{"id":"aa7022e1-7e93-440d-af1b-9e9eb2dadcac","arxiv_id":"2509.09529","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"MRIME-CD, a RIME variant with covariance learning, average bootstrapping, and stochastic covariance resets, reports top rankings on CEC2017 and CEC2022 benchmarks.","lead":"This paper modifies the RIME optimizer with three added mechanisms: Gaussian covariance learning, average bootstrapping, and a stagnation-triggered diversity reset. The authors report that the modified algorithm beats RIME and eight other optimizers on the CEC2017 and CEC2022 benchmark suites.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Algorithm 1 references the wrong equations for two of the three proposed mechanisms, so the reported MRIME-CD results cannot be tied to a uniquely specified method.","rationale":"The paper offers a plausible improvement to RIME and provides an ablation study suggesting each of the three mechanisms contributes. The benchmark results are extensive and include multiple statistical tests. However, the algorithm as written is not uniquely defined because the pseudocode and flowchart cite equations that perform different computations than the text. This is a direct threat to the central claim: if a reader cannot tell which update rule was actually executed, the reported superiority of MRIME-CD is not verifiable from the manuscript. The reader's identified assumption about NP is genuine—population size can affect metaheuristic rankings—but it is a parameter omission that could be fixed by reporting a number. The equation-reference mismatches are more fundamental because they affect the definition of the algorithm itself, not just its configuration. I therefore partially agree with the reader: both concerns are about reproducibility, but the algorithmic ambiguity should be resolved first. The appropriate verdict remains CONDITIONAL, contingent on correcting the pseudocode/flowchart, reporting NP, and ideally releasing code.","tokens_in":63385,"tokens_out":3502,"duration_ms":43947,"concrete_test":"Re-implement MRIME-CD in two versions from the paper: (A) strictly following Algorithm 1 and Figure 2 with the equations as cited (Eq.(11) for GCLS, Eq.(16) for SPDM, threshold 0.1), and (B) following the mathematical formulation in Section 3 (Eq.(13) for GCLS, Eq.(18) for SPDM, threshold 0.01). Run both on CEC2017 D=10 with 51 independent runs and 3000*D evaluations, then compare Friedman average rankings. If the rankings differ materially (e.g., MRIME-CD's rank changes by more than one position on any function), the published results correspond to an unspecified variant; if they are identical, the mismatches are typographical and the central claim survives.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that MRIME-CD improves on RIME, supported by extensive benchmark tables. However, the algorithm specification is internally inconsistent. In Algorithm 1, the GCLS branch says 'Compute the rime agent’s position using Eq.(11)', but Eq.(11) defines the covariance matrix C, not a position update; the actual Gaussian-sampling update is Eq.(12)/(13). Similarly, the SPDM branch says 'Compute the rime agent’s position using Eq.(16)', but Eq.(16) defines the population volume V_pop, not an update; the stochastic covariance learning update is Eq.(18). Additionally, the stagnation threshold is 0.01 in Section 3.3 but 0.1 in Algorithm 1 and Figure 2. These are not cosmetic: a reader implementing from the pseudocode would produce a different algorithm from one implementing the equations in Section 3. Since all comparative results were generated by some implementation that is not fully specified in the manuscript, the central claim is not reproducible from the paper alone. This is more load-bearing than the unstated population size NP: even if NP were reported, the algorithm would still be ambiguous. The missing NP is a real concern, but it is secondary to the inconsistency in the core algorithmic definition.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":63659,"tokens_out":5766,"duration_ms":72521,"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":[{"comment":"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).","section":"Algorithm 1 and §3.4"},{"comment":"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.","section":"§3.1 and Table 2"},{"comment":"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.","section":"§3.3 vs Algorithm 1/Figure 2"},{"comment":"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.","section":"Table 2 and §4 experimental setup"}],"minor_comments":[{"comment":"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.","section":"Introduction, reference [15]"},{"comment":"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.","section":"Various sections"},{"comment":"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.","section":"Table 6 caption"},{"comment":"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.","section":"Section 5, Table 16"},{"comment":"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.","section":"Section 3.1, Eqs. (13)-(14)"},{"comment":"The last column header reads 'D=20D' and should be 'D=20'.","section":"Table 7 header"}],"recommendation":"major_revision","confidential_remarks":"The empirical study is extensive and the ablation is useful, but the algorithmic specification must be corrected before this paper can be considered for publication. In particular, the pseudocode-to-equation mismatches and the missing NP/S values mean the reported results are not reproducible from the manuscript alone. If the authors can provide a precise pseudocode, all parameter values, and ideally a reference implementation, the paper may become publishable after revision. I also noticed the citation for the original RIME algorithm is incorrect, which suggests the references need a full check."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The core claim is plausible, but the paper is not reproducible as written. MRIME-CD combines three mechanisms – Gaussian-based covariance learning (GCLS), average bootstrapping (ABS), and a stochastic covariance-based diversity mechanism (SPDM) – on top of RIME. That specific combination is genuinely new, not present in ACGRIME, IRIME, or TERIME. The experimental work is extensive and above average for this subfield: 51 runs per function, four dimensions for CEC2017, two for CEC2022, a full ablation, three rank-based statistical tests, and ten engineering problems. The ablation is useful and shows each mechanism contributes; the quantitative tables support the qualitative claim that MRIME-CD improves on basic RIME.\n\nThe soft spots are real and load-bearing. The most serious is that Algorithm 1 and Figure 2 reference the wrong equations. The GCLS branch says \"compute the rime agent's position using Eq.(11)\", but Eq.(11) is the covariance matrix; the actual Gaussian-sampling update is Eq.(12)/(13). The SPDM branch says \"using Eq.(16)\", but Eq.(16) is the population volume; the stochastic covariance update is Eq.(18). The stagnation threshold is 0.01 in Section 3.3 but 0.1 in Algorithm 1. These are not cosmetic – a reader implementing from the pseudocode produces a different algorithm from the one described in the equations. Since all comparative results come from some implementation that the manuscript does not fully specify, the central claim cannot be verified from the paper alone.\n\nThe unstated population size NP is a second issue, as the reader notes. Metaheuristics are sensitive to population size, and Table 2 does not report it. But it is secondary: even with NP stated, the equation mismatches would still make the method ambiguous. The hand-set parameters (w=5, thresholds, dominant group size) also lack sensitivity analysis, which is a minor but legitimate concern.\n\nTo be fair, the paper acknowledges its own limitations, including the computational cost of covariance learning and the need for parallelization. That is honest. The CEC2022 results also show MRIME-CD is not first on every function, which the paper admits.\n\nIs this worth a serious referee? Yes, but with a clear request for major revision. The empirical scope is solid and the proposed mechanism is reasonable. The authors need to fix the pseudocode and flowchart, report NP, and ideally release code. If they do, the rankings become checkable; if they don't, the paper should not be accepted. I would send it to peer review, but I would not trust the numerical tables until the specification is fixed.","headline":"Plausible empirical claim, but the algorithm as written is ambiguous and the reported numbers can't be tied to a uniquely specified method.","tokens_in":64165,"tokens_out":2501,"would_cite":false,"duration_ms":31187,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68T20","90C59"],"pacs":[],"model":"deepseek-v4-flash","headline":"A covariance-learning RIME variant claims top rankings on CEC2017, CEC2022, and 8 of 10 engineering problems.","keywords":["RIME algorithm","MRIME-CD","covariance learning strategy","population diversity","metaheuristic optimization","CEC2017","CEC2022","engineering optimization problems"],"falsifier":"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.","tokens_in":63262,"feed_emoji":"🧊","tokens_out":10130,"duration_ms":91628,"temperature":0.7,"pith_summary":"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.","feed_headline":"Three tweaks lift RIME optimizer to top rank on most CEC benchmarks","feed_subtitle":"Covariance learning and diversity fixes put the ice-fog optimizer first on CEC2017 and 8 of 10 engineering problems.","key_machinery":"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","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Covariance learning boosts RIME optimizer's diversity and wins CEC tests","RIME optimizer upgraded with covariance learning, tops CEC benchmarks","Diversity-aware RIME variant outranks original on CEC2017 and 2022","Modified RIME with covariance learning beats base on most benchmarks","RIME get a diversity fix, ranking first on most CEC functions"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Covariance learning boosts RIME optimizer's diversity and wins CEC tests","RIME optimizer upgraded with covariance learning, tops CEC benchmarks","Diversity-aware RIME variant outranks original on CEC2017 and 2022","Modified RIME with covariance learning beats base on most benchmarks","RIME get a diversity fix, ranking first on most CEC functions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000193,"raw_usage":{"total_tokens":1243,"prompt_tokens":857,"completion_tokens":386,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":601,"completion_tokens_details":{"reasoning_tokens":303}},"tokens_in":601,"tokens_out":386,"duration_ms":5052,"temperature":1.0,"reasoning_tokens":303,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T18:54:14.681217+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}