Pith. sign in

REVIEW 3 major objections 4 minor 52 references

Robustness and Invariance of Hybrid Metaheuristics under Objective Function Transformations

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Differential-evolution hybrids keep their accuracy and rankings when benchmark problems are translated, scaled, or rotated.

desk verdict The invariance study rests on tables with arithmetically impossible statistics and duplicated rows, so the central claim is unsupported as printed. read the letter →

arxiv 2509.05445 v1 pith:CKGV622T submitted 2025-09-05 cs.NE

Grzegorz Sroka , S{l}awomir T. Wierzchoń This is my paper · ORCID
classification cs.NE
keywords hybridmetaheuristicsdifferentialevolutioninvarianceanalysisobjectivefunctiontransformationsCEC-2017benchmarkBayesiandominanceplug-and-playhybridizationparticleswarmoptimization
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 a lightweight, plug-and-play hybridization operator—one that predicts a target objective value from the current population and replaces the weakest members with the corresponding candidate solutions—can be added to nineteen population-based metaheuristics without changing their internals. Benchmarking on the CEC-2017 suite under translation, scaling, rotation, and constant output shift, the authors find that differential-evolution-based hybrids (hIMODE, hSHADE, hDMSSA) preserve accuracy, low variance, and top rankings across all four transformations, whereas PSO- and HHO-based hybrids degrade on non-separable or distorted landscapes. This matters because real-world optimization problems often present shifted, scaled, or rotated objective functions; an algorithm whose performance is invariant to such deformations can be used without re-tuning. The additive-shift transformation is reported to be performance-neutral, confirming that the tested hybrids do not depend on absolute objective values.

What carries the argument

The carrying mechanism is the population-based operator introduced by the paper as a plug-and-play hybridization module: it reads only current objective function values, predicts a target quality using inverse regression (calibration), and replaces the weakest 10% of the population with predicted candidate solutions while leaving the base algorithm's mutation, crossover, and update logic untouched. Its work is to intensify exploitation without disturbing the base search architecture. The paper pairs this operator with a benchmark protocol—CEC-2017 functions, four fixed transformation types, four dimensionalities, 30 independent runs per function, and Wilcoxon, Friedman, Nemenyi, Bayesian, bo

What would settle it

Re-run the transformed benchmarks and recover raw samples. In Table 2, hMPA_f(x+8) at dim=10 is reported with Mean 2.3E+10, median 2.9E+04, and std 1.3E+01—a combination that cannot arise from a sample of non-negative objective values. In Table 4, several rotated rows (hSHADE_f(xM), hIMODE_f(xM), hHGS_f(xM), hSMA_f(xM), hHHO_f(xM)) match the unrotated row for the same algorithm in the same table across dimensions; independent re-runs of a genuine rotation would not reproduce identical summary statistics unless the rotation matrix were the identity.

Watch

Extended reading notes

Core claim

The paper's central claim is that the tested plug-and-play operator confers structural robustness when grafted onto differential-evolution-based algorithms. The operator examines the current population, estimates a target objective value from the fitness distribution, solves a calibration/inverse-regression problem to produce a candidate feature vector, and replaces the g worst-performing individuals with those predicted candidates. Under f(x+8), f(5x), f(xM), and f(x)+6 on 29 CEC-2017 functions at dimensions 10, 30, 50, and 100, the hybrid variants hIMODE, hSHADE, and hDMSSA retain low medians, tight spread, high Bayesian win probabilities, and top critical-difference ranks. In contrast, va

Load-bearing premise

The transformed-benchmark results in Tables 2–5 were genuinely measured and reported accurately, because the invariance conclusions rest entirely on those runs; if they were not, the claims lose their evidentiary support.

Editorial extensions

If this is right

  • DE-based hybrids hIMODE, hSHADE, and hDMSSA can be treated as near drop-in solvers for black-box problems where preprocessing or normalization shifts, scales, or rotates the objective landscape, without retuning.
  • PSO- and HHO-based variants should not be the default choice for non-separable or distorted problems, since their rankings and variance degrade under transformation.
  • Additive shifts of the objective function should not change algorithm rankings, convergence speed, or dominance structure for methods that rely on relative rather than absolute function values.
  • The plug-and-play operator can be attached to many population-based algorithms, but its benefit is uneven: it is most pronounced for adaptive, differential-evolution-based methods.
  • Despite large rank gaps to weaker methods, the top DE hybrids are often not statistically distinguishable from one another, so selecting among hIMODE, hSHADE, and hDMSSA should use secondary criteria such as implementation cost or constraint compatibility.

Reading between the lines

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

  • Editorial extension: the paper tests one magnitude per transformation (a=8, α=5, c=6, and a single orthonormal rotation); a natural next step is to sweep transformation magnitudes to map where the claimed invariance breaks.
  • Editorial extension: the results suggest that invariance is governed by whether an algorithm's variation operators are relative and coordinate-free, which predicts that customizing the plug-in to preserve those properties would extend robustness to non-DE bases—a claim the paper does not directly test.
  • Editorial extension: with a fixed 100,000 function-evaluation budget and population size 20, the rankings reported here may not transfer unchanged to other budgets or population sizes; treating the invariance ranking as universal would over-read the experiments.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper evaluates a plug-and-play hybridization operator (ref. [38]) applied to 19 population-based metaheuristics on the CEC-2017 suite, under four objective/decision-space transformations: translation f(x+8), scaling f(5x), rotation f(xM), and additive shift f(x)+6, across dimensions 10, 30, 50, and 100. The authors report summary statistics, Wilcoxon and Friedman tests, CD diagrams, Bayesian dominance matrices, boxplots, and convergence profiles, and conclude that differential-evolution-based hybrids (hIMODE, hSHADE, hDMSSA) are robust and invariant under these deformations, while PSO- and HHO-based variants degrade. The central invariance claims rest on the empirical measurements in Tables 2–5 and their associated analyses.

Significance. If the reported measurements were trustworthy, the paper would provide a useful, broad empirical comparison of a lightweight hybridization operator across many algorithms and transformation types, and the claim that DE-based hybrids retain performance under translation, scaling, rotation, and additive shifts would be a practically relevant, falsifiable statement. However, the paper supplies no code or raw data, and the printed statistics contain internal inconsistencies that invalidate the measurement basis. The central conclusion is therefore unsupported by the evidence as presented.

major comments (3)
  1. [Table 2, §9.1] Several entries in Table 2 are arithmetically impossible for 30 independent runs. For example, hMPA_f(x+8) at dim=10 reports Mean=2.3E+10, Med=2.9E+04, Std=1.3E+01. Since at least 15 of 30 runs must be at or below the median 2.9E+04, their total contribution is at most 15×2.9E+04 ≈ 4.4E+05, while the total sum implied by the mean is 30×2.3E+10 = 6.9E+11. The remaining 15 runs must therefore average ≈4.6E+10, forcing a sample standard deviation of at least ~1.6E+10, not 13. The same impossible pattern appears for hHGS_f(x+8), hSMA_f(x+8), hAROA_f(x+8), and hDMSSA_f(x+8). The invariance conclusions drawn from Table 2 are therefore not supported by valid measurements.
  2. [Table 4, §9.5] The rotation rows for several algorithms are numerically identical to the baseline rows. At dim=10, hIMODE_f(xM) and hIMODE have identical Mean, Med, Std, Sum rank, Mean rank, +/-, and p-value (all printed digits), and hHHO_f(xM)/hHHO and hSMA_f(xM)/hSMA match exactly as well; hSHADE_f(xM)/hSHADE match in all statistics except a one-digit difference in Sum rank (96 vs 95). Independent 30-run executions would not agree to every digit, including Wilcoxon win/loss counts and p-values, even for a perfectly invariant algorithm, especially because uniform initialization on a hypercube is not rotation-invariant. These rotation rows cannot be treated as new measurements, and the related invariance claims for hSHADE, hIMODE, hHHO, and hSMA are unsupported.
  3. [§9.6 and Table 5] The additive-shift analysis is internally contradictory. §9.6 reports Friedman p-values of 0.152, 0.142, 0.118, and 0.109 for f(x)+6, while Table 5 lists Friedman p-values 5.1E-82, 9.7E-78, 5.4E-78, and 1.0E-78 for the same four dimensions; these differ by about 76 orders of magnitude. The narrative also claims that hSPSO2011's mean 'drops' from 1.6E+04 to 8.2E+03 under an additive +6 shift, which is impossible for a pure objective-function shift, and claims that hIMODE in dim=100 shifts 'from 0.8 (baseline) to 3.2 ... exactly matches the added constant of +6', which is arithmetically false (Table 5 shows 2.2E+00 vs -8.9E-01). These inconsistencies undermine the claim in §10 that 'no anomalies were identified' and remove the empirical basis for the additive-shift invariance conclusion.
minor comments (4)
  1. [§6.1] The definition of Mean as 'the average final objective function value (calculated as the mean of the means obtained across 30 runs for each function)' is confusing: Table 1 appears to report one mean per algorithm-function-dimension over 30 runs, not a mean of means. Please clarify the reporting pipeline.
  2. [Abstract and §9.1/§9.6] The additive-shift magnitude is not specified in the abstract, while §9.1 uses a=8 for translation and §9.6 uses c=6 for the vertical shift. Define c explicitly and use consistent notation for f(x+a), f(αx), f(xM), and f(x)+c.
  3. [§9.6] The text states that for hSPSO2011 in dim=10 the mean 'drops from 1.6×10^4 to 8.2×10^3' under f(x)+6. Apart from being arithmetically incompatible with an additive shift, this contradicts Table 5, which lists hSPSO2011_f(x)+6 at 8.2E+03 and hSPSO2011 at 1.6E+04. If the shifted runs are separate, the difference may be stochastic, but the characterization as a drop under +6 is misleading.
  4. [Data availability] The paper states that data are 'available for academic purposes upon reasonable request.' Given the anomalies above, the raw per-run results and code should be made publicly available so the invariance claims can be independently verified.

Circularity Check

1 steps flagged · score 6.0 of 10

Rotation-invariance claim for hSHADE/hIMODE is forced by Table 4 rows numerically identical to baseline rows; other claims are externally benchmarked but undermined by data inconsistencies.

  1. self definitional [Table 4 / §9.5 (rotated variants), rows hSHADE_f(xM), hIMODE_f(xM), hHHO_f(xM), hSMA_f(xM)]
    "Table 4 (dim=10): 'hSHADE_f(xM) -6.1E-01 1.4E+00 4.7E+01 96 3.3 378/4 1.8E-01' vs 'hSHADE -6.1E-01 1.4E+00 4.7E+01 95 3.3 378/4 1.8E-01'; hIMODE_f(xM) and hIMODE dim=10 identical; hHHO and hSMA dim=10 identical; hSHADE dim=30 rows identical."

    The paper's rotation-invariance conclusion for the headline DE hybrids (hSHADE, hIMODE) is drawn from Table 4, but the rotated-condition rows equal the baseline rows in Mean, Med, Std, +/-, and p-value (e.g., hSHADE dim=10: both -6.1E-01 / 1.4E+00 / 4.7E+01, 378/4, 1.8E-01; hIMODE dim=10 identical). With 30 stochastic runs, independent measurements would not match digit-for-digit. Thus the 'rotated' statistics are the baseline statistics by construction, and the claimed invariance is a restatement of the input rather than a measured result.

full rationale

Most of the paper is an empirical benchmark on the external CEC-2017 suite: the hybridization operator of [38] (a self-citation, since Sroka is an author) is applied to 19 algorithms, and no fitted parameter is converted into a prediction; the central invariance claims are supposedly supported by Tables 2–5. That external basis, however, is broken in a way that is circular for the rotation sub-claim: Table 4 contains rotated-condition rows that are numerically identical to the baseline rows for hSHADE, hIMODE, hHHO and hSMA (dim=10; hSHADE also dim=30), so the conclusion that these algorithms are rotation-invariant reduces to the identity of the input rows. Additional data-integrity problems are not circular but are severe: Table 2 reports impossible summary statistics (e.g., hMPA_f(x+8) dim=10 Mean=2.3E+10, Med=2.9E+04, Std=1.3E+01), and §9.6's Friedman p-values (0.152, 0.142, 0.118, 0.109) contradict Table 5's listed p-values (5.1E-82, 9.7E-78, 5.4E-78, 1.0E-78), undermining the claim in §10 that 'no anomalies were identified'. The self-citation of [38] is not itself load-bearing because the operator's prior publication is external evidence; the score is raised to 6 by the by-construction rotation rows, not by self-citation alone.

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

The paper introduces no new theoretical entities. Its free parameters are experimental constants (ROPE=10, population 20, replacement rate 10%, transformation constants) that are hand-set rather than fitted to data. The central claim rests on the domain assumptions that CEC-2017 is representative, that recommended algorithm settings (with a uniform population override) are fair, and that the transformed runs were genuinely executed. The last assumption is directly contradicted by the printed statistics.

free parameters (4)
  • ROPE threshold = 10
    Hand-set in 8.2 for Bayesian practical equivalence; changes the classification of wins versus draws and affects the reported dominance probabilities.
  • population size = 20
    Fixed in 5 for all algorithms and dimensions to ensure uniform settings; this handicaps algorithms that normally use larger populations, e.g., CMA-ES, and biases the comparison.
  • replacement rate g = 10% of agents
    Fixed in 5, taken from the authors' prior paper [38], not tuned or justified for each base algorithm.
  • transformation constants a, alpha, shift = a=8, alpha=5, +6
    Ad hoc choices in 9.1, 9.3, and 9.6 that define the tested deformations; the results are specific to these magnitudes and no sensitivity analysis is given.
assumptions (4)
  • domain assumption CEC-2017 benchmark functions are a valid proxy for real-world optimization problems
    Invoked in 3 to justify the benchmark choice and used to support the practical-transfer claims in 10.1.
  • domain assumption Algorithms were run with parameter settings recommended in their original papers
    Stated in 5; however, the common population size of 20 is an imposed deviation from recommended settings for several algorithms, which may bias the comparisons.
  • domain assumption The hybridization operator from [38] is correctly implemented and applied as described
    The paper does not re-derive or re-implement the operator's internals; it relies on the prior paper's description and presumes correct integration into each base algorithm.
  • standard math The Wilcoxon signed-rank test treats per-function medians as paired data and ignores within-function run-to-run variance
    Standard practice in metaheuristic comparisons (6.1, 8.1), but it does not account for the distribution width within each of the 30 runs.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Robustness and Invariance of Hybrid Metaheuristics under Objective Function Transformations." pith.science (2026). https://pith.science/paper/CKGV622T

@misc{pith2026250905445,
  author       = {Pith},
  title        = {Pith review of: Robustness and Invariance of Hybrid Metaheuristics under Objective Function Transformations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CKGV622T}},
  note         = {Machine review of arXiv:2509.05445}
}
read the original abstract

This paper evaluates the robustness and structural invariance of hybrid population-based metaheuristics under various objective space transformations. A lightweight plug-and-play hybridization operator is applied to nineteen state-of-the-art algorithms-including differential evolution (DE), particle swarm optimization (PSO), and recent bio-inspired methods-without modifying their internal logic. Benchmarking on the CEC-2017 suite across four dimensions (10, 30, 50, 100) is performed under five transformation types: baseline, translation, scaling, rotation, and constant shift. Statistical comparisons based on Wilcoxon and Friedman tests, Bayesian dominance analysis, and convergence trajectory profiling consistently show that differential-based hybrids (e.g., hIMODE, hSHADE, hDMSSA) maintain high accuracy, stability, and invariance under all tested deformations. In contrast, classical algorithms-especially PSO- and HHO-based variants-exhibit significant performance degradation under non-separable or distorted landscapes. The findings confirm the superiority of adaptive, structurally resilient hybrids for real-world optimization tasks subject to domain-specific transformations.

Figures

Figures reproduced from arXiv: 2509.05445 by the authors.

Figure 6
Figure 6. Boxplots of final results for 10 algorithms and their 9 hybrids on original CEC-2017 functions across 4 dims. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 8
Figure 8. Critical difference diagrams for 10 algorithms and 9 hybrids on original CEC-2017 functions across 4 dims. [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 10
Figure 10. Bayesian test results for 10 algorithms and their 9 hybrids on original CEC-2017 functions across 4 dims. For the lowest dimensionality dim = 10 (Fig.10), a clear dominance of the group of hybrid algo￾rithms was observed: hIMODE, hSHADE, hMPA, hSMA, and hDMSSA consistently outperformed the remaining methods, achieving performance values around ∼ 0.03 against most competitors. Their superiority was particularly evide… view at source ↗
Figures from the paper (17 more)
Figure 16
Figure 16. Figure 16: Convergence trajectories of metaheuristic algorithms on a representative CEC-2017 benchmark function. Convergence Characteristics and Analysis. In the case of f1 (Fig.16), a very rapid convergence rate is observed for most hybrid algorithms, particularly hSHADE, hIMOD…
Figure 22
Figure 22. Figure 22: Boxplots of final objective values for 9 hybrid algorithms evaluated on original CEC-2017 functions and their transformed variants [PITH_FULL_IMAGE:figures/full_fig_p018_22.png]
Figure 24
Figure 24. Figure 24: CD diagrams for 9 hybrid algorithms tested on original CEC-2017 functions and their translated variants [PITH_FULL_IMAGE:figures/full_fig_p019_24.png]
Figure 26
Figure 26. Figure 26: Bayesian heatmaps for 9 hybrid algorithms evaluated on original CEC-2017 functions and their translated variants across 4 dims. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_26.png]
Figure 32
Figure 32. Figure 32: Convergence trajectories of metaheuristic algorithms on a representative CEC-2017 benchmark function. 9.2 Conclusions from the Analysis of Objective Function Translation. Following the translation transformation, many algorithms exhibit a drastic decline in optimizati…
Figure 38
Figure 38. Figure 38: Boxplots of final objective values for 9 hybrid algorithms evaluated on original CEC-2017 functions and their transformed variants [PITH_FULL_IMAGE:figures/full_fig_p025_38.png]
Figure 40
Figure 40. Figure 40: CD diagrams for 9 hybrid algorithms tested on original CEC-2017 functions and their scaled variants [PITH_FULL_IMAGE:figures/full_fig_p025_40.png]
Figure 42
Figure 42. Figure 42: Bayesian heatmaps for 9 hybrid algorithms evaluated on original CEC-2017 functions and their scaled variants across 4 dims. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_42.png]
Figure 48
Figure 48. Figure 48: Convergence trajectories of metaheuristic algorithms on a representative CEC-2017 benchmark function. 9.4 Scaling of the Objective Function: Analysis of f(5x) This subsection analyzes the impact of scaling the decision space by a factor of 5 on the performance of opti…
Figure 54
Figure 54. Figure 54: Boxplots of final objective values for 9 hybrid algorithms evaluated on original CEC-2017 functions and their transformed variants [PITH_FULL_IMAGE:figures/full_fig_p032_54.png]
Figure 56
Figure 56. Figure 56: CD diagrams for 9 hybrid algorithms tested on original CEC-2017 functions and their rotated variants [PITH_FULL_IMAGE:figures/full_fig_p033_56.png]
Figure 58
Figure 58. Figure 58: Bayesian heatmaps for 9 hybrid algorithms evaluated on original CEC-2017 functions and their rotated [PITH_FULL_IMAGE:figures/full_fig_p033_58.png]
Figure 64
Figure 64. Figure 64: Convergence trajectories of metaheuristic algorithms on a representative CEC-2017 benchmark function. Conclusions from the Analysis of Results after Rotational Transformation of the Objective Function The rotational transformation of the decision space, in the form f(…
Figure 68
Figure 68. Figure 68: Boxplots of final objective values for 9 hybrid algorithms evaluated on original CEC-2017 functions and their shifted-output variants [PITH_FULL_IMAGE:figures/full_fig_p038_68.png]
Figure 70
Figure 70. Figure 70: CD diagrams for 9 hybrid algorithms tested on original CEC-2017 functions and their shifted-output [PITH_FULL_IMAGE:figures/full_fig_p039_70.png]
Figure 72
Figure 72. Figure 72: Bayesian comparison results for 9 hybrid algorithms on original CEC-2017 functions and their shifted [PITH_FULL_IMAGE:figures/full_fig_p040_72.png]
Figure 78
Figure 78. Figure 78: Convergence trajectories of metaheuristic algorithms on a representative CEC-2017 benchmark function. [PITH_FULL_IMAGE:figures/full_fig_p041_78.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

52 extracted references · 43 canonical work pages

  1. [38]

    Oszust, G

    M. Oszust, G. Sroka, and K. Cymerys,A hybridization approach with predicted solution candidates for improving population-based optimization algorithms, Information Sciences, vol. 574, pp. 133-161, (2021),https://doi.org/10.1016/j.ins.2021.04.082

    work page doi:10.1016/j.ins.2021.04.082 2021

  2. [1]

    Abualigah and et al.Hybrid Harris hawks optimization with differential evolu- tion for data clustering, Metaheuristics in machine learning: theory and applications

    L. Abualigah and et al.Hybrid Harris hawks optimization with differential evolu- tion for data clustering, Metaheuristics in machine learning: theory and applications. Cham: SpringerInternationalPublishing, pp.267-299, (2021),https://doi.org/10.1007/ 978-3-030-70542-8_12

    work page 2021

  3. [2]

    O. Alsayyed and et al.Giant armadillo optimization: A new bio-inspired metaheuristic algorithm for solving optimization problems, Biomimetics, 8 (8), 619, (2023),https:// doi.org/10.3390/biomimetics8080619

    work page doi:10.3390/biomimetics8080619 2023

  4. [3]

    Aranha and et al.Metaphor-based metaheuristics, a call for action: the ele- phant in the room, Swarm Intelligence, 16(1), 1-6, (2022),https://doi.org/10.1007/ s11721-021-00202-9

    C. Aranha and et al.Metaphor-based metaheuristics, a call for action: the ele- phant in the room, Swarm Intelligence, 16(1), 1-6, (2022),https://doi.org/10.1007/ s11721-021-00202-9

    work page 2022

  5. [4]

    N. Awad, M. Ali, J. Liang, B. Qu and P. Suganthan,Problem Definitions and Evalua- tion Criteria for the CEC 2017 Special Session and Competition on Single Objective Real- Parameter Numerical Optimization, Technical Report, Nanyang Technological University: Singapore, (2016),https://github.com/P-N-Suganthan/CEC2017-BoundContrained

    work page 2017

  6. [5]

    Auger and N

    A. Auger and N. Hansen,A restart CMA evolution strategy with increasing population size, In 2005 IEEE Congress on Evolutionary Computation, Vol. 2, pp. 1769-1776, IEEE, (2005), https://doi.org/10.1109/CEC.2005.1554902

    work page arXiv 2005

  7. [6]

    A. Benavoli and et al.Time for a change: a tutorial for comparing multiple classifiers through Bayesian analysis, Journal of Machine Learning Research, 18 (77), 1-36, (2017), http://jmlr.org/papers/v18/16-305.html

    work page 2017

  8. [7]

    Brest and M

    J. Brest and M. Sepesy Maučec,Comparative Study of Modern Differential Evolution Algo- rithms: Perspectives on Mechanisms and Performance, Mathematics, 13(10), 1556, (2025), https://doi.org/10.3390/math13101556

    work page doi:10.3390/math13101556 2025

Show all 52 references
  1. [8]

    Clerc,Standard Particle Swarm Optimisation, (2012),https://hal.science/ hal-00764996v1

    M. Clerc,Standard Particle Swarm Optimisation, (2012),https://hal.science/ hal-00764996v1

    2012

  2. [9]

    J. Carrasco and et al.Recent trends in the use of statistical tests for comparing swarm and evolutionary computing algorithms: Practical guidelines and a critical review, Swarm and Evolutionary Computation, 54, 100665, (2020),https://arxiv.org/pdf/2002.09227

    2020 arXiv

  3. [10]

    Chen and et al.Improved slime mould algorithm hybridizing chaotic maps and differential evolution strategy for global optimization, IEEE Access 10, pp

    H. Chen and et al.Improved slime mould algorithm hybridizing chaotic maps and differential evolution strategy for global optimization, IEEE Access 10, pp. 66811-66830, (2022),https: //doi.org/10.1109/ACCESS.2022.3183627

    2022

  4. [11]

    L. Chen, C. Hao and Y. Ma,A multi-disturbance marine predator algorithm based on oppositional learning and compound mutation, Electronics, 11(24), 4087, (2022),https: //doi.org/10.3390/electronics11244087

    2022 doi

  5. [12]

    T. Chen, K. Tang, G. Chen and X. Yao,A large population size can be unhelpful in evolu- tionary algorithms, Theoretical Computer Science, 436, 54-70, (2012),https://doi.org/ 10.1016/j.tcs.2011.02.016 44

    2012 doi

  6. [13]

    C.A. Coello Coello and et al.Evolutionary multiobjective optimization: open research areas and some challenges lying ahead, Complex&Intelligent Systems 6, 221-236, (2020),https: //doi.org/10.1007/s40747-019-0113-4

    2020 doi

  7. [14]

    Cymerys and M

    K. Cymerys and M. Oszust,Attraction-repulsion optimization algorithm for global opti- mization problems, Swarm and Evolutionary Computation, 84, 101459, (2024),https: //doi.org/10.1016/j.swevo.2023.101459

    2024

  8. [15]

    J. Demšar,Statistical comparisons of classifiers over multiple data sets, Journal of Ma- chine learning research, 7, (Jan), 1-30, (2006),https://www.jmlr.org/papers/volume7/ demsar06a/demsar06a.pdf

    2006

  9. [16]

    Derrac, S

    J. Derrac, S. García, D. Molina and F. Herrera,A practical tutorial on the use of non- parametric statistical tests as a methodology for comparing evolutionary and swarm in- telligence algorithms, Swarm and Evolutionary Computation, 1 (1), 3-18, (2011),https: //doi.org/10.1016...

    2011 doi

  10. [17]

    Dhawale, V.K

    D. Dhawale, V.K. Kamboj and P. Anand,An improved Chaotic Harris Hawks Optimizer for solving numerical and engineering optimization problems, Engineering with Computers, 39(2), pp. 1183-1228, (2023),https://doi.org/10.1007/s00366-021-01487-4

    2023 doi

  11. [18]

    J. Duda,Biology-inspired joint distribution neurons based on Hierarchical Cor- relation Reconstruction allowing for multidirectional neural networks,arXiv preprint arXiv:2405.05097,(2024)

    2024 arXiv

  12. [19]

    Faramarzi, M

    A. Faramarzi, M. Heidarinejad, S. Mirjalili and A.H. Gandomi,Marine predators algo- rithm: A nature-inspired metaheuristic, Expert Systems with Applications, 152, 113377, (2020),https://doi.org/10.1016/j.eswa.2020.113377

    2020

  13. [20]

    Hassan and N

    A. Hassan and N. Pillay,An improved meta-genetic algorithm for hybridizing metaheuristics in: 2018 IEEE Congress on Evolutionary Computation (CEC), pp. 1-8, (2018),https: //doi.org/10.1109/CEC.2018.8477881

    2018

  14. [21]

    Hansen and A

    N. Hansen and A. Ostermeier,Completely derandomized self-adaptation in evolution strate- gies, Evolutionary Computation, vol. 9, no.2, pp.159-195,(2001),http://www.bionik. tu-berlin.de/user/niko/cmaartic.pdf

    2001

  15. [22]

    Hansen, S.D

    N. Hansen, S.D. Muller and P. Koumoutsakos,Reducing the time complexity of the de- randomized evolution strategy with covariance matrix adaptation (CMA-ES), Evolutionary Computation, vol. 11, no. 1, pp. 1-18,(2003),http://mitpress.mit.edu/journals/pdf/ evco_11_1_1_0.pdf

    2003

  16. [23]

    282–291, Berlin: Springer, (2004),http://www.bionik.tu-berlin.de/ user/niko/ppsn2004hansenkern.pdf

    N.HansenandS.Kern,Evaluating the CMA evolution strategy on multimodal test functions, In Proceedings of the 8th International Conference on Parallel Problem Solving from Nature (PPSN VIII), pp. 282–291, Berlin: Springer, (2004),http://www.bionik.tu-berlin.de/ user/niko/ppsn200...

    2004

  17. [25]

    D.S. Hochbaum,A polynomial time algorithm for rayleigh ratio on discrete variables: Re- placing spectral techniques for expander ratio, normalized cut, and cheeger constant, Oper- ations Research, 61(1), 184-198, (2013),http://dx.doi.org/10.1287/opre.1120.1126

    2013

  18. [26]

    Hong and et al.A variant of the united multi-operator evolutionary algorithms using sequential quadratic programming and improved SHADE-cnEpSin, Information Sciences, 622, pp

    L. Hong and et al.A variant of the united multi-operator evolutionary algorithms using sequential quadratic programming and improved SHADE-cnEpSin, Information Sciences, 622, pp. 652-681, (2023),https://doi.org/10.1016/j.ins.2022.11.131

    2023 doi

  19. [27]

    E.H. Houssein and et al.Hybrid Harris hawks optimization with cuckoo search for drug design and discovery in chemoinformatics, Scientific Reports 10(1), 14439, (2020),https: //doi.org/10.1038/s41598-020-71502-z 45

    2020 doi

  20. [28]

    D. Izci,An enhanced slime mould algorithm for function optimization, In 2021 3rd Interna- tional Congress on Human-Computer Interaction, Optimization and Rrobotic Aapplications (HORA), pp. 1-5, IEEE, (2021),https://doi.org/10.1109/HORA52670.2021.9461325

    2021

  21. [29]

    Kumagai and Y

    W. Kumagai and Y. Keiichiro,Particle swarm optimization with rotational invariance us- ing correlativity, 2018 IEEE International Conference on Systems, Man, and Cybernetics (SMC). IEEE, (2018),https://doi.org/10.1109/SMC.2018.00211

    2018

  22. [30]

    S. Kumar and et al.Chaotic marine predators algorithm for global optimization of real-world engineering problems, Knowledge-Based Systems, 261, 110192, (2023),https://doi.org/ 10.1016/j.knosys.2022.110192

    2023

  23. [31]

    S. Li, J. Li, J. Yi, H. Yu, S. Wang and S. Gao,Incorporation of improved differential evolution into hunger games search algorithm, In 2021 13th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC), pp. 39-43, IEEE, (2021), https://doi.org/10.1...

    2021

  24. [32]

    Li and et al.Slime mould algorithm: A new method for stochastic optimization, Future generationcomputersystems, 111, 300-323, (2020),https://doi.org/10.1016/j.future

    S. Li and et al.Slime mould algorithm: A new method for stochastic optimization, Future generationcomputersystems, 111, 300-323, (2020),https://doi.org/10.1016/j.future. 2020.03.055

    2020 doi

  25. [33]

    C. Lin, P. Wang, X. Zhao and H. Chen,Double mutational salp swarm algorithm: from op- timal performance design to analysis, Journal of Bionic Engineering, 20(1), 184-211, (2023), https://doi.org/10.1007/s42235-022-00262-5

    2023 doi

  26. [34]

    X. Luo, B. Du, P. Gui, D. Zhang and W. Hu,A Hunger Games Search algorithm with opposition-based learning for solving multimodal medical image registration, Neurocomput- ing, 540, 126204, (2023),https://doi.org/10.1016/j.neucom.2023.03.065

    2023 doi

  27. [35]

    Mazarei, et al.Online boxplot derived outlier detection, International journal of data sci- ence and analytics, 19(1), 83-97, (2025),https://doi.org/10.1007/s41060-024-00559-0

    Aa. Mazarei, et al.Online boxplot derived outlier detection, International journal of data sci- ence and analytics, 19(1), 83-97, (2025),https://doi.org/10.1007/s41060-024-00559-0

    2025 doi

  28. [36]

    Meng and Li

    X. Meng and Li. Hecheng,Heterogeneous pbest-guided comprehensive learning particle swarm optimization, Applied Soft Computing, 162, 111874, (2024),https://doi.org/10. 1016/j.asoc.2024.111874

    2024

  29. [37]

    Onay and S.B

    F.K. Onay and S.B. Aydemir,Chaotic hunger games search optimization algorithm for global optimization and engineering problems, Mathematics and Computers in Simulation, 192, pp.514-536, (2022),https://doi.org/10.1016/j.matcom.2021.09.014

    2022 doi

  30. [39]

    Pacheco-Del-Moral and C.A

    O. Pacheco-Del-Moral and C.A. Coello Coello,A SHADE-based algorithm for large scale global optimization, In International Conference on Parallel Problem Solving from Nature, Cham: SpringerInternationalPublishing, pp.650-663, (2020),https://doi.org/10.1007/ 978-3-030-58112-1_45

    2020

  31. [40]

    N.Panagantandetal.A novel hybrid marine predators-Nelder-Mead optimization algorithm for the optimal design of engineering problems, MaterialsTesting, 63(5), pp.453-457, (2021), https://doi.org/10.1515/mt-2020-0077

    2021 doi

  32. [41]

    C. Ren, Q. Xu, Z. Meng and J.S. Pan,Surrogate-assisted fully-informed particle swarm optimization for high-dimensional expensive optimization, Applied Soft Computing, 167, 112464, (2024),https://doi.org/10.1016/j.asoc.2024.112464

    2024

  33. [42]

    K.M. Sallam and et al.Improved multi-operator differential evolution algorithm for solving unconstrained problems, 2020 IEEE Congress on Evolutionary Computation (CEC), IEEE, pp.1-8, (2020),https://doi.org/10.1109/CEC48606.2020.9185577 46

    2020

  34. [43]

    Sallam and et al.IMODEII: An Improved IMODE algorithm based on the Reinforce- ment Learning, 2022 IEEE Congress on Evolutionary Computation (CEC)

    K.M. Sallam and et al.IMODEII: An Improved IMODE algorithm based on the Reinforce- ment Learning, 2022 IEEE Congress on Evolutionary Computation (CEC). IEEE, pp.1-8, (2022),https://doi.org/10.1109/CEC55065.2022.9870420

    2022

  35. [44]

    Satapathy, D

    S.M. Satapathy, D. Das, A. Chaki, H. Agarwal and V. Shah,A Hybrid Quantum Particle Swarm Optimization based on Differential Evolution Strategy for Healthcare Applications, In 2025 AI-Driven Smart Healthcare for Society 5.0, pp. 188-193, IEEE, (2025),https: //doi.org/10.1109/IE...

    2025

  36. [45]

    Sroka and M

    G. Sroka and M. Oszust,Approximation of the Constant in a Markov-Type Inequality on a Simplex Using Meta-Heuristics, Mathematics, 9(3), 264, (2021),https://doi.org/10. 3390/math9030264

    2021

  37. [46]

    org/10.1109/CEC.2013.6557555

    R.TanabeandF.Alex,Success-history based parameter adaptation for differential evolution, 2013 IEEE Congress on Evolutionary Computation, IEEE, pp.71-78, (2013),https://doi. org/10.1109/CEC.2013.6557555

    2013

  38. [47]

    Thangaraj, M

    R. Thangaraj, M. Pant, A. Abraham and P. Bouvry,Particle swarm optimization: Hy- bridization perspectives and experimental illustrations, Applied Mathematics and Compu- tation, 217 (12), pp.5208-5226, (2011),https://doi.org/10.1016/j.amc.2010.12.053

    2011 doi

  39. [48]

    Ye Tian and et al.Principled design of translation, scale, and rotation invariant variation operators for metaheuristics, Chinese Journal of Electronics 32.1, 111-129, (2023),https: //doi.org/10.23919/cje.2022.00.100

    2023 doi

  40. [49]

    IEEE, pp.27-33, (2019),https://doi.org/10.1109/ CEC.2019.8789912

    P.Xuandetal.Hybrid of PSO and CMA-ES for global optimization, 2019IEEECongresson Evolutionary Computation (CEC). IEEE, pp.27-33, (2019),https://doi.org/10.1109/ CEC.2019.8789912

    2019

  41. [50]

    Y. Yang and et al.Hunger games search: Visions, conception, implementation, deep anal- ysis, perspectives, and towards performance shifts, Expert Systems with Applications, 177, 114864, (2021),https://doi.org/10.1016/j.eswa.2021.114864

    2021

  42. [51]

    Yıldız, B.S

    A.R. Yıldız, B.S. Yıldız, S.M. Sait, S. Bureerat and N. Pholdee,A new hybrid Harris hawks-Nelder-Mead optimization algorithm for solving design and manufacturing problems, Materials Testing, 61(8), pp. 735-743, (2019),https://doi.org/10.3139/120.111378

    2019 doi

  43. [52]

    Z.H. Zhan, L. Shi, K.C. Tan and J. Zhang,A survey on evolutionary computation for complex continuous optimization, Artificial Intelligence Review, 55(1), 59-110, (2022), https://doi.org/10.1007/s10462-021-10042-y

    2022 doi

  44. [53]

    Zhang, Q

    X. Zhang, Q. Liu and X. Bai,Improved slime mould algorithm based on hybrid strategy op- timization of Cauchy mutation and simulated annealing, Plos One, 18(1), e0280512, (2023), https://doi.org/10.1371/journal.pone.0280512 47

    2023 doi

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.