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arxiv: 2605.05198 · v1 · submitted 2026-05-06 · 🧮 math.OC · cs.NE

S-LCG: Structured Linear Congruential Generator-Based Deterministic Algorithm for Search and Optimization

Ahmed Qasim Mohammed , Haider Banka , Anamika Singh This is my paper

Pith reviewed 2026-05-08 16:49 UTC · model grok-4.3

classification 🧮 math.OC cs.NE
keywords deterministic optimizationlinear congruential generatorglobal optimizationbenchmark functionsengineering designreproducible algorithmtwo-level architecturebit splitting
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The pith

S-LCG is a deterministic optimization algorithm that uses a structured linear congruential generator in a two-level architecture to reach near-global optima on most benchmark problems with only one tunable parameter.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces S-LCG as a deterministic search method built on a variant of the linear congruential generator. An outer loop adaptively shifts between exploring new regions and exploiting promising ones while an inner loop evaluates candidate points. The generator supplies memoryless non-overlapping sequences, a bit-splitting step that turns states into multi-dimensional points, and constant-rate information gathering that sidesteps early stopping. On 26 standard test functions in dimensions from 2 to 30 the method lands within 1 percent of the known best value in 83 percent of runs, beating the nearest competitor and solving three real engineering design tasks.

Core claim

The Structured Linear Congruential Generator follows a two-level architecture in which an external adaptive loop balances exploration and exploitation of the generator space while the internal loop evaluates solutions; its defining traits are a memoryless scheme that produces non-overlapping sequences from distinct seeds, a bit-splitting representation that converts generator states into multi-dimensional points to avoid lattice artifacts, adaptive exploration-exploitation that implicitly optimizes the objective, and constant information-gathering speed that prevents premature convergence, yielding a strictly reproducible framework controlled by a single sensitive parameter.

What carries the argument

The S-LCG two-level architecture that combines an adaptive outer loop for exploration-exploitation balance with bit splitting of generator states to produce non-redundant multi-dimensional search points.

If this is right

  • S-LCG reaches within 1 percent of the global optimum in 83.3 percent of 138 cases across 26 functions and dimensions 2 to 30.
  • The method statistically outperforms eight binary optimization algorithms including genetic algorithms.
  • S-LCG successfully solves three constrained engineering design problems.
  • All runs are strictly reproducible because the generator is deterministic and only one parameter requires tuning.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The memoryless non-overlapping property could allow S-LCG to be distributed across independent processors without duplicate evaluations.
  • Because the algorithm gathers information at constant speed, it may remain effective on problems where other methods slow down as dimension grows beyond 30.
  • The single-parameter design could simplify embedding S-LCG inside larger hybrid solvers that combine deterministic and stochastic steps.
  • If the bit-splitting step generalizes, similar mappings might improve other pseudo-random generators used for optimization.

Load-bearing premise

The bit-splitting representation and adaptive exploration-exploitation loop actually produce implicit optimization of the objective function and avoid premature convergence without post-hoc adjustments or hidden parameters beyond the single stated one.

What would settle it

Running S-LCG on a fresh collection of 30-dimensional benchmark functions with the single parameter held fixed and recording whether the fraction of cases reaching within 1 percent of the global optimum falls below 70 percent or whether any evaluation sequences from distinct seeds overlap.

Figures

Figures reproduced from arXiv: 2605.05198 by Ahmed Qasim Mohammed, Anamika Singh, Haider Banka.

Figure 1
Figure 1. Figure 1: Three-dimensional representations of the spatial distributions produced by S-LCG, RANDU, and Uniform view at source ↗
Figure 2
Figure 2. Figure 2: Exhaustive versus adaptive evaluation of the surrogate landscape view at source ↗
Figure 3
Figure 3. Figure 3: Lag-k autocorrelation in the surrogate landscape, demonstrating localized topological. 4.3 Information Acquisition Rate One of the limitations of existing stochastic optimization methods is that they revisit the same points again and again, which results in a waste of resources, especially in population-based methods, in which they tend to cluster in regions that are already explored. This results in a dec… view at source ↗
Figure 4
Figure 4. Figure 4: How to get around in the generator space in view at source ↗
Figure 5
Figure 5. Figure 5: Visual analysis of the S-LCG algorithm on selected scalable functions from (F1-F16). The columns display the view at source ↗
Figure 6
Figure 6. Figure 6: Visual analysis of the S-LCG algorithm on fixed-dimension multimodal functions. view at source ↗
Figure 7
Figure 7. Figure 7: Convergence curves for the ten￾sion/compression spring. 16 view at source ↗
Figure 8
Figure 8. Figure 8: Convergence curves for the welded beam design problem. Algorithm Name Dimension Achieved Cost Mean STD x1 x2 x3 x4 S-LCG 0.8125 0.4375 41.45648 185.00077 6145.06920 - - BDE 0.8125 0.4375 42.08664 186.12366 6279.47710 + 6.463972e+03 1.43600e+02 BPSO 0.875 0.4375 44.84471 146.39341 6175.77147 + 6.758928e+03 3.83635e+02 GA 0.875 0.4375 44.17487 152.50006 6227.52031 + 6.83492e+03 3.973271e+02 T-PSO 0.875 0.437… view at source ↗
Figure 9
Figure 9. Figure 9: Convergence curves for the pres￾sure vessel design problem. 6.4 Statistical and Efficiency Analysis Statistical validation is conducted using the Friedman mean rank test and the one-sample Wilcoxon signed-rank test because S-LCG yielded a single solution due to its deterministic design, compared with the median across 30 runs of the opposing algorithms with (α = 0.05). Finally, to check the significance of… view at source ↗
Figure 10
Figure 10. Figure 10: WTL comparison across dimensions. The Holm Post Hoc Test: used to evaluate the actual significance of the proposed algorithm against the competitor, where the Critical Difference (CD) view at source ↗
Figure 11
Figure 11. Figure 11: Critical Difference Diagram. Competitor Rank S-LCG Rank Comp. Z Praw Pholm Decision BSA 1.99 4.80 9.0402 < 0.0001 < 0.0001 Significant BPSO 1.99 5.22 10.3914 < 0.0001 < 0.0001 Significant T-BPSO 1.99 6.20 13.5442 < 0.0001 < 0.0001 Significant BTS 1.99 6.24 13.6729 < 0.0001 < 0.0001 Significant BDE 1.99 6.31 13.8981 < 0.0001 < 0.0001 Significant BGWO 1.99 7.93 19.1098 < 0.0001 < 0.0001 Significant BACO 1.9… view at source ↗
read the original abstract

This study presents a novel deterministic optimization algorithm based on a special variant of the Linear Congruential Generator (LCG). While conventional algorithms generally operate within the search space, the introduced technique follows a two-level architecture. In particular, an external loop that adaptively balances between exploration and exploitation, while the internal loop evaluates solutions. It is motivated by the intrinsic structure of the generator, the reason behind naming it the Structured Linear Congruential Generator (S- LCG). which enjoys a number of unique characteristics as follows: 1) a memoryless scheme, which ensures non-overlapping sequences based on distinct seeds, thus ensuring no evaluation redundancy; 2) bit splitting representation, which converts LCG states into multi-dimensional points to overcome the Marsaglia lattice effect; 3) adaptive exploration-exploitation of the generator space, which leads to implicit optimization of the surrogate smooth objective function; and 4) constant information gathering speed to avoid the problem of premature convergence. Extensive testing on 26 benchmark functions across dimensions d = 2 to 30 demonstrates that S-LCG comes within 1% of the global optimum in 83.3% of 138 cases (100% at d = 2, 81.2% at d = 30) while the nearest competitor GA achieved 75.4%. Statistical validation shows that S-LCG outperforms eight cutting-edge binary algorithms. Furthermore, its practical value is confirmed by validation on three constrained engineering design problems. In the end, S-LCG offers an optimization framework that is strictly reproducible and requires only one sensitive parameter to be tuned.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces the Structured Linear Congruential Generator (S-LCG), a deterministic optimization algorithm employing a two-level architecture: an external adaptive loop that balances exploration and exploitation of the generator space, and an internal loop that evaluates candidate solutions. It highlights four claimed properties: memoryless non-overlapping sequences from distinct seeds, bit-splitting representation to eliminate the Marsaglia lattice effect, adaptive exploration-exploitation that implicitly optimizes a surrogate smooth objective function, and constant information-gathering speed to prevent premature convergence. The authors report that S-LCG reaches within 1% of the global optimum on 83.3% of 138 benchmark instances (26 functions, dimensions 2–30), outperforming a genetic algorithm (75.4%) and eight other binary methods, with additional validation on three constrained engineering design problems. The method is presented as strictly reproducible and requiring only a single sensitive parameter.

Significance. If the adaptive mechanism can be shown to operate with exactly one tunable parameter and to deliver the stated performance without hidden constants or post-hoc adjustments, the work would constitute a meaningful contribution by supplying a fully deterministic, reproducible alternative to stochastic global optimizers. The breadth of the benchmark suite (138 cases across dimensions) and the engineering validation provide a solid empirical foundation for assessing practical utility.

major comments (2)
  1. [Abstract] Abstract: the central claim that the external adaptive loop produces 'implicit optimization of the surrogate smooth objective function' while using only one sensitive parameter is not supported by any explicit rule, equation, or pseudocode. Without the precise definition of how the exploration-exploitation balance is updated (including any thresholds, scaling factors, or iteration limits), it is impossible to verify that the adaptation does not embed additional constants or create circular dependence on the objective values it is supposed to optimize.
  2. [Abstract] Abstract (two-level architecture description): the bit-splitting representation is asserted to remove the Marsaglia lattice effect and enable the reported performance, yet no mathematical mapping from LCG states to multi-dimensional points or proof of non-overlapping coverage is supplied. This mechanism is load-bearing for both the determinism claim and the comparison against GA; its absence prevents assessment of whether the 83.3% success rate is reproducible or relies on implementation-specific choices.
minor comments (2)
  1. [Abstract] Abstract: the phrasing 'S- LCG' contains an extraneous space; standardize to 'S-LCG'.
  2. [Abstract] Abstract: the sentence 'It is motivated by the intrinsic structure of the generator, the reason behind naming it the Structured Linear Congruential Generator (S-LCG). which enjoys' is grammatically incomplete and should be restructured for readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and constructive criticism of our manuscript. We address each major comment point by point below, providing clarifications and committing to revisions where the comments identify gaps in explicit detail or supporting mathematics.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the external adaptive loop produces 'implicit optimization of the surrogate smooth objective function' while using only one sensitive parameter is not supported by any explicit rule, equation, or pseudocode. Without the precise definition of how the exploration-exploitation balance is updated (including any thresholds, scaling factors, or iteration limits), it is impossible to verify that the adaptation does not embed additional constants or create circular dependence on the objective values it is supposed to optimize.

    Authors: We agree that the abstract lacks the explicit update rule and pseudocode for the adaptive loop. The full manuscript (Section 3) defines the single sensitive parameter as the adaptation rate that governs the shift between exploration and exploitation phases based solely on the generator state sequence, without direct dependence on objective function values. However, to fully support the claim of implicit surrogate optimization and strict one-parameter reproducibility, we will insert the governing equations and pseudocode into the abstract and expand Section 3 with a dedicated derivation showing the absence of hidden constants or circularity. This revision will make the mechanism verifiable from the abstract onward. revision: yes

  2. Referee: [Abstract] Abstract (two-level architecture description): the bit-splitting representation is asserted to remove the Marsaglia lattice effect and enable the reported performance, yet no mathematical mapping from LCG states to multi-dimensional points or proof of non-overlapping coverage is supplied. This mechanism is load-bearing for both the determinism claim and the comparison against GA; its absence prevents assessment of whether the 83.3% success rate is reproducible or relies on implementation-specific choices.

    Authors: The manuscript (Section 4) introduces bit-splitting as the conversion of LCG integer states into coordinate tuples via fixed-width bit extraction, which is intended to produce uniform coverage without lattice artifacts. We acknowledge that a formal mathematical mapping and a proof of non-overlapping sequences from distinct seeds are not provided. To address this, we will add the explicit state-to-point mapping function, together with a short proof sketch demonstrating that distinct seeds generate disjoint subsequences and that the bit-extraction step eliminates the Marsaglia lattice structure in the projected space. These additions will be placed in a new subsection and referenced from the abstract, thereby strengthening the determinism and reproducibility claims. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation; algorithm properties presented as design features with external validation

full rationale

The paper introduces an algorithm via a two-level architecture and lists four characteristics (memoryless scheme, bit splitting, adaptive loop, constant speed) as intrinsic to the S-LCG generator. Performance claims rest on empirical testing against 26 benchmarks and three engineering problems, not on any closed-form derivation or prediction that reduces to fitted inputs. The adaptive exploration-exploitation is stated as a listed property leading to implicit optimization, but no equations or self-referential definitions are provided that would make the optimization tautological by construction. No self-citations, uniqueness theorems, or ansatzes are invoked in the given text to justify core claims. The single-parameter claim is presented as a design choice, with results shown to be reproducible on standard test suites.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

Based solely on the abstract, the central claim rests on standard properties of linear congruential generators plus newly introduced structuring rules whose correctness is supported only by empirical results rather than derivation.

free parameters (1)
  • one sensitive parameter
    The paper states that only one parameter requires tuning for the entire framework.
axioms (1)
  • standard math Linear congruential generators produce deterministic pseudo-random sequences from a seed via linear recurrence.
    Invoked as the foundation for the memoryless non-overlapping property.
invented entities (1)
  • S-LCG with bit splitting representation no independent evidence
    purpose: Converts LCG states into multi-dimensional points to overcome the Marsaglia lattice effect and enable non-redundant search.
    Newly introduced structuring technique described in the abstract.

pith-pipeline@v0.9.0 · 5601 in / 1575 out tokens · 101886 ms · 2026-05-08T16:49:58.119275+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages

  1. [1]

    Sörensen and F

    K. Sörensen and F. Glover. Metaheuristics. InEncyclopedia of Operations Research and Management Science. Springer, 2013

    work page 2013

  2. [2]

    H. R. Lourenço, O. C. Martin, and T. Stützle. Iterated local search. InHandbook of Metaheuristics, pages 321–353. Kluwer Academic Publishers, Norwell, MA, 2003

    work page 2003

  3. [3]

    Derrac, S

    J. Derrac, S. García, D. Molina, and F. Herrera. A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms.Swarm and Evolutionary Computation, 1(1):3–18, 2011

    work page 2011

  4. [4]

    Springer, 2010

    Thomas Bartz-Beielstein, Marco Chiarandini, Luís Paquete, and Mike Preuss, editors.Experimental Methods for the Analysis of Optimization Algorithms. Springer, 2010

    work page 2010

  5. [5]

    D. E. Knuth.The Art of Computer Programming, Volume 2: Seminumerical Algorithms. Addison–Wesley, Reading, MA, 3rd edition, 1997

    work page 1997

  6. [6]

    Lulu, 2nd edition, 2013

    Sean Luke.Essentials of Metaheuristics. Lulu, 2nd edition, 2013. Available for free at http://cs.gmu.edu/˜ sean/book/metaheuristics/

    work page 2013

  7. [7]

    I. M. Sobol’. On the distribution of points in a cube and the approximate evaluation of integrals.USSR Computational Mathematics and Mathematical Physics, 7(4):86–112, 1967

    work page 1967

  8. [8]

    J. H. Halton. On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik, 2(1):84–90, 1960

    work page 1960

  9. [9]

    D. H. Lehmer. Mathematical methods in large-scale computing units.Proceedings of the Second Symposium on Large-Scale Digital Calculating Machinery, pages 141–146, 1951

    work page 1951

  10. [10]

    A collection of selected pseudorandom number generators with linear structures

    Karl Entacher. A collection of selected pseudorandom number generators with linear structures. Technical report, Austrian Center for Parallel Computation, 2001. Extended version (Originally published 1997)

    work page 2001

  11. [11]

    X. Yao, Y. Liu, and G. Lin. Evolutionary programming made faster.IEEE Transactions on Evolutionary Computation, 3(2):82–102, 1999

    work page 1999

  12. [12]

    Test problems in optimization

    Xin-She Yang. Test problems in optimization. InEngineering Optimization: An Introduction with Metaheuristic Applications, pages 261–266. John Wiley & Sons, 2010

    work page 2010

  13. [13]

    Kirkpatrick, C

    S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. Optimization by simulated annealing.Science, 220(4598):671–680, 1983

    work page 1983

  14. [14]

    V. Černý. Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm.Journal of Optimization Theory and Applications, 45(1):41–51, 1985

    work page 1985

  15. [15]

    F. Glover. Future paths for integer programming and links to artificial intelligence.Computers & Operations Research, 13(5):533–549, 1986

    work page 1986

  16. [16]

    Mladenović and P

    N. Mladenović and P. Hansen. Variable neighborhood search.Computers & Operations Research, 24(11):1097–1100, 1997

    work page 1997

  17. [17]

    J. H. Holland.Adaptation in Natural and Artificial Systems. University of Michigan Press, 1975. 2nd ed., MIT Press, 1992

    work page 1975

  18. [18]

    D. E. Goldberg.Genetic Algorithms in Search, Optimization, and Machine Learning. Addison–Wesley, 1989

    work page 1989

  19. [19]

    Mitchell.An Introduction to Genetic Algorithms

    M. Mitchell.An Introduction to Genetic Algorithms. MIT Press, 1996

    work page 1996

  20. [20]

    Storn and K

    R. Storn and K. Price. Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces.Journal of Global Optimization, 11:341–359, 1997

    work page 1997

  21. [21]

    K. V. Price, R. M. Storn, and J. A. Lampinen.Differential Evolution: A Practical Approach to Global Optimization. Springer, 2005

    work page 2005

  22. [22]

    L. J. Fogel, A. J. Owens, and M. J. Walsh.Artificial Intelligence through Simulated Evolution. John Wiley & Sons, 1966

    work page 1966

  23. [23]

    D. B. Fogel.Evolutionary Computation: Toward a New Philosophy of Machine Intelligence. IEEE Press, 1995

    work page 1995

  24. [24]

    Kennedy and R

    J. Kennedy and R. C. Eberhart. Particle swarm optimization. InProc. IEEE International Conference on Neural Networks, pages 1942–1948, 1995. 20

    work page 1942

  25. [25]

    R. Poli, J. Kennedy, and T. Blackwell. Particle swarm optimization: an overview.Swarm Intelligence, 1(1):33–57, 2007

    work page 2007

  26. [26]

    Dorigo, V

    M. Dorigo, V. Maniezzo, and A. Colorni. The ant system: Optimization by a colony of cooperating agents.IEEE Trans. Systems, Man, and Cybernetics B, 26(1):29–41, 1996

    work page 1996

  27. [27]

    Dorigo and L

    M. Dorigo and L. M. Gambardella. Ant colony system: A cooperative learning approach to the traveling salesman problem.IEEE Trans. Evolutionary Computation, 1(1):53–66, 1997

    work page 1997

  28. [28]

    Dorigo and T

    M. Dorigo and T. Stützle.Ant Colony Optimization. MIT Press, 2004

    work page 2004

  29. [29]

    R. A. Formato. Central force optimization: A new metaheuristic with applications in applied electromagnetics.Progress in Electromagnetics Research, 77:425–491, 2007

    work page 2007

  30. [30]

    R. A. Formato. Central force optimization: a new deterministic gradient-like optimization metaheuristic.OPSEARCH, 46(1):25–51, 2009

    work page 2009

  31. [31]

    Rashedi, H

    E. Rashedi, H. Nezamabadi-Pour, and S. Saryazdi. Gsa: A gravitational search algorithm.Information Sciences, 179(13):2232–2248, 2009

    work page 2009

  32. [32]

    A. Y. S. Lam and V. O. K. Li. Chemical-reaction-inspired metaheuristic for optimization.IEEE Transactions on Evolutionary Computation, 14(3):381–399, 2010

    work page 2010

  33. [33]

    A. Y. S. Lam and V. O. K. Li. Chemical reaction optimization: a tutorial.Memetic Computing, 4(1):3–17, 2012

    work page 2012

  34. [34]

    Mirjalili, S

    S. Mirjalili, S. M. Mirjalili, and A. Lewis. Grey Wolf Optimizer.Advances in Engineering Software, 69:46–61, 2014

    work page 2014

  35. [35]

    Mirjalili and A

    S. Mirjalili and A. Lewis. The Whale Optimization Algorithm.Advances in Engineering Software, 95:51–67, 2016

    work page 2016

  36. [36]

    Mirjalili

    S. Mirjalili. The Ant Lion Optimizer.Advances in Engineering Software, 83:80–98, 2015

    work page 2015

  37. [37]

    Dhiman and V

    G. Dhiman and V. Kumar. Spotted Hyena Optimizer: A novel bio-inspired based metaheuristic technique for engineering applications.Advances in Engineering Software, 114:48–70, 2017

    work page 2017

  38. [38]

    Saremi, S

    S. Saremi, S. Mirjalili, and A. Lewis. Grasshopper Optimisation Algorithm: Theory and application.Advances in Engineering Software, 105:30–47, 2017

    work page 2017

  39. [39]

    A. A. Heidari, S. Mirjalili, H. Faris, I. Aljarah, M. Mafarja, and H. Chen. Harris Hawks Optimization: Algorithm and applications.Future Generation Computer Systems, 97:849–872, 2019

    work page 2019

  40. [40]

    Mirjalili, A

    S. Mirjalili, A. H. Gandomi, S. Z. Mirjalili, S. Saremi, H. Faris, and S. M. Mirjalili. Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems.Advances in Engineering Software, 114:163–191, 2017

    work page 2017

  41. [41]

    Abdollahzadeh, F

    B. Abdollahzadeh, F. S. Gharehchopogh, N. Khodadadi, and S. Mirjalili. Mountain Gazelle Optimizer: A new nature- inspired metaheuristic algorithm for global optimization problems.Advances in Engineering Software, 174:103282, 2022

    work page 2022

  42. [42]

    Arctic puffin optimization: A bio-inspired metaheuristic algorithm for solving engineering design optimization.Advances in Engineering Software, 195:103694, 2024

    Wen chuan Wang, Wei can Tian, Dong mei Xu, and Hong fei Zang. Arctic puffin optimization: A bio-inspired metaheuristic algorithm for solving engineering design optimization.Advances in Engineering Software, 195:103694, 2024

    work page 2024

  43. [43]

    D. H. Wolpert and W. G. Macready. No free lunch theorems for optimization.IEEE Transactions on Evolutionary Computation, 1(1):67–82, 1997

    work page 1997

  44. [44]

    Maucher, U

    M. Maucher, U. Schöning, and H. A. Kestler. Search heuristics and the influence of non-perfect randomness: examining genetic algorithms and simulated annealing.Computational Statistics, 26(2):303–319, 2011

    work page 2011

  45. [45]

    S. K. Park and K. W. Miller. Random number generators: good ones are hard to find.Communications of the ACM, 31(10):1192–1201, 1988

    work page 1988

  46. [46]

    Marsaglia

    G. Marsaglia. Random numbers fall mainly in the planes.Proceedings of the National Academy of Sciences, 61(1):25–28, 1968

    work page 1968

  47. [47]

    L’Ecuyer

    P. L’Ecuyer. Good parameters and implementations for combined multiple recursive random number generators. Operations Research, 47(1):159–164, 1999

    work page 1999

  48. [48]

    Niederreiter.Random Number Generation and Quasi-Monte Carlo Methods

    H. Niederreiter.Random Number Generation and Quasi-Monte Carlo Methods. SIAM, 1992

    work page 1992

  49. [49]

    Maaranen, K

    H. Maaranen, K. Miettinen, and M. M. Mäkelä. Quasi-random initial population for genetic algorithms.Computers & Mathematics with Applications, 47:1885–1895, 2004. 21

    work page 2004

  50. [50]

    Müller, and Petros Koumoutsakos

    Nikolaus Hansen, Sibylle D. Müller, and Petros Koumoutsakos. Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (cma-es).Evolutionary Computation, 11(1):1–18, 2003

    work page 2003

  51. [51]

    T. E. Hull and A. R. Dobell. Random number generators.SIAM Review, 4(3):230–254, 1962

    work page 1962

  52. [52]

    Certain topics in telegraph transmission theory.Proceedings of the IEEE, 90(2):280–305, 2002

    Harry Nyquist. Certain topics in telegraph transmission theory.Proceedings of the IEEE, 90(2):280–305, 2002. Reprint of the classic 1928 paper

    work page 2002

  53. [53]

    Claude E. Shannon. Communication in the presence of noise.Proceedings of the IEEE, 86(2):447–457, 1998. Reprint of the classic 1949 paper

    work page 1998

  54. [54]

    Gandomi, Xuefeng Chu, and Huiling Chen

    Iman Ahmadianfar, Ali Asghar Heidari, Amir H. Gandomi, Xuefeng Chu, and Huiling Chen. RUN beyond the metaphor: An efficient optimization algorithm based on runge kutta method.Expert Systems with Applications, 181:115079, 2021. 22

    work page 2021