's central claims are (i) that solving the problem as two sequential multi-objective submodels is substantially faster than a monolithic augmented epsilon-constraint method, and (ii) that the resulting non-dominated sets are competitive or better in hyper-volume on larger instances. Neither claim reduces to its own inputs by construction. The speed gain follows from the smaller second-stage problem, where committees are fixed and the second-stage eligibility sets are restricted accordingly (Section 5); it is demonstrated by runtime measurements, not derived from a fitted parameter. The proxy objective z5 (Eq. 25), which counts fully available time slots per defence, is introduced as a heuristic predictor of the second-stage objectives z3 and z4 (Sections 5.2 and 8.1) and is never calibrated to those objectives, so the later comparison of z3 and z4 is not a fitted-input-called-prediction. The paper explicitly reports the proxy's weak relationship with z4 in Section 10.4, giving a concrete mechanism (a member with many available slots may still be scheduled on different days), and Section 9.2 notes that longer first stages can hurt Instance 96 because 'some relations and interactions between different assignments might not be as well represented by the proxy objective.' These are limitations of a heuristic assumption, not evidence of circularity. The self-citations to Almeida et al. (2024) are used for the problem formulation, instance generation, and the monolithic baseline implementation; the monolithic model is fully restated in Section 4, and the experimental runs are performed in this paper, so the cited prior work is not load-bearing for the claimed novelty. No uniqueness theorem or self-citation chain is invoked to force the method's design, and the hyper-volume advantage on large instances is explicitly conditioned on the 120-second-per-iteration time limit, which is a benchmarking artifact rather than a circular derivation.

Assumptions & free parameters 7 free parameters · 5 assumptions · 1 invented entities

The central claim rests on the decomposability of the problem, on the predictive power of the proxy objective, and on the correctness of the two solver technologies. The proxy objective is a modeling invention with no external validation; no new physical entities are introduced.

free parameters (7)
  • GA population size ns = 200 (random instances); 136 (case study)
    Chosen by hand; not swept in experiments.
  • Number of generations ng = 100 and 2000 (random instances); 5 (case study)
    Swept values; results depend on this budget.
  • Mutation probability m = 1%, 5%, 10%
    Swept values; higher mutation improved hypervolume in some instances.
  • Crowding tournament rounds nr = 2
    Fixed by design; not tested.
  • Epsilon increment epsilon' = 1 or (zmax-zmin)/10
    Monolithic baseline uses 10 increments; decomposition uses 1; affects number of solver calls.
  • Per-iteration time limit = 120 seconds
    Applied to every epsilon-constraint solve; drives the time-limited comparison.
  • Large constant M in initialisation = not specified numerically
    Chosen large enough so augmentation term is smaller than 1; no value reported.
assumptions (5)
  • domain assumption The thesis defence scheduling problem can be decomposed into two sequential stages, committee assignment and time-slot scheduling, without unacceptable loss of solution quality.
    Invoked in Sections 5 and 8.1; if false, the decomposition is biased.
  • domain assumption The number of fully available time slots (z5) is a valid proxy for the second-stage objectives z3 and z4.
    Defined in Section 5.2; the paper itself shows it predicts z3 well but z4 weakly (Section 10.4).
  • standard math The augmented epsilon-constraint method of Mavrotas and Florios (2013) yields only non-dominated solutions and can skip redundant iterations.
    Relied on for both monolithic and stage-2 solvers; stated in Section 6.2.
  • domain assumption NSGA-II and NSGA-III with the specified operators adequately sample the first-stage Pareto front within the generation budget.
    The quality of partial solutions depends on GA convergence; no convergence guarantee is given (Section 7).
  • domain assumption The Gurobi solver is used as an exact oracle for the MILP subproblems within the time limit.
    All optimality claims depend on solver correctness; stated in Section 9.
invented entities (1)
  • Proxy objective z5 (maximise number of fully available time slots)
    purpose: Predict the potential of a committee configuration to yield good schedule-quality objectives in stage 2.
    Introduced in Section 5.2; its predictive power is only evaluated indirectly through final hypervolume in this paper, with acknowledged failure for the committee-days objective.

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Pith. "Pith review of New Multi-objective Partial Optimisation Decomposition Strategies for the Thesis Defence Scheduling Problem." pith.science (2026). https://pith.science/paper/HAUREN76

@misc{pith2026241116297,
  author       = {Pith},
  title        = {Pith review of: New Multi-objective Partial Optimisation Decomposition Strategies for the Thesis Defence Scheduling Problem},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HAUREN76}},
  note         = {Machine review of arXiv:2411.16297}
}
read the original abstract

A new multi-objective method for the thesis defence scheduling problem is introduced. The problem involves appointing committees to defences and assigning them to a time slot and room. A multi-objective approach is necessary to provide a better understanding of possible solutions and trade-offs to decision-makers. However, this type of approach is often time-consuming. The new multi-objective optimisation approach decomposes the monolithic problem into a sequence of multi-objective problems. This leads to significant efficiency gains compared to the augmented-e constraint method. The monolithic model is decomposed into two submodels solved sequentially. In the first stage, genetic algorithms find multiple committee configurations. The performance of these solutions is assessed based on committee assignment quality objectives and a proxy objective predicting performance in the next stage. In the second stage, considering multiple partial solutions found previously, an augmented e-constraint method is solved to find non-dominated solutions regarding the assignment of time slots to defences. These solutions consider schedule quality objectives. Finally, non-dominated solutions are presented based on objective function performance for both points of view. For small-size instances, the method takes 8-32% of the time of an augmented e-constraint method but finds non-dominated sets with slightly worse hyper-volume indicator values. For larger instances, times are 6-18% of monolithic resolutions, and hyper-volume indicator values are better. A real-world case study is presented. The experiment with decomposition found 39 non-dominated solutions in 1600 seconds. The augmented e-constraint method found 9 solutions in 2400 seconds. For the three objectives, the new method found a solution improving the best-performing solution with the other method in the time limit.

Figures

Figures reproduced from arXiv: 2411.16297 by the authors.

Figure 1
Figure 1. Time slot availability of six members Given these availabilities, it is necessary to determine the time slots that align for all committee members assigned to each defence, to ascertain when it is feasible to schedule them ( [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Feasible slots for each defence Besides being an arduous task, scheduling thesis defences often leads to unsatisfactory timetables for the committee members. Their preferences over some time slots are not always respected, and there are unfair choices which cause some members to have defences scheduled and spread out over several days in an attempt to reduce the number of days of other members. Automating thesis def… view at source ↗
Figure 3
Figure 3. Chromosome representation for a problem with three defences, three roles, and five committee members. [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Generate feasible committee diagram the output is an offspring chromosome, s of f . For every defence, j, a random parent is chosen, s p , and the nt genes of the parent representing the committee for the defence are passed down to the offspring chromosome, s of f ⌢ s …
Figure 5
Figure 5. Figure 5: Crossover representative diagram for a problem with three defences, three roles, and five committee members. [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]
Figure 6
Figure 6. Figure 6: Non-dominated fronts The crowding distance tournament is defined in Algorithm 5. Its inputs are a set of solutions, S, and the number of rounds, nr, and the output is the set of winners, S win. In each round, a set of solutions, S rand, is obtained by a random shuffle …
Figure 7
Figure 7. Figure 7: Method overview value the objective, zi(x), took in this sum, min z ′ i (x), i′ = 1, . . . , nz. This ensures that the lower bounds are small enough such that the maximum values are attainable in the ϵ-constraint method. In the genetic algorithms, the committee composi…
Figure 8
Figure 8. Figure 8: Decomposed multi-objective algorithms applied to thesis defence scheduling [PITH_FULL_IMAGE:figures/full_fig_p024_8.png]
Figure 10
Figure 10. Figure 10: Computational experiments with large size randomly generated instances [PITH_FULL_IMAGE:figures/full_fig_p027_10.png]
Figure 11
Figure 11. Figure 11: Percentage of committee members with a number of committees in two solutions with different workload balance [PITH_FULL_IMAGE:figures/full_fig_p030_11.png]
Figure 12
Figure 12. Figure 12: Percentage of committee members with a number of scheduled days in two solutions with different committee days [PITH_FULL_IMAGE:figures/full_fig_p031_12.png]
Figure 13
Figure 13. Figure 13: Non-dominated solutions for the DEG case study [PITH_FULL_IMAGE:figures/full_fig_p031_13.png]
Figure 14
Figure 14. Figure 14: Pairwise trade-off profiles between the three objective functions [PITH_FULL_IMAGE:figures/full_fig_p032_14.png]

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    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.