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REVIEW 3 major objections 5 minor 91 references

A Fast and Efficient Stochastic Opposition-Based Learning for Differential Evolution in Numerical Optimization

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper claims that a linear-time diversity measure and multiple exponential crossover turn BetaCOBL into a faster, more separable-problem-friendly opposition-based learning module that stays competitive with ten alternatives.

desk verdict Solid engineering extension with a real complexity win and heavy empirical support; the math around Eq. 22 is mislabeled but the main claim survives. read the letter →

arxiv 1908.08011 v2 pith:WO34QCNS submitted 2019-08-09 cs.NE

Tae Jong Choi , Julian Togelius , Yun-Gyung Cheong This is my paper · ORCID
classification cs.NE
keywords opposition-basedlearningdifferentialevolutioniBetaCOBLlineartimediversitymeasuremultipleexponentialcrossovernumericaloptimizationCECbenchmark
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 tries to establish that an opposition-based learning (OBL) module for differential evolution can be made much cheaper and more useful without losing accuracy. It proposes iBetaCOBL, a reworking of the stochastic OBL variant BetaCOBL, and argues that swapping the expensive power-mean population-diversity statistic for a linear-time root-mean-square-of-variances statistic cuts the cost from $O(NP^2 \cdot D)$ to $O(NP \cdot D)$ while preserving convergence behavior. It also replaces the binomial crossover used to form partial opposite solutions with multiple exponential crossover, which keeps adjacent decision variables together and should help on inseparable problems. On 58 functions from the CEC 2013 and 2017 suites, the paper reports that iBetaCOBL ranks first among ten OBL variants and outperforms its predecessor with about three times less computational time.

What carries the argument

The load-bearing object is the linear-time diversity measure $D'_d(P_g)=\frac{1}{D}\sqrt{\sum_{k=1}^{D}\big((x^k_g)^2-(\overline{x^k_g})^2\big)}$, a root-mean-square of per-dimension variances that can be computed in one pass over the population; it replaces the power-mean pairwise-distance measure, which costs $O(NP^2 \cdot D)$, in the selection-switching scheme that decides whether to merge all original solutions or discard the worst half. The second mechanism is multiple exponential crossover, a semi-consecutive recombination that copies alternating blocks from the complete opposite solution and the original solution, with expected block lengths set by the crossover rate and a fixed component length $T=10$. The first mechanism supplies the speed-up, and the second addresses inseparability by preserving adjacent dependent variables.

What would settle it

Time iBetaCOBL and BetaCOBL on the same benchmark with population sizes 100, 200, and 400: if the runtime ratio does not track linear versus quadratic growth, the complexity claim is wrong; separately, on a population artificially collapsed to a tight cluster near the diversity threshold, record whether the two algorithms pick different selection operators.

Watch

Extended reading notes

Core claim

The central claim, stated as the authors would state it, is that the two perceived weaknesses of BetaCOBL can be fixed separately: diversity monitoring does not need pairwise distances, and partial opposition does not need to assume variables are independent. Replacing the power-mean diversity measure with a linear-time reformulation of mean pairwise distance keeps the selection-switching behavior intact while reducing the cost from quadratic to linear in population size, and replacing binomial crossover with multiple exponential crossover preserves blocks of strongly dependent adjacent variables. The supporting evidence is a comparison on the CEC 2013 and 2017 test suites at 30 and 50 dimensions using three differential evolution variants and ten OBL variants, with the paper reporting that iBetaCOBL is competitive with or better than all of them and clearly better than BetaCOBL at roughly one-third the runtime.

Load-bearing premise

The speed-up rests on the assumption that the fast diversity statistic sends the same 'still exploring or already converged' signal as the slow pairwise measure, so the algorithm switches selection operators at the right moments; if the two disagree on collapsed or clustered populations, accuracy could suffer even though the clock time drops.

Editorial extensions

If this is right

  • Any differential evolution variant can embed iBetaCOBL as a module and inherit a linear-time diversity check instead of a pairwise one.
  • On multimodal and composition functions, where exploration matters, the paper's results show iBetaCOBL tends to find more accurate solutions than the original DE and most OBL variants.
  • Cost-sensitive and large-population optimization becomes more feasible because the per-jump overhead no longer grows quadratically with population size.
  • Modern DE engines such as EDEV and LSHADE-RSP improve when iBetaCOBL is attached, with the largest gain appearing in the late stage where the algorithm must escape local optima.

Reading between the lines

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

  • One extension the authors do not explore: the same linear-time diversity statistic could replace pairwise measures in the selection logic of other population-based optimizers, not only OBL variants of DE.
  • A testable prediction follows from the crossover change: on hybrid or composition functions whose variable blocks are permuted, the advantage of iBetaCOBL over BetaCOBL should shrink, because multiple exponential crossover only preserves adjacency in the given coordinate order.
  • The diversity threshold $D_T$ was tuned for the old measure; with the new statistic its scale differs, so the reported gains might be sensitive to $D_T$ and could be improved or degraded by re-calibrating it.
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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

3 major / 5 minor

Summary. The paper proposes iBetaCOBL, a modified BetaCOBL for differential evolution, with two main changes: replacement of the O(NP^2 D) power-mean diversity measure in the selection-switching scheme with a claimed O(NP D) linear-time diversity measure (Eq. 22), and replacement of the binomial crossover in the partial-opposite-solution construction with multiple exponential crossover. The method is evaluated on the CEC 2013 and CEC 2017 suites at 30 and 50 dimensions, embedded in three DE variants (DE/rand/1/bin, EDEV, and LSHADE-RSP), and compared against ten OBL variants using 51 runs, Wilcoxon rank-sum tests, Friedman tests, and algorithm-complexity measurements. The authors claim that iBetaCOBL remains competitive with or outperforms the predecessor BetaCOBL while reducing computational cost.

Significance. If the claims are accepted, the paper offers a practical, low-cost drop-in OBL module for DE: the complexity reduction from O(NP^2 D) to O(NP D) is real and the experimental campaign is unusually thorough, spanning 58 benchmark functions, two dimensions, three DE base algorithms, 51 independent runs, and standard nonparametric statistical tests. The ablation study in Section 6.2, which compares BetaCOBL against BetaCOBL with each of the two linear-time diversity measures, is a commendable attempt to isolate the effect of the diversity-measure replacement. However, the paper's mathematical description of Eq. (22) as a reformulation of Eq. (21) is incorrect, and the conclusion that iBetaCOBL 'significantly outperformed its predecessor BetaCOBL' is not supported by the paper's own Friedman post-hoc results. The practical contribution remains useful, but the manuscript needs correction and more careful claims.

major comments (3)
  1. [4.2.2, Eq. (22)] Equation (22) is not a reformulation of Equation (21), as the text asserts. Equation (21) is the average pairwise Euclidean distance, whereas Eq. (22) is the square root of the average per-dimension variance. A simple counterexample shows the difference: for a two-point population in one dimension with coordinates a and b, Eq. (21) equals |a-b|, while Eq. (22) equals |a-b|/2. The two statistics have different scales and can rank different populations differently, so the subsequent use of the same threshold DT = 1e-6 cannot be justified by algebraic equivalence. The authors should either correct this statement to describe Eq. (22) as a different, approximating diversity measure, or provide a rigorous derivation of the claimed equivalence.
  2. [4.2.2, Algorithm 2, Section 6.2] Because Eq. (22) is a different statistic with a different scale and distribution from the original power-mean measure, the (mu+lambda) versus (mu,lambda) branch in the selection-switching scheme may fire at different generations or with different frequencies when DT is left unchanged. The ablation in Section 6.2 reports only final FEV means and Wilcoxon comparisons; it does not log which selection branch was taken, when the first switch occurred, or how many generation jumps used each branch. Without such trace-level evidence, the comparison against BetaCOBL conflates the intended complexity improvement with a potentially different switching schedule, and the claim that the cheaper measure 'maintains the performance' of BetaCOBL is not fully demonstrated.
  3. [Section 8; Section 6.1.1; Tables 2, 4, 6, 8, 16, 18, 22, 24] The conclusion that iBetaCOBL 'significantly outperformed its predecessor BetaCOBL' is not supported by the paper's own statistical analysis. In every Friedman test with Hochberg post-hoc comparison, BetaCOBL is not flagged as significantly different from iBetaCOBL; for example, Table 2 reports an adjusted p-value of 0.781 for the BetaCOBL comparison. The per-function Wilcoxon counts (e.g., 12 wins versus 6 losses on CEC 2013 at 30-D) show a favorable trend, but they are not a global test of significance. The authors should either temper the claim to 'competitive with lower computational cost' or conduct and report a proper paired statistical test across the benchmark suites.
minor comments (5)
  1. [4.2.2, Eq. (22)] The notation in Eq. (22) is ambiguous: the two overline expressions are typeset identically, but one should denote the mean of squares and the other the square of the mean. Please use distinct symbols, e.g., \overline{(x^k)^2} and (\overline{x^k})^2, and clarify the normalization described immediately after the equation.
  2. [2.2] There is an empty citation bracket after the sentence claiming that opposite values are more likely to be located near the optimal solution than random values; a reference is missing here.
  3. [7, Algorithm 2] The text states that LSHADE-RSP starts OBL only after three-fourths of the maximum number of function evaluations, but Algorithm 2 does not include this variant-specific delay and instead executes iBetaCOBL from the initialization phase. The pseudocode and the experimental description should be reconciled for reproducibility.
  4. [Throughout] There are several typographical inconsistencies, including 'LSAHDE-RSP' instead of 'LSHADE-RSP' and 'BetaCODE' instead of 'BetaCOBL' in Section 4.2.3. These should be corrected.
  5. [Experimental Setup] The paper reports aggregate mean and standard deviation values but does not provide per-run results, random seeds, or a code/data availability statement. Providing this material would improve reproducibility and allow independent verification of the Wilcoxon and Friedman results.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the performance claims are empirical comparisons on external CEC benchmarks, and the complexity reduction follows directly from replacing an O(NP^2*D) diversity computation with an O(NP*D) one.

full rationale

The paper's central claims are (1) iBetaCOBL is competitive with or better than ten OBL variants on CEC 2013 and CEC 2017 suites, and (2) it reduces the cost of BetaCOBL's diversity-based selection switching from O(NP^2*D) to O(NP*D). Both claims are supported by experiments and by a direct algebraic complexity comparison, not by a parameter fitted to the benchmark results and then renamed as a prediction. The two algorithmic modifications — the linear-time diversity measure D'_d in Eq. 22 and the multiple exponential crossover in Section 4.3.2 — are taken from external prior work (Wineberg and Oppacher; Qiu et al.) and are not justified by self-citation. Self-citations by the first author appear only in the related-work enumeration of DE variants and are not load-bearing for the proposed algorithm's design or evaluation. Even if Eq. 22 is not an exact algebraic reformulation of Eq. 21 — a point that could affect the fidelity of the switching behavior — the paper does not rely on that equivalence by construction: Section 6.2 empirically compares BetaCOBL with the linear-time diversity variants and reports no significant degradation, which is a legitimate external check rather than a circular reduction. The threshold DT and jumping rate Jr are reused from the prior BetaCOBL paper, not fitted to make the proposed algorithm win. Thus no derivation step reduces to its own inputs, and the appropriate circularity finding is no significant circularity.

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

The central performance claim rests on two engineering substitutions. The linear-time diversity measure is mathematically not equivalent to the pairwise-distance measure, so the adequacy of the substitution is an empirical domain assumption. The crossover substitution assumes problem variables have adjacent dependencies. Parameters DT, Jr, T, and CR are fixed by hand from prior work.

free parameters (4)
  • Diversity threshold DT = 1e-6
    Hand-set threshold for switching between (mu+lambda) and (mu,lambda) selection in the modified selection switching scheme; used in Sections 6.2 and 7, not fitted to the benchmark results.
  • Jumping rate Jr = 0.05
    Probability of applying iBetaCOBL instead of DE operators; inherited from BetaCOBL in reference [14].
  • Exchanged component length T = 10
    Controls the size of copied segments in multiple exponential crossover; taken from reference [26].
  • Crossover rates for partial opposite solutions CR = 0.1 and 0.9
    Two fixed crossover rates used in Algorithm 3 and Algorithm 4 to generate partial opposite solutions.
assumptions (4)
  • domain assumption The linear-time diversity measure D'_d in Equation 22 preserves the selection-switching behavior of the power-mean-based measure in Equation 19 closely enough for BetaCOBL's convergence control.
    The paper replaces Equation 19 with Equation 22 and validates empirically on CEC 2013 and 2017 in Section 6.2, but Equation 22 is not algebraically equivalent to the pairwise-distance measure in Equation 21, so this is a load-bearing empirical assumption.
  • domain assumption Strongly dependent decision variables are adjacent in the coordinate ordering of the problem.
    Section 4.3.3 argues that multiple exponential crossover preserves strongly dependent variables that are adjacent to each other; this is only true for problems whose dependency structure aligns with variable ordering, which is not the case for rotated or shuffled benchmark functions.
  • domain assumption CEC 2013 and CEC 2017 benchmark suites are representative of the target class of cost-sensitive, inseparable numerical optimization problems.
    The paper's performance claims are entirely empirical on these two suites in Sections 6 and 7; generalizing beyond them is an unsupported assumption.
  • standard math Opposite solutions are, with higher probability, closer to the optimum than random solutions.
    Invoked in Section 2.2 to justify OBL; the paper says it was mathematically proved but cites an empty bracket '[]', so the reader must take it as an unverified background claim.

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Cite this review

Pith. "Pith review of A Fast and Efficient Stochastic Opposition-Based Learning for Differential Evolution in Numerical Optimization." pith.science (2026). https://pith.science/paper/WO34QCNS

@misc{pith2026190808011,
  author       = {Pith},
  title        = {Pith review of: A Fast and Efficient Stochastic Opposition-Based Learning for Differential Evolution in Numerical Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WO34QCNS}},
  note         = {Machine review of arXiv:1908.08011}
}
abstract

A fast and efficient stochastic opposition-based learning (OBL) variant is proposed in this paper. OBL is a machine learning concept to accelerate the convergence of soft computing algorithms, which consists of simultaneously calculating an original solution and its opposite. Recently, a stochastic OBL variant called BetaCOBL was proposed, which is capable of controlling the degree of opposite solutions, preserving useful information held by original solutions, and preventing the waste of fitness evaluations. While it has shown outstanding performance compared to several state-of-the-art OBL variants, the high computational cost of BetaCOBL may hinder it from cost-sensitive optimization problems. Also, as it assumes that the decision variables of a given problem are independent, BetaCOBL may be ineffective for optimizing inseparable problems. In this paper, we propose an improved BetaCOBL that mitigates all the limitations. The proposed algorithm called iBetaCOBL reduces the computational cost from $O(NP^{2} \cdot D)$ to $O(NP \cdot D)$ ($NP$ and $D$ stand for population size and a dimension, respectively) using a linear time diversity measure. Also, the proposed algorithm preserves strongly dependent variables that are adjacent to each other using multiple exponential crossover. We used differential evolution (DE) variants to evaluate the performance of the proposed algorithm. The results of the performance evaluations on a set of 58 test functions show the excellent performance of iBetaCOBL compared to ten state-of-the-art OBL variants, including BetaCOBL.

Figures

Figures reproduced from arXiv: 1908.08011 by the authors.

Figure 1
Figure 1. Example of concave and convex opposite points [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Two linear time diversity measures [70, 71, 72, 73, 21, 22, 23], where it can be defined as the map￾ping Dv : IRNP×D → IR Dv(Pg) = Xn i=1 kxi,g − xgk (23) where xg = (M1 , M2 , · · · , MD) and the centroid of the popula￾tion with Mk = 1 NP PNP i=1 x k i,g , k = 1, 2, · · · , D [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Behavior of three crossover operators To improve the performance on inseparable problems, we employed the multiple exponential crossover [26] in the par￾tial dimensional change scheme. The multiple exponential crossover is a semi-consecutive crossover operator that divides a trial vector into several components, and each component is a copy of the component at the location of either the tar￾get or the mutant vector … view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Convergence graphs of EDEV assisted by OBL variants on CEC 2013 and 2017 test suites at 50- [PITH_FULL_IMAGE:figures/full_fig_p020_4.png]
Figure 5
Figure 5. Figure 5: Convergence graphs of LSHADE-RSP assisted by OBL variants on CEC 2013 and 2017 test suites at 50- [PITH_FULL_IMAGE:figures/full_fig_p022_5.png]

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Works this paper leans on

91 extracted references · 80 canonical work pages

  1. [1]

    Storn, K

    R. Storn, K. Price, Di fferential evolution–a simple and efficient heuristic for global optimization over continuous spaces, Journal of global opti- mization 11 (4) (1997) 341–359

    1997

  2. [2]

    Price, R

    K. Price, R. M. Storn, J. A. Lampinen, Di fferential evolution: a practi- cal approach to global optimization, Springer Science & Business Media, 2006

    2006

  3. [3]

    S. Das, P. N. Suganthan, Di fferential evolution: A survey of the state- of-the-art, IEEE transactions on evolutionary computation 15 (1) (2011) 4–31

    2011

  4. [4]

    Hansen, A

    N. Hansen, A. Ostermeier, Completely derandomized self-adaptation in evolution strategies, Evolutionary computation 9 (2) (2001) 159–195

    2001

  5. [5]

    F. Neri, V . Tirronen, Recent advances in di fferential evolution: a survey and experimental analysis, Artificial Intelligence Review 33 (1-2) (2010) 61–106

    2010

  6. [6]

    S. Das, S. S. Mullick, P. N. Suganthan, Recent advances in di fferential evolution–an updated survey, Swarm and Evolutionary Computation 27 (2016) 1–30

    2016

  7. [7]

    R. D. Al-Dabbagh, F. Neri, N. Idris, M. S. Baba, Algorithmic design is- sues in adaptive di fferential evolution schemes: Review and taxonomy, Swarm and Evolutionary Computation 43 (2018) 284–311

    2018

  8. [8]

    H. R. Tizhoosh, Opposition-based learning: a new scheme for machine intelligence, in: International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA- IAWTIC’06), V ol. 1, IEEE, 2005, pp. 695–701

    2005

Show all 91 references
  1. [9]

    H. R. Tizhoosh, M. Ventresca, Oppositional concepts in computational intelligence, V ol. 155, Springer, 2008

    2008

  2. [10]

    F. S. Al-Qunaieer, H. R. Tizhoosh, S. Rahnamayan, Opposition based computinga survey, in: The 2010 International Joint Conference on Neu- ral Networks (IJCNN), IEEE, 2010, pp. 1–7

    2010

  3. [11]

    Q. Xu, L. Wang, N. Wang, X. Hei, L. Zhao, A review of opposition- based learning from 2005 to 2012, Engineering Applications of Artificial Intelligence 29 (2014) 1–12. 23

    2014

  4. [12]

    Mahdavi, S

    S. Mahdavi, S. Rahnamayan, K. Deb, Opposition based learning: A liter- ature review, Swarm and evolutionary computation 39 (2018) 1–23

    2018

  5. [13]

    Rahnamayan, H

    S. Rahnamayan, H. R. Tizhoosh, M. M. Salama, Opposition-based di ffer- ential evolution, IEEE Transactions on Evolutionary computation 12 (1) (2008) 64–79

    2008

  6. [14]

    Park, J.-J

    S.-Y . Park, J.-J. Lee, Stochastic opposition-based learning using a beta distribution in di fferential evolution, IEEE transactions on cybernetics 46 (10) (2016) 2184–2194

    2016

  7. [15]

    Haimin, W

    L. Haimin, W. Chengke, Genetic algorithm with adaptive mutation prob- ability and analysis of its property, Acta Electron. Sin.(China) 27 (5) (1999) 90–92

    1999

  8. [16]

    Lozano, F

    M. Lozano, F. Herrera, J. R. Cano, Replacement strategies to preserve useful diversity in steady-state genetic algorithms, Information Sciences 178 (23) (2008) 4421–4433

    2008

  9. [17]

    Myers, E

    R. Myers, E. R. Hancock, Genetic algorithms for ambiguous labelling problems, Pattern Recognition 33 (4) (2000) 685–704

    2000

  10. [18]

    A. L. Barker, W. N. Martin, Population diversity and fitness measures based on genomic distances

  11. [19]

    A. L. Barker, W. N. Martin, Dynamics of a distance-based population diversity measure, in: Proceedings of the 2000 Congress on Evolution- ary Computation. CEC00 (Cat. No. 00TH8512), V ol. 2, IEEE, 2000, pp. 1002–1009

    2000

  12. [20]

    Mattiussi, M

    C. Mattiussi, M. Waibel, D. Floreano, Measures of diversity for pop- ulations and distances between individuals with highly reorganizable genomes, Evolutionary Computation 12 (4) (2004) 495–515

    2004

  13. [21]

    Wineberg, F

    M. Wineberg, F. Oppacher, Distance between populations, in: Genetic and Evolutionary Computation Conference, Springer, 2003, pp. 1481– 1492

    2003

  14. [22]

    Y . Shi, R. C. Eberhart, Population diversity of particle swarms, in: 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence), IEEE, 2008, pp. 1063–1067

    2008

  15. [23]

    Mallipeddi, P

    R. Mallipeddi, P. N. Suganthan, B.-Y . Qu, Diversity enhanced adap- tive evolutionary programming for solving single objective constrained problems, in: 2009 IEEE Congress on Evolutionary Computation, IEEE, 2009, pp. 2106–2113

    2009

  16. [24]

    Wineberg, F

    M. Wineberg, F. Oppacher, The underlying similarity of diversity mea- sures used in evolutionary computation, in: Genetic and Evolutionary Computation Conference, Springer, 2003, pp. 1493–1504

    2003

  17. [25]

    Wineberg, F

    M. Wineberg, F. Oppacher, A linear time algorithm for determining population diversity in evolutionary computation, Proceedings of the IASTED International Confererence on Intelligent Systems and Control (ICS 2003)

    2003

  18. [26]

    X. Qiu, K. C. Tan, J.-X. Xu, Multiple exponential recombination for dif- ferential evolution, IEEE transactions on cybernetics 47 (4) (2017) 995– 1006

    2017

  19. [27]

    Liang, B

    J. Liang, B. Qu, P. Suganthan, A. G. Hern´andez-D´ıaz, Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization, Computational Intelligence Laboratory, Zhengzhou Univer- sity, Zhengzhou, China and Nanyang Technological Universi...

    2013

  20. [28]

    N. Awad, M. Ali, J. Liang, B. Qu, P. Suganthan, Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective bound constrained real-parameter numerical optimiza- tion, in: Technical Report, NTU, Singapore, 2016

    2017

  21. [29]

    G. Wu, X. Shen, H. Li, H. Chen, A. Lin, P. N. Suganthan, Ensemble of differential evolution variants, Information Sciences 423 (2018) 172–186

    2018

  22. [30]

    Stanovov, S

    V . Stanovov, S. Akhmedova, E. Semenkin, LSHADE algorithm with rank-based selective pressure strategy for solving CEC 2017 benchmark problems, in: 2018 IEEE Congress on Evolutionary Computation (CEC), IEEE, 2018, pp. 1–8

    2017

  23. [31]

    A. K. Qin, V . L. Huang, P. N. Suganthan, Differential evolution algorithm with strategy adaptation for global numerical optimization, IEEE transac- tions on Evolutionary Computation 13 (2) (2008) 398–417

    2008

  24. [32]

    W. Gong, Z. Cai, C. X. Ling, H. Li, Enhanced di fferential evolution with adaptive strategies for numerical optimization, IEEE Transactions on Sys- tems, Man, and Cybernetics, Part B (Cybernetics) 41 (2) (2010) 397–413

    2010

  25. [33]

    S.-Z. Zhao, P. N. Suganthan, S. Das, Self-adaptive di fferential evolution with multi-trajectory search for large-scale optimization, Soft Computing 15 (11) (2011) 2175–2185

    2011

  26. [34]

    T. J. Choi, C. W. Ahn, An Adaptive Cauchy Di fferential Evolution Al- gorithm with Bias Strategy Adaptation Mechanism for Global Numerical Optimization., JCP 9 (9) (2014) 2139–2145

    2014

  27. [35]

    T. J. Choi, C. W. Ahn, An adaptive cauchy differential evolution algorithm with population size reduction and modified multiple mutation strategies, in: Proceedings of the 18th Asia Pacific Symposium on Intelligent and Evolutionary Systems-V olume 2, Springer, 2015, pp. 13–26

    2015

  28. [36]

    T. J. Choi, C. W. Ahn, Adaptive Cauchy Differential Evolution with Strat- egy Adaptation and Its Application to Training Large-Scale Artificial Neural Networks, in: International Conference on Bio-Inspired Comput- ing: Theories and Applications, Springer, 2017, pp. 502–510

    2017

  29. [37]

    Brest, S

    J. Brest, S. Greiner, B. Boskovic, M. Mernik, V . Zumer, Self-adapting control parameters in differential evolution: A comparative study on nu- merical benchmark problems, IEEE transactions on evolutionary compu- tation 10 (6) (2006) 646–657

    2006

  30. [38]

    M. Leon, N. Xiong, Adapting di fferential evolution algorithms for con- tinuous optimization via greedy adjustment of control parameters, Jour- nal of Artificial Intelligence and Soft Computing Research 6 (2) (2016) 103–118

    2016

  31. [39]

    S. M. Islam, S. Das, S. Ghosh, S. Roy, P. N. Suganthan, An adaptive dif- ferential evolution algorithm with novel mutation and crossover strategies for global numerical optimization, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 42 (2) (2011) 482–500

    2011

  32. [40]

    T. J. Choi, C. W. Ahn, J. An, An adaptive cauchy di fferential evolution algorithm for global numerical optimization, The Scientific World Journal 2013

    2013

  33. [41]

    T. J. Choi, C. W. Ahn, An adaptive di fferential evolution algorithm with automatic population resizing for global numerical optimization, in: Bio- Inspired Computing-Theories and Applications, Springer, 2014, pp. 68– 72

    2014

  34. [42]

    T. J. Choi, C. W. Ahn, An adaptive population resizing scheme for differ- ential evolution in numerical optimization, Journal of Computational and Theoretical Nanoscience 12 (7) (2015) 1336–1350

    2015

  35. [43]

    T. J. Choi, C. W. Ahn, Adaptive α-stable differential evolution in numeri- cal optimization, Natural Computing 16 (4) (2017) 637–657

    2017

  36. [44]

    T. J. Choi, C. W. Ahn, An Improved Differential Evolution Algorithm and Its Application to Large-Scale Artificial Neural Networks, in: Journal of Physics: Conference Series, V ol. 806, IOP Publishing, 2017, p. 012010

    2017

  37. [45]

    Mallipeddi, P

    R. Mallipeddi, P. N. Suganthan, Q.-K. Pan, M. F. Tasgetiren, Di fferential evolution algorithm with ensemble of parameters and mutation strategies, Applied soft computing 11 (2) (2011) 1679–1696

    2011

  38. [46]

    G. Wu, R. Mallipeddi, P. N. Suganthan, R. Wang, H. Chen, Di fferential evolution with multi-population based ensemble of mutation strategies, Information Sciences 329 (2016) 329–345

    2016

  39. [47]

    M. Ali, M. Pant, Improving the performance of di fferential evolution al- gorithm using Cauchy mutation, Soft Computing 15 (5) (2011) 991–1007

    2011

  40. [48]

    H. Qin, J. Zhou, Y . Lu, Y . Wang, Y . Zhang, Multi-objective differential evolution with adaptive Cauchy mutation for short-term multi-objective optimal hydro-thermal scheduling, Energy Conversion and Management 51 (4) (2010) 788–794

    2010

  41. [49]

    T. J. Choi, C. W. Ahn, Accelerating di fferential evolution using multiple exponential cauchy mutation, in: Proceedings of the Genetic and Evolu- tionary Computation Conference Companion, ACM, 2018, pp. 207–208

    2018

  42. [50]

    T. J. Choi, J. Togelius, Y .-G. Cheong, ACM-DE: Adaptive p-best Cauchy Mutation with linear failure threshold reduction for Differential Evolution in numerical optimization, arXiv preprint arXiv:1907.01095

    1907 arXiv

  43. [51]

    T. J. Choi, J. Togelius, Y .-G. Cheong, Advanced cauchy mutation for differential evolution in numerical optimization, IEEE Access 8 (2020) 8720–8734

    2020

  44. [52]

    S. Das, A. Abraham, U. K. Chakraborty, A. Konar, Di fferential evolu- tion using a neighborhood-based mutation operator, IEEE Transactions on Evolutionary Computation 13 (3) (2009) 526–553

    2009

  45. [53]

    Basu, Quasi-oppositional di fferential evolution for optimal reactive power dispatch, International Journal of Electrical Power & Energy Sys- tems 78 (2016) 29–40

    M. Basu, Quasi-oppositional di fferential evolution for optimal reactive power dispatch, International Journal of Electrical Power & Energy Sys- tems 78 (2016) 29–40

    2016

  46. [54]

    T. R. Chelliah, R. Thangaraj, S. Allamsetty, M. Pant, Coordination of directional overcurrent relays using opposition based chaotic di fferential evolution algorithm, International Journal of Electrical Power & Energy Systems 55 (2014) 341–350

    2014

  47. [55]

    H. V . H. Ayala, L. dos Santos Coelho, V . C. Mariani, A. Askarzadeh, An improved free search di fferential evolution algorithm: A case study on parameters identification of one diode equivalent circuit of a solar cell module, Energy 93 (2015) 1515–1522. 24

    2015

  48. [56]

    Subudhi, D

    B. Subudhi, D. Jena, A di fferential evolution based neural network ap- proach to nonlinear system identification, Applied Soft Computing 11 (1) (2011) 861–871

    2011

  49. [57]

    Koohi-Moghadam, A

    M. Koohi-Moghadam, A. T. Rahmani, Molecular docking with opposition-based differential evolution, in: Proceedings of the 27th An- nual ACM Symposium on Applied Computing, ACM, 2012, pp. 1387– 1392

    2012

  50. [58]

    Dragoi, S

    E.-N. Dragoi, S. Curteanu, A.-I. Galaction, D. Cascaval, Optimization methodology based on neural networks and self-adaptive differential evo- lution algorithm applied to an aerobic fermentation process, Applied Soft Computing 13 (1) (2013) 222–238

    2013

  51. [59]

    Sidhu, J

    D. Sidhu, J. Dhillon, D. Kaur, Hybrid heuristic search method for design of digital IIR filter with conflicting objectives, Soft Computing 21 (12) (2017) 3461–3476

    2017

  52. [60]

    T. J. Choi, J.-H. Lee, H. Y . Youn, C. W. Ahn, Adaptive Differential Evolu- tion with Elite Opposition-Based Learning and its Application to Training Artificial Neural Networks, Fundamenta Informaticae 164 (2-3) (2019) 227–242

    2019

  53. [61]

    Rahnamayan, H

    S. Rahnamayan, H. R. Tizhoosh, M. M. Salama, Opposition-based dif- ferential evolution (ODE) with variable jumping rate, in: Foundations of Computational Intelligence, 2007. FOCI 2007. IEEE Symposium on, IEEE, 2007, pp. 81–88

    2007

  54. [62]

    Esmailzadeh, S

    A. Esmailzadeh, S. Rahnamayan, Opposition-based di fferential evolution with protective generation jumping, in: Di fferential Evolution (SDE), 2011 IEEE Symposium on, IEEE, 2011, pp. 1–8

    2011

  55. [63]

    Rahnamayan, H

    S. Rahnamayan, H. R. Tizhoosh, M. M. Salama, Quasi-oppositional dif- ferential evolution, in: Evolutionary Computation, 2007. CEC 2007. IEEE Congress on, IEEE, 2007, pp. 2229–2236

    2007

  56. [64]

    Ergezer, D

    M. Ergezer, D. Simon, D. Du, Oppositional biogeography-based opti- mization, in: Systems, Man and Cybernetics, 2009. SMC 2009. IEEE International Conference on, IEEE, 2009, pp. 1009–1014

    2009

  57. [65]

    Q. Xu, L. Wang, B. He, N. Wang, Modified opposition-based di fferential evolution for function optimization, Journal of Computational Informa- tion Systems 7 (5) (2011) 1582–1591

    2011

  58. [66]

    H. Wang, Z. Wu, S. Rahnamayan, Enhanced opposition-based di fferen- tial evolution for solving high-dimensional continuous optimization prob- lems, Soft Computing 15 (11) (2011) 2127–2140

    2011

  59. [67]

    X. Zhou, Z. Wu, H. Wang, Elite opposition-based di fferential evolution for solving large-scale optimization problems and its implementation on GPU, in: Parallel and Distributed Computing, Applications and Tech- nologies (PDCAT), 2012 13th International Conference on, IEEE, 201...

    2012

  60. [68]

    H. Liu, Z. Wu, H. Wang, S. Rahnamayan, C. Deng, Improved di fferential evolution with adaptive opposition strategy, in: 2014 IEEE Congress on Evolutionary Computation (CEC), IEEE, 2014, pp. 1776–1783

    2014

  61. [69]

    Lacevic, E

    B. Lacevic, E. Amaldi, Ectropy of diversity measures for populations in Euclidean space, Information Sciences 181 (11) (2011) 2316–2339

    2011

  62. [70]

    R. K. Ursem, Diversity-guided evolutionary algorithms, in: International Conference on Parallel Problem Solving from Nature, Springer, 2002, pp. 462–471

    2002

  63. [71]

    M. A. Bedau, M. Zwick, A. Bahm, Variance and uncertainty measures of population diversity dynamics, Advances in Systems Science and Appli- cations (1995) 7

    1995

  64. [72]

    Riget, J

    J. Riget, J. S. Vesterstrøm, A diversity-guided particle swarm optimizer- the ARPSO, Dept. Comput. Sci., Univ. of Aarhus, Aarhus, Denmark, Tech. Rep 2 (2002) 2002

    2002

  65. [73]

    J. Jie, J. Zeng, Particle swarm optimization with diversity-controlled ac- celeration coe fficients, in: Third International Conference on Natural Computation (ICNC 2007), V ol. 4, IEEE, 2007, pp. 150–154

    2007

  66. [74]

    C. Lin, A. Qing, Q. Feng, A comparative study of crossover in differential evolution, Journal of Heuristics 17 (6) (2011) 675–703

    2011

  67. [75]

    Zaharie, Influence of crossover on the behavior of differential evolution algorithms, Applied soft computing 9 (3) (2009) 1126–1138

    D. Zaharie, Influence of crossover on the behavior of differential evolution algorithms, Applied soft computing 9 (3) (2009) 1126–1138

    2009

  68. [76]

    Dem ˇsar, Statistical comparisons of classifiers over multiple data sets, Journal of Machine learning research 7 (Jan) (2006) 1–30

    J. Dem ˇsar, Statistical comparisons of classifiers over multiple data sets, Journal of Machine learning research 7 (Jan) (2006) 1–30

    2006

  69. [77]

    Zhang, A

    J. Zhang, A. C. Sanderson, JADE: adaptive differential evolution with op- tional external archive, IEEE Transactions on evolutionary computation 13 (5) (2009) 945–958

    2009

  70. [78]

    Y . Wang, Z. Cai, Q. Zhang, Di fferential evolution with composite trial vector generation strategies and control parameters, IEEE Transactions on Evolutionary Computation 15 (1) (2011) 55–66

    2011

  71. [79]

    M. Yang, C. Li, Z. Cai, J. Guan, Differential evolution with auto-enhanced population diversity, IEEE transactions on cybernetics 45 (2) (2014) 302– 315

    2014

  72. [80]

    Kova ˇcevi´c, N

    D. Kova ˇcevi´c, N. Mladenovi ´c, B. Petrovi ´c, P. Miloˇsevi´c, De-vns: Self- adaptive differential evolution with crossover neighborhood search for continuous global optimization, Computers & Operations Research 52 (2014) 157–169

    2014

  73. [81]

    W. Gong, Z. Cai, Di fferential evolution with ranking-based mutation op- erators, IEEE Transactions on Cybernetics 43 (6) (2013) 2066–2081

    2013

  74. [82]

    A. Draa, S. Bouzoubia, I. Boukhalfa, A sinusoidal di fferential evolution algorithm for numerical optimisation, Applied Soft Computing 27 (2015) 99–126

    2015

  75. [83]

    N. H. Awad, M. Z. Ali, P. N. Suganthan, R. G. Reynolds, An ensemble sinusoidal parameter adaptation incorporated with L-SHADE for solving CEC2014 benchmark problems, in: 2016 IEEE congress on evolutionary computation (CEC), IEEE, 2016, pp. 2958–2965

    2016

  76. [84]

    Brest, M

    J. Brest, M. S. Mau ˇcec, B. Bo ˇskovi´c, il-shade: Improved l-shade algo- rithm for single objective real-parameter optimization, in: 2016 IEEE Congress on Evolutionary Computation (CEC), IEEE, 2016, pp. 1188– 1195

    2016

  77. [85]

    Brest, M

    J. Brest, M. S. Mau ˇcec, B. Boˇskovi´c, Single objective real-parameter op- timization: Algorithm jso, in: 2017 IEEE congress on evolutionary com- putation (CEC), IEEE, 2017, pp. 1311–1318

    2017

  78. [86]

    N. H. Awad, M. Z. Ali, P. N. Suganthan, R. G. Reynolds, An ensem- ble sinusoidal parameter adaptation incorporated with l-shade for solving cec2014 benchmark problems, in: 2016 IEEE congress on evolutionary computation (CEC), IEEE, 2016, pp. 2958–2965

    2016

  79. [87]

    N. H. Awad, M. Z. Ali, P. N. Suganthan, Ensemble sinusoidal di fferen- tial covariance matrix adaptation with euclidean neighborhood for solving cec2017 benchmark problems, in: 2017 IEEE Congress on Evolutionary Computation (CEC), IEEE, 2017, pp. 372–379

    2017

  80. [88]

    N. H. Awad, M. Z. Ali, P. N. Suganthan, R. G. Reynolds, A. M. Shat- nawi, A novel differential crossover strategy based on covariance matrix learning with euclidean neighborhood for solving real-world problems, in: 2017 IEEE Congress on Evolutionary Computation (CEC), IEEE, 201...

    2017

  81. [89]

    N. H. Awad, M. Z. Ali, P. N. Suganthan, Ensemble of parameters in a sinusoidal differential evolution with niching-based population reduction, Swarm and evolutionary computation 39 (2018) 141–156

    2018

  82. [90]

    A. W. Mohamed, A. A. Hadi, A. M. Fattouh, K. M. Jambi, Lshade with semi-parameter adaptation hybrid with cma-es for solving cec 2017 benchmark problems, in: 2017 IEEE Congress on evolutionary computa- tion (CEC), IEEE, 2017, pp. 145–152

    2017

  83. [91]

    Yeh, T.-Y

    J.-F. Yeh, T.-Y . Chen, T.-C. Chiang, Modified l-shade for single objective real-parameter optimization, in: 2019 IEEE Congress on Evolutionary Computation (CEC), IEEE, 2019, pp. 381–386. 25

    2019

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.