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REVIEW 2 major objections 7 minor 30 references

Sensitivity of hMPA to Controlled CEC 2017 Transformations

T0 review · 2 major / 7 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A hybrid optimizer's results depend on which benchmark transformations are active, with shift doing most of the damage and no consistent ordering across functions.

desk verdict Solid, well-scoped empirical diagnostic study of hMPA on parameterized CEC 2017; the main claims hold, but the composition-function parameterization is underspecified and needs clarification or code release. read the letter →

arxiv 2607.22862 v1 pith:AJ4CEWX6 submitted 2026-07-24 cs.NE

Grzegorz Sroka , S{l}awomir T. Wierzchoń This is my paper · ORCID
classification cs.NE
keywords CEC2017benchmarkparameterizationtransformationsensitivitymetaheuristicoptimizationDeepStatisticalComparisonextendedhybridMarinePredatorsAlgorithmbias-shift-rotationconfigurations
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 sets out to explain why a hybrid optimizer's results change when the transformations built into a benchmark are switched on or off. It introduces a parameterized version of the CEC 2017 benchmark in which bias, shift, and rotation are controlled independently while the original functions and transformation data are preserved, and it applies this layer to the hybrid Marine Predators Algorithm (hMPA), whose predicted-candidate operator reconstructs solutions from numerical objective values and coordinate-wise models. Using Deep Statistical Comparison (DSC) and extended DSC (eDSC) re-purposed from algorithm ranking to configuration ranking, it claims that the eight bias-shift-rotation configurations differ statistically significantly at every dimension tested, yet the ordering is not consistent across the 29 functions. The concrete pattern is that shift generally worsens objective values, isolated rotation causes no systematic deterioration, isolated bias has little effect on final-solution distributions, and configurations combining shift with rotation differ most consistently from the untransformed control. This matters because the standard benchmark activates all three transformations at once, so ordinary rankings cannot say which part of a landscape an algorithm is actually responding to.

What carries the argument

The load-bearing object is the parameterization layer: each benchmark function is written as $F_i(x)=f_i(M_i(x-o_i))+F^*_i$, with a binary configuration vector $C=(C_1,C_2,C_3)$ deciding whether the bias $F^*_i$, the shift $o_i$, and the rotation matrix $M_i$ are active, so $C(000)$ is the untransformed control and $C(111)$ reproduces the standard CEC 2017 benchmark. The second piece is the re-purposed statistical machinery: DSC compares distributions of final objective values using pairwise distribution tests with a multiple-comparison correction, while eDSC compares final solution vectors using a multivariate E-test and covariance hypervolumes, with explicit numerical handling of rank-deficient covariance matrices when the dimension exceeds the number of runs. The mechanism under diagnosis is hMPA's predicted-candidate operator, which builds a one-dimensional linear regression of objective value on each coordinate and inverts it to reconstruct a candidate from a target value; that is why bias, shift, and rotation can probe different parts of the algorithm.

What would settle it

Re-run the standard CEC 2017 benchmark and verify that the full configuration C(111) in the parameterized implementation produces identical result distributions; then check that deactivating shift leaves the optimum at the search-space center for hybrid and composition functions, not only for simple functions. If either check fails, the shift and rotation attributions are artifacts of the parameterization layer rather than properties of hMPA.

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Extended reading notes

Core claim

The discovery is that hMPA is transformation-sensitive in a way that is statistically clear but not monotonically ordered. Across 29 CEC 2017 functions, four dimensions (10, 30, 50, 100), 30 runs per setting, and a fixed budget of 10000*dim evaluations, rank-based significance tests on both DSC and eDSC rankings show significant differences among the eight configurations at every dimension, and the same holds for nearly all 56 three-configuration subsets. The directional effects are separable: shift is the transformation that generally worsens final objective values; isolated rotation does not systematically degrade results; isolated bias barely changes the distribution of final solutions; and configurations containing both shift and rotation differ from the control most consistently. Crucially, the rankings flip from function to function, so the configurations cannot be arranged on a single difficulty scale, and the effect of a combined configuration is not the sum of its components' effects. The paper therefore claims the eight configurations are diagnostic conditions rather than ordered difficulty levels.

Load-bearing premise

The diagnosis assumes that turning off a transformation only removes that transformation (zero shift vectors and identity rotations must not alter the hybrid or composition functions in unintended ways) and that the hMPA implementation faithfully combines the published base MPA and predicted-candidate operator, with no MPA-only baseline to rule out inherited base-algorithm sensitivity.

Editorial extensions

If this is right

  • A standard CEC 2017 ranking cannot attribute performance to bias, shift, or rotation; configuration-level testing is required to know which transformation caused an outcome.
  • Benchmark designers using hMPA should expect shift, and especially shift combined with rotation, to be the conditions that separate behavior, while isolated rotation and bias are weak levers.
  • Because rankings vary across functions and dimensions, statements about a configuration being harder or easier must be qualified by the specific function and dimension.
  • The same parameterization and DSC/eDSC workflow can be transferred to other continuous optimizers and to CEC 2024 and CEC 2025 suites that reuse CEC 2017 problems.
  • Fixed-budget results are not asymptotic: configurations at different convergence stages when the budget ends may reorder under a larger budget, so transformation effects should be reported together with the budget.

Reading between the lines

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

  • The predicted-candidate operator is the most plausible coupling point for the observed sensitivity: coordinate-wise inverse regression should be disturbed most by rotation, which mixes coordinates, and by shift, which changes the population-mean target values; a matched MPA-only ablation would likely show weaker transformation effects, though the paper runs no such baseline.
  • The weaker eDSC separation at dimension 100 may be an artifact of estimating a 100-dimensional distribution from only 30 final vectors, so the apparent convergence of configurations at high dimension should not be read as genuine similarity without more runs or projected summaries.
  • Subtracting each configuration's optimum from its final solutions before running eDSC would separate the deterministic displacement caused by shift from genuine distributional change; the paper itself signals this as a natural complement.
  • The configuration set is naturally a factorial design (bias by shift by rotation), so a factorial analysis of variance on ranks could estimate interactions formally; the paper declines to fit such a model, leaving interaction claims untested.
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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

2 major / 7 minor

Summary. This paper introduces a parameterized variant of the CEC 2017 benchmark in which bias, shift, and rotation are controlled independently, producing eight configurations C(000)-C(111), while the original functions and transformation data are said to be preserved. Using this framework, the authors diagnose the hybrid Marine Predators Algorithm (hMPA), whose predicted-candidate operator depends on raw objective values and coordinate-wise reconstruction. DSC and eDSC are adapted from algorithm-level to configuration-level comparison, and the paper reports an exhaustive analysis of all eight configurations, all 56 three-configuration subsets, and control comparisons against C(000), across 29 functions at dimensions 10-100 with 30 runs under a budget of 10000*dim evaluations. The main findings are that DSC and eDSC detect statistically significant global differences at every dimension, that configuration rankings vary across functions and preclude a consistent ordering, that shift generally worsens objective-value outcomes, that isolated rotation and isolated bias have weak effects, and that shift-rotation combinations differ most consistently from the control. The authors explicitly hedge that the results are limited to hMPA, the chosen parameters, 30 runs, the fixed budget, and the analyzed functions, and they note that no factorial interactions or operator attribution are established.

Significance. If the reported results hold, the paper's main value is methodological: a parameterization layer that independently controls bias, shift, and rotation in CEC 2017, combined with a configuration-level adaptation of DSC/eDSC applied exhaustively (8 configurations, 56 three-way subsets, control comparisons, 29 functions, four dimensions). The exhaustive design, the explicit numerical handling of rank-deficient covariance matrices, and the repeated acknowledgment of the bias-offset confound in RankY, the informational limits of 30 solutions in 100 dimensions, and the absence of an MPA-only baseline are strengths; the paper does not overclaim factorial interactions and presents the conclusions as fixed-budget results. The empirical novelty is moderate, being a case study of one hybrid algorithm with fixed parameter settings, and the function-level reversals (e.g., C(010) ranking best on F23, F27, and F29) are the most interesting output. Overall significance is moderate and depends on the parameterization being correct for the hybrid and composition functions, which is exactly the point that the manuscript leaves unspecified.

major comments (2)
  1. [Section 3 (Eq. (1)), Table 1] The parameterization of hybrid and composition functions is not specified at the component level. The CEC 2017 reference implementation [1] stores component-level shift and rotation data for the hybrid functions F11-F20 and the composition functions F21-F30 (o and M are D x N and D x D x N arrays for N=10 components). Section 3 states only that "the parameterization is limited to the controlled activation of F_i^*, o_i, and M_i" and describes the deactivation as "using a zero vector" and "using an identity matrix with a dimension consistent with the given function"; this does not establish whether every component-level shift is zeroed and every component-level rotation is set to identity for configurations such as C(000), C(001), and C(010). If only top-level transformations were toggled, the isolation of shift and rotation would fail for 20 of the 29 test functions, which would directly contaminate the central claims that shift generally worsens objective-value outcomes, that isolated rotation causes no systematic deterioration, and the function-level reversals highlighted for F23, F27, and F29. Since no code is released, the ambiguity cannot be resolved from the manuscript; the authors should specify the component-level substitution explicitly and/or release the implementation for verification.
  2. [Section 7.3, Table 7] The DSC control p-values for C(100), C(101), C(110), and C(111) versus C(000) are reported as identical (7.8E-08) at every dimension. Table 3 shows that the function-wise rank differences for these four configurations are not identical (for example, at dim=10 on F9 the differences from C(000) are 3.5, 5.5, 4.5, and 6.5, respectively), so the Wilcoxon statistics on RankY values would not generally coincide; the same holds across dimensions, where the rank patterns also differ. The authors should report the exact quantities paired (per-function RankY values or aggregated raw values), the test statistics, and the tie-handling procedure, and verify the printed p-values; as reported, these entries are not reproducible from the displayed ranks.
minor comments (7)
  1. [Sections 2 and 9] Section 2 contains an unprocessed LaTeX command ("textbf Centre-bias"), and Section 9 contains corrupted text ("comp etition", "we- re evaluated", "Analogical transfor - mation"); the manuscript should be carefully proofread before resubmission.
  2. [Figure 8] The single figure is numbered "Figure 8" although no Figures 1-7 exist, so it should be renumbered; additionally, the convergence plots use raw objective values, and error-relative-to-optimum curves would be more informative, as the paper itself acknowledges in Section 8.
  3. [Section 6] The combined significance value pvalue = 1 - prod(1-p_j) is applied to seven Wilcoxon comparisons that share the same control data, so the constituent p-values are not independent; the text should state that this combined value is a descriptive summary rather than a calibrated meta-test.
  4. [Data Availability] The Data Availability statement says the datasets are available from the corresponding author upon reasonable request, but the paper's explicit claim of a reproducible diagnostic protocol would be better supported by releasing the parameterized benchmark layer and the adapted DSC/eDSC scripts, which would also resolve the component-level ambiguity raised in the first major comment.
  5. [Section 8] The statement that reversals for composition functions "do not contradict" the shift mechanism would be easier to evaluate if the paper reported the magnitudes behind the rank reversals (for example, median final objective values per configuration for F23, F27, and F29), since DSC ranks alone conflate small and large differences.
  6. [Sections 7 and 8] DSC comparisons involving bias-containing configurations (C(100), C(101), C(110), and C(111)) include the imposed additive offset, as the Discussion acknowledges; the caveat should also appear at the point of the first such comparison in the Results, and a DSC re-analysis on error-to-optimum values would strengthen the bias-related conclusions.
  7. [References] Verify that all listed references are cited in the body text, since reference [12] does not appear to be cited.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the paper reports empirical sensitivity measurements against an external benchmark, with no fitted inputs or load-bearing self-citation.

full rationale

The paper's derivation chain is empirical: it defines configurations C(000) through C(111) as toggles of bias, shift, and rotation, runs hMPA under a fixed budget, and applies DSC/eDSC to the resulting output distributions. No quantity used in the conclusions is defined in terms of the conclusions. The mean-rank claims and Wilcoxon/Friedman results are computed from fresh runs on the external CEC 2017 reference implementation [1]; no parameter is fitted to the compared configurations. The only self-citations are to [25] (the hMPA/predicted-candidate definition, which is the object under test) and [29] (background motivation); neither supplies a result that the present measurements reduce to. The paper explicitly flags the bias-offset confound in Section 8 ('RankY is derived from raw objective values. Therefore, comparisons between biased and unbiased configurations include the imposed additive offset'), so it does not present DSC differences for bias-toggled pairs as evidence of hMPA sensitivity. The remaining concerns identified by the reader (underspecified component-level transformations for composition functions, absence of an MPA-only baseline, no released code) are correctness or scope limitations, not circularity. The central sensitivity claims are self-contained against the external benchmark and the recorded runs.

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

This is an empirical benchmark study with no fitted model parameters. The 'free parameters' are experimental and statistical choices that bound the claims. The axioms are implementation-faithfulness and statistical-validity assumptions; none is a new physical or mathematical entity.

free parameters (6)
  • population size n=20
    Chosen by hand in Section 4 to keep variability low; affects all reported rankings.
  • newNopar=0.1 = 0.1
    Fraction of population replaced by predicted candidates, fixed from [25]; directly controls the hybrid operator under study.
  • FADs and P (MPA parameters) = FADs=0.2, P=0.5
    Standard MPA parameters taken from [8]; influence search dynamics and hence configuration sensitivity.
  • evaluation budget FES_max=10000*dim = 10000*dim
    Fixed budget; the paper notes ordering depends on this limit and results are not asymptotic.
  • number of runs q=30 = 30
    30 independent runs; at dim=100 this makes empirical covariance rank-deficient, acknowledged in Section 8.
  • significance and resampling settings = alpha=0.05, R=4999, seed=1234
    Statistical analysis choices; R increased to 4999 to resolve Bonferroni thresholds.
assumptions (5)
  • domain assumption CEC 2017 function definitions, shift data, rotation matrices, and bias values from [1] are reproduced correctly.
    Invoked throughout Section 3; if the base implementation is wrong, all configurations are affected.
  • domain assumption Deactivating shift with a zero vector and rotation with an identity matrix preserves the internal structure of hybrid and composition functions.
    Section 3 states parameterization is limited to activation of F*_i, o_i, M_i; no evidence is given that variable partitioning and shuffle data remain meaningful under these replacements.
  • domain assumption The hMPA implementation faithfully combines the public MPA code [8] with the predicted-candidate operator [25].
    Section 4 describes the combination but no verification, code, or ablation is provided; this is the central object of study.
  • domain assumption DSC/eDSC ranking logic remains valid when applied to benchmark configurations instead of algorithms.
    Section 6 adapts scripts from [7]; the authors retain core logic but do not validate that configuration-level use has the same statistical properties.
  • standard math The 30 runs are independent and the Anderson-Darling and multivariate E-tests are used appropriately.
    Section 6 uses p-values and transitivity checks; independence is assumed though no seed is reported for the optimizer runs.

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Cite this review

Pith. "Pith review of Sensitivity of hMPA to Controlled CEC 2017 Transformations." pith.science (2026). https://pith.science/paper/AJ4CEWX6

@misc{pith2026260722862,
  author       = {Pith},
  title        = {Pith review of: Sensitivity of hMPA to Controlled CEC 2017 Transformations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AJ4CEWX6}},
  note         = {Machine review of arXiv:2607.22862}
}
read the original abstract

The standard CEC 2017 benchmark applies bias, shift, and rotation simultaneously, confounding their individual effects on algorithmic behavior. We introduce a parameterized implementation that controls these transformations independently while preserving the original functions and transformation data. The framework diagnoses the hybrid Marine Predators Algorithm (hMPA), whose predicted-candidate mechanism depends on numerical objective values and coordinate-wise reconstruction. DSC and extended DSC (eDSC) are adapted from algorithm-level comparison to configuration-level diagnosis, enabling, to our knowledge, the first exhaustive analysis of all eight bias-shift-rotation configurations of a parameterized CEC 2017 benchmark. We examine all 56 three-configuration subsets and comparisons with the untransformed control. Experiments cover 29 functions, dimensions 10-100, 30 independent runs, and a budget of 10000*dim objective-function evaluations. DSC and eDSC detect statistically significant differences among configurations at every dimension, but rankings vary across functions, preventing a consistent ordering. Shift generally worsens objective values; isolated rotation causes no systematic deterioration, while isolated bias has little effect on final-solution distributions. Shift-rotation combinations differ most consistently from the control. Convergence plots reveal function- and dimension-dependent separation, plateaus, and late improvement. Results are limited to hMPA, the chosen parameters, 30 runs, the fixed budget, and the analyzed CEC 2017 functions. Within this scope, the framework provides a reproducible diagnostic protocol extensible to other continuous optimizers and related CEC benchmarks, including CEC 2024 and CEC 2025.

Figures

Figures reproduced from arXiv: 2607.22862 by the authors.

Figure 8
Figure 8. Convergence profiles for F1, F9, F14, and F23 across the eight parameterized CEC 2017 configurations at dim ∈ {10, 30, 50, 100}. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗

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