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REVIEW 4 major objections 6 minor 64 references

A modified RIME algorithm with covariance learning and diversity enhancement for numerical optimization

T0 review · 4 major / 6 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read A covariance-learning RIME variant claims top rankings on CEC2017, CEC2022, and 8 of 10 engineering problems.

desk verdict Plausible empirical claim, but the algorithm as written is ambiguous and the reported numbers can't be tied to a uniquely specified method. read the letter →

arxiv 2509.09529 v1 pith:OQ5EYJFC submitted 2025-09-11 cs.NE cs.AIcs.CE

Shangqing Shi , Luoxiao Zhang , Yuchen Yin , Xiong Yang , Hoileong Lee This is my paper · ORCID
classification cs.NEcs.AIcs.CE MSC 68T2090C59
keywords RIMEalgorithmMRIME-CDcovariancelearningstrategypopulationdiversitymetaheuristicoptimizationCEC2017CEC2022engineeringproblems
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

This paper argues that the RIME metaheuristic's main weakness—rapid loss of population diversity and premature convergence—can be fixed by three coordinated strategies: Gaussian-based covariance learning, an average bootstrapping step, and a stochastic covariance restart triggered by a stagnation indicator. On 29 CEC2017 functions at four dimensions and 12 CEC2022 functions at two dimensions, the resulting MRIME-CD ranks first among ten algorithms in overall Friedman tests, with average ranks of 1.51 and 1.67 versus 7.43 and 7.21 for basic RIME. The same algorithm ranks first on 8 of 10 constrained engineering design problems. A sympathetic reader would take the paper as establishing that these mutually reinforcing modifications convert RIME into a consistently more accurate, faster-converging, and more stable optimizer.

What carries the argument

The central object is MRIME-CD, a variant of the physics-based RIME algorithm (rime-ice growth) with three mechanisms: GCLS (Gaussian-based covariance learning) fits a weighted Gaussian to a roulette-selected dominant population and samples new candidates from it; ABS (average bootstrapping) replaces early hard-rime jumps to the best individual with jumps to a weighted average of best and dominant positions; SPDM (stochastic covariance learning-based population diversity mechanism) watches a normalized population-volume ratio and an improvement count, and regenerates stagnant agents with a covariance-guided random update. Together they shift RIME toward diversity-preserving exploration while

What would settle it

Re-run the CEC2017 D=30 experiment with every algorithm using the same population size in a small grid (e.g., NP=20, 50, 100) while keeping all other settings from Table 2; if MRIME-CD is not Friedman-first at all three sizes, the claimed advantage depends on the unspecified NP.

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Extended reading notes

Core claim

The central discovery is that replacing RIME's naive attraction to the current best individual with distribution-aware updates preserves fast convergence while restoring population diversity. In the soft-rime phase, a Gaussian covariance model of the dominant population generates new candidates; in the hard-rime phase, a weighted average of best and dominant positions replaces the direct jump to the best; and when a new volume-and-improvement stagnation test fires, stagnant individuals are refreshed by a stochastic covariance update. On CEC2017, MRIME-CD ranks first on 15, 20, 17, and 15 of the 29 functions at D=10,30,50,100, and on CEC2022 it ranks first overall with Friedman averages 3.17

Load-bearing premise

The reported superiority assumes that the population size, which the paper never states, is not a decisive factor; if another NP changes the rankings, the comparison collapses.

Editorial extensions

If this is right

  • Each of the three strategies individually improves RIME, and the full MRIME-CD beats every single- or double-strategy variant in Friedman rankings, suggesting the mechanisms reinforce each other.
  • GCLS is the largest single contributor to the gain; ABS contributes more on CEC2017 and SPDM more on CEC2022.
  • The stagnation restart is conditional and rare by design, so for most iterations MRIME-CD adds no cost beyond the base RIME update; the overhead is confined to the agents that trigger SPDM.
  • On ten constrained engineering problems, MRIME-CD ranks first in eight, indicating the benchmark improvements transfer to penalty-function formulations.
  • The authors themselves note two limitations: the covariance-matrix computation is time-consuming (making MRIME-CD better suited to problems without strict time budgets), and on some CEC2022 composition functions the early fast convergence does not translate into top final accuracy.

Reading between the lines

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

  • The paper never states the population size NP used in any experiment, so the reported Friedman rankings cannot be replicated exactly; re-running with a different NP could shrink or reverse the margins.
  • The complexity analysis treats GCLS as cost-neutral, but computing and sampling a full D-dimensional covariance normally costs more than O(NP*D), so wall-clock overhead may exceed the stated asymptotic bound.
  • The stagnation test multiplies per-dimension ranges; in high dimensions that product can underflow or be dominated by one tight dimension, so the 0.01 threshold is worth probing separately from the 2D count threshold.
  • The pseudocode's equation pointers are internally inconsistent—updates reference Eq. (11) and Eq. (16), which define the covariance and volume ratio rather than the generation formulas in Eq. (12) and Eq. (18)—so reproduction should follow the displayed formulas.
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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 MRIME-CD, a modified RIME algorithm with three added mechanisms: Gaussian-based covariance learning strategies (GCLS), an average bootstrapping strategy (ABS), and a stochastic covariance learning-based population diversity mechanism (SPDM). The authors evaluate MRIME-CD on the CEC2017 (10/30/50/100-D) and CEC2022 (10/20-D) benchmarks, compare it with RIME and eight other published optimizers, and support the comparison with 51 independent runs, an ablation study over the three mechanisms, and Friedman, Wilcoxon, and Kruskal-Wallis tests. They report that MRIME-CD achieves the best average Friedman rank on all tested settings and also performs well on ten engineering design problems. The central claim is that MRIME-CD improves solution accuracy, convergence speed, and stability relative to basic RIME and the considered competitors.

Significance. If the algorithm were fully specified, the experimental evidence would be substantial. The paper uses standard benchmarks, a large number of runs, a complete ablation of the proposed mechanisms, and detailed appendix tables, which are real strengths. The reported gains over RIME are large and consistent across dimensions, and the ablation indicates that all three mechanisms contribute. However, the current manuscript contains load-bearing specification problems: the pseudocode references equations that are not position updates, the stagnation threshold is inconsistent between the text and the pseudocode, and key parameters such as the population size and dominant-group size are not reported. These issues prevent exact replication and mean the quantitative results cannot yet be attributed to a unique algorithm. The paper is therefore not acceptable in its present form, but the problems are fixable with a careful revision.

major comments (4)
  1. [Algorithm 1 and §3.4] The pseudocode's GCLS branch says 'Compute the rime agent's position using Eq.(11)' and the SPDM branch says 'Compute the rime agent's position using Eq.(16)'. Eq.(11) defines the weighted covariance matrix C, and Eq.(16) defines the population volume V_pop; neither is a position update. The intended updates appear to be Eq.(12)/(13) for GCLS and Eq.(18) for SPDM. As printed, Algorithm 1 and Figure 2 do not specify a unique algorithm, so the benchmark results cannot be reproduced from the paper alone. Please correct the equation references in the pseudocode and flowchart and make the branch conditions consistent with Eqs. (12)-(14).
  2. [§3.1 and Table 2] The dominant-group construction is incompletely specified. Section 3.1 describes a 'roulette domain selection mechanism' that first selects X_r and then selects nearby individuals by Euclidean distance, but the roulette probabilities, the distance criterion, and the group size S are not defined. S does not appear in Table 2. Since S controls the covariance estimate underlying both GCLS and SPDM, this is not a cosmetic omission: the method is not fully specified unless S and the selection procedure are given. Please provide the exact construction and the value(s) used in the experiments.
  3. [§3.3 vs Algorithm 1/Figure 2] The stagnation threshold is inconsistent. Section 3.3 states that SPDM is triggered when nVOL<0.01 and Count>2D, while Algorithm 1 and Figure 2 use nVOL<0.1. This is a ten-fold difference in the activation criterion, which changes how often stagnant individuals are updated and therefore affects all reported results. Please unify the threshold, state it in Table 2, and ideally include a sensitivity analysis over reasonable threshold values.
  4. [Table 2 and §4 experimental setup] The population size NP is never reported for MRIME-CD or any of the nine competitors, even though maxFEs, dimension, and run counts are given. Metaheuristic rankings are often sensitive to population size; the absence of NP prevents exact replication and leaves open the possibility that some of the observed gains depend on a favorable population sizing. Please report NP for every algorithm and show that the main conclusions are stable across a range of NP values. The same table should also state the default values for w, S, and the two stagnation thresholds. The authors' own conclusion that 'the parameter sensitivity of MRIME-CD can be further investigated' is not a substitute for this analysis.
minor comments (6)
  1. [Introduction, reference [15]] The text says 'RIME algorithm [15]' and credits Su et al., but reference [15] is Alpha Evolution by Gao and Zhang. The original RIME paper is not cited. This should be corrected because the entire comparison depends on the baseline RIME implementation.
  2. [Various sections] There are many typos and inconsistent abbreviations, e.g., 'MRIMR-CD', 'MRIMME-CD', 'MRIMR- CD', 'MRIME-CD' vs 'MRIMR-CD' in the same sentence. The manuscript needs a careful proofreading pass.
  3. [Table 6 caption] Table 6 has the caption 'Description of MRIME-CD variants', which duplicates the caption of Table 5. The table actually presents Friedman test results. Please renumber and re-caption.
  4. [Section 5, Table 16] The text says the engineering experiments used 30 independent runs, while Table 2 states 51 runs for the benchmark experiments. If the engineering results use a different number of runs, that should be stated explicitly in Section 5.
  5. [Section 3.1, Eqs. (13)-(14)] The typesetting of Eq. (13) and Eq. (14) is garbled, with the branch conditions not clearly aligned to the two cases. Since these equations are central to GCLS and ABS, please reformat them carefully.
  6. [Table 7 header] The last column header reads 'D=20D' and should be 'D=20'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: MRIME-CD's central claim is tested against external CEC benchmarks and external algorithms, and the three proposed mechanisms are defined by explicit equations independent of the measured results.

full rationale

The paper's central claim is that the proposed MRIME-CD improves upon basic RIME. This is supported by benchmark experiments on the independent CEC2017 and CEC2022 test suites and by comparisons with nine external algorithms. The three proposed mechanisms (GCLS, ABS, SPDM) are each given explicit mathematical definitions: Eq. (9)-(13) define the Gaussian-based covariance learning strategy, Eq. (14) defines the average bootstrapping strategy, and Eq. (15)-(18) define the stochastic covariance learning-based population diversity mechanism. None of these equations is defined in terms of the final benchmark rankings or the paper's concluding superiority claim. The algorithm's parameters (w=5, the stagnation thresholds, the dominant-group size) are hand-set or stated with reference to the original RIME paper, but they are not fitted to the CEC functions in a way that would make the benchmark outcomes a tautology. There is no self-citation chain carrying the argument: the paper cites ordinary prior art for RIME and comparator algorithms, and does not invoke a uniqueness theorem or an ansatz from the authors' own prior work as the reason its choices are forced. The observed internal inconsistencies in Algorithm 1 (e.g., referencing Eq. (11) or Eq. (16) for position updates when those equations define covariance and volume, respectively, and the 0.01 vs 0.1 threshold discrepancy) are serious reproducibility defects, but they are not circularity: they make the exact implemented algorithm ambiguous, yet they do not make the claimed result equivalent to an input or to a fitted constant. Similarly, the omission of population size NP in the experimental setup undermines replicability but does not constitute circular reasoning. Therefore, no load-bearing circular step is present, and the circularity score is 0.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The paper does not introduce new physical entities or dimensions. Its load-bearing assumptions are the accuracy of the base RIME model, the representativeness of the CEC suites, the well-posedness of the estimated covariance, and the validity of the rank-based statistical tests. The free parameters are all hand-set or unstated, most notably the population size NP, which weakens reproducibility.

free parameters (5)
  • w = 5
    Controls the exploration schedule in Eq. (6), inherited from RIME and set to 5 without sensitivity analysis.
  • nVOL threshold = 0.01 (text) / 0.1 (Algorithm 1)
    Stagnation trigger in SPDM; values differ between Section 3.3 and Algorithm 1, and no sensitivity study is provided.
  • Count threshold = 2*D
    Second SPDM stagnation condition; chosen ad hoc with no analysis of how it scales with dimension.
  • Dominant group size S and roulette selection parameters = not specified
    GCLS depends on selecting a dominant population via an 'adaptive distance balance mechanism'; the group size and distance criteria are never quantified.
  • Population size NP = not reported
    The most consequential unstated parameter: Table 2 lists maxFEs, dimensions, and runs but no NP; rankings across algorithms could depend on it.
assumptions (4)
  • domain assumption The RIME algorithm as referenced [15] behaves as the base described in Eqs. (1)-(8).
    The improvements are grafted onto RIME; if the base model is inaccurate, the ablation and comparisons are not validated against the correct baseline. Entered in Section 2.
  • domain assumption CEC2017 and CEC2022 benchmark functions are representative of hard numerical optimization problems.
    The central claim of superiority is made on these synthetic suites; their transferability to real problems is asserted but only tested on a small set of engineering cases with no best-known-baseline context. Entered in Section 4.1.
  • domain assumption The Gaussian covariance computed from the dominant population remains invertible and useful in all tested dimensions, including D=100.
    GCLS samples from Gaussian(X_mean, C); in high dimensions with a small dominant group, C can be singular or ill-conditioned. No regularization or fallback is described. Entered in Section 3.1, Eq. (11)-(12).
  • standard math Friedman, Wilcoxon, and Kruskal-Wallis tests are applied under assumptions that hold for 51 independent runs across functions.
    The statistical claims of significant differences rest on these tests; tied ranks, effect sizes, and correction for multiple comparisons are not discussed. Entered in Section 4.2.

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Pith. "Pith review of A modified RIME algorithm with covariance learning and diversity enhancement for numerical optimization." pith.science (2026). https://pith.science/paper/OQ5EYJFC

@misc{pith2026250909529,
  author       = {Pith},
  title        = {Pith review of: A modified RIME algorithm with covariance learning and diversity enhancement for numerical optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OQ5EYJFC}},
  note         = {Machine review of arXiv:2509.09529}
}
read the original abstract

Metaheuristics are widely applied for their ability to provide more efficient solutions. The RIME algorithm is a recently proposed physical-based metaheuristic algorithm with certain advantages. However, it suffers from rapid loss of population diversity during optimization and is prone to fall into local optima, leading to unbalanced exploitation and exploration. To address the shortcomings of RIME, this paper proposes a modified RIME with covariance learning and diversity enhancement (MRIME-CD). The algorithm applies three strategies to improve the optimization capability. First, a covariance learning strategy is introduced in the soft-rime search stage to increase the population diversity and balance the over-exploitation ability of RIME through the bootstrapping effect of dominant populations. Second, in order to moderate the tendency of RIME population to approach the optimal individual in the early search stage, an average bootstrapping strategy is introduced into the hard-rime puncture mechanism, which guides the population search through the weighted position of the dominant populations, thus enhancing the global search ability of RIME in the early stage. Finally, a new stagnation indicator is proposed, and a stochastic covariance learning strategy is used to update the stagnant individuals in the population when the algorithm gets stagnant, thus enhancing the ability to jump out of the local optimal solution. The proposed MRIME-CD algorithm is subjected to a series of validations on the CEC2017 test set, the CEC2022 test set, and the experimental results are analyzed using the Friedman test, the Wilcoxon rank sum test, and the Kruskal Wallis test. The results show that MRIME-CD can effectively improve the performance of basic RIME and has obvious superiorities in terms of solution accuracy, convergence speed and stability.

Figures

Figures reproduced from arXiv: 2509.09529 by the authors.

Figure 1
Figure 1. A complete outline of this work. 2. An overview of RIME algorithm This section will provide a detailed explanation of the basic RIME algorithm. 2.1. Population initialization In RIME, each rime ice agent represents a proposed solution to a problem. Mathematically, each population member is a vector Xi . These vectors together form the population matrix of the RIME algorithm X . Like other metaheuristic algorithms, t… view at source ↗
Figure 2
Figure 2. The flowchart of the proposed MRIME-CD algorithm Complexity analysis is a measure of the system as a whole and evaluates the efficiency of the algorithm. We set the number of populations as NP , the maximum number of iterations as T , and the problems number of variables as D . The complexity of the basic RIME is O T NP D ( ) × × . As for MRIME-CD, at each updating, each rime particle randomly selects one from GCLS … view at source ↗
Figure 4
Figure 4. Kruskal Wallis ranking of MRIME-CD and other variants 4.3. Experimental case 1: CEC2017 test function analysis In this subsection, the performance of the proposed MRIME-CD is further validated using the four dimensional functions of the CEC2017 test set. Apart from the basic RIME, two basic algorithms EO [46], SAO [44], three RIME variants ACGRIME [59], IRIME [60], TERIME [61], and three advance improved algorithms … view at source ↗
Figures from the paper (5 more)
Figure 5
Figure 5. Figure 5: Ranking of MRIME-CD and other competitors based on mean values According to [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Convergence curves of MRIME-CD and other competitors based on CEC2017 4.3.3. Analysis of statistical results In order to eliminate the randomness and chance introduced by the experiment, the results are further analyzed in this section using statistical tests based on …
Figure 8
Figure 8. Figure 8: The visualization of Friedman test results of MRIME-CD and other competitors based on CEC2017. 4.4. Experimental case 2: CEC2022 test function analysis In this section, we further validate the performance of MRIME-CD on the CEC2022 test set to illustrate the broad adap…
Figure 10
Figure 10. Figure 10: Convergence curves of MRIME-CD and other competitors based on CEC2022 4.4.3. Analysis of statistical results The Kruskal Wallis test was used to analyze the experimental results of MRIMR-CD and competitors on the CEC2022 test set. The different dimensional Kruskal Wal…
Figure 12
Figure 12. Figure 12: The visualization of Kruskal Wallis test results of MRIME-CD and other competitors based on CEC2022 [PITH_FULL_IMAGE:figures/full_fig_p019_12.png]

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Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.