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Cosm: Collective Switched Motion for Fast and Accurate Sparse Ising Optimization

T0 review · 0 major / 4 minor · reviewed 2026-07-12 · grok-4.5

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Pith's one-line read A switched dynamical heuristic finds certified optima on the largest Gset spin-glass Ising problems and cuts time-to-target from hours to minutes on sparse graphs.

desk verdict Cosm delivers the first heuristic optima on the three largest Gset lattices (Gurobi-certified) and multi-order TTT cuts on G61/G70; the algorithmic mix is real and the sparsity limit is stated honestly. read the letter →

arxiv 2605.30355 v2 pith:OIEHXE7K submitted 2026-04-16 cs.CE math.OCphysics.comp-ph

Kenneth M. Zick , Nikhil Shukla , Alexander Marakov This is my paper
classification cs.CEmath.OCphysics.comp-ph
keywords IsingoptimizationMax-Cutswitcheddynamicalsystemscircularvariablessparsegraphscollectivecomputationedgecoloringdualwindowtwist
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

The paper introduces Cosm, a dynamical-system heuristic that treats Ising variables as continuous angles on a circle and updates them through a periodic sequence of conflict-free edge matchings together with occasional coordinated twists of opposing phase windows. The switching dynamics keep interactions finite-magnitude and non-smooth so that collective fluctuations never freeze, while the dual-window twists encourage whole clusters of variables to rotate together toward lower-energy configurations. On the three largest Gset lattice spin glasses (10 000–20 000 variables) Cosm reaches the optimal cuts for the first time; an exact solver later certifies those cuts. On two large irregular bounded-degree graphs it reaches the previous best-known solutions in tens to hundreds of seconds rather than hundreds of hours. On a family of tile-planted lattices with controlled hardness its median time-to-solution scales more gently than seven earlier dynamical solvers. The authors argue that the combination of local switched interactions and global cluster motion is what lets the method traverse the rugged energy landscapes that defeat ordinary gradient or annealing approaches on sparse graphs.

What carries the argument

Sequential Conflict-free Search (SCS): the edges are colored into matchings and the system is advanced one matching at a time, producing a periodically switched interaction network whose finite-magnitude signum updates sustain structured intra-sweep fluctuations and prevent force cancellation.

What would settle it

Run Cosm on a sequence of the same lattice family while systematically raising average degree (or on dense Erdős–Rényi graphs of comparable size) and measure whether success probability and scaling exponent degrade sharply once typical intra-sweep angular displacement approaches 180 degrees.

Watch

Extended reading notes

Core claim

Cosm’s periodically switched, edge-partitioned dynamics plus dual-window twist perturbations enable a continuous circular-variable system to discover certified optimal solutions on the three largest Gset 2-D spin-glass instances and to reach best-known cuts on large bounded-degree non-lattice graphs orders of magnitude faster than prior heuristics.

Load-bearing premise

The method works only while the graph stays sparse and bounded-degree so that no variable rotates by roughly 180 degrees or more inside a single full sweep of color classes; denser graphs break that bound and the circular representation collapses.

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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

0 major / 4 minor

Summary. The paper introduces Collective Switched Motion (Cosm), a dynamical-system heuristic for sparse Ising/Max-Cut/QUBO problems. Continuous circular variables interact via finite-magnitude sgn-based couplings applied sequentially over a proper edge coloring (Sequential Conflict-free Search, SCS), producing a periodically switched network; a Dual Window Twist (DWT) correlated perturbation is applied at regular intervals to promote cluster motion. After annealing, variables are binarized by testing multiple bisectors. On the three largest Gset 2-D toroidal spin glasses (G72, G77, G81; 10k–20k variables) Cosm reaches cuts 7008/9940/14060 that Gurobi certifies as optimal—the first heuristic attainment of these optima. On the largest bounded-degree non-lattice instances G61 and G70 it reaches the best-known cuts with wall-clock times-to-target of 303 s and 36 s. Ablation on G70 shows both SCS and DWT are essential; scaling exponents on tile-planted lattices are lower than those reported for seven prior dynamical solvers.

Significance. If the numerical claims hold, Cosm supplies the first heuristic solutions that match Gurobi-certified optima on three long-standing large Gset spin-glass instances and multi-order-of-magnitude reductions in time-to-target on two hard non-lattice benchmarks. The combination of edge-colored switched dynamics, non-smooth finite-magnitude interactions, and a simple correlated perturbation is a concrete algorithmic contribution that is shown by ablation to be load-bearing. The work is carefully scoped to sparse bounded-degree graphs (explicitly stated in Sec. V-B), reports large trial counts, success probabilities, R99, STS and wall-clock TTT, and posts solution bitstrings for independent verification. These elements make the empirical advance reproducible and useful both for combinatorial optimization practice and for the design of future dynamical solvers.

minor comments (4)
  1. A short public reference implementation (or at least the precise C parameter files used for the Gset runs) would strengthen reproducibility; the manuscript already supplies bitstrings and detailed parameter tables, so this is a modest addition.
  2. Fig. 9 caption and surrounding text should state more explicitly that the seven comparison exponents were extracted from the arXiv version of Hou et al. and are therefore approximate; the Cosm confidence interval is already shown.
  3. In Sec. II-A the definition of the biased signum (Eq. 4) and the selected generalized gradient (Eq. 5) could be cross-referenced more clearly to the piecewise-linear potential of Eq. 2 so that readers immediately see the non-differentiable points.
  4. Appendix B lists the number of edges per color for G61/G70; a one-sentence remark that the greedy coloring already attains the chromatic index would help readers who might otherwise re-run a more expensive coloring routine.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: empirical heuristic whose claims rest on external Gurobi certification and published benchmarks, not on self-defined or fitted-as-prediction quantities.

full rationale

Cosm is presented as a constructive dynamical heuristic (circular variables, sgn-based pairwise updates, sequential conflict-free edge-colored search, dual-window twist) whose performance is measured against independent external standards: Gurobi-certified optima on G72/G77/G81, previously published best-known cuts and TTTs on G61/G70, and the Hou et al. tile-planted suite with known planted ground states. No equation defines a quantity in terms of a later-reported prediction; annealing and DWT parameters are stated as tunable solver settings, not fitted inputs re-labeled as first-principles results. Self-citations ([34], [35], [39]) archive bitstrings or prior engineering notes and are not load-bearing uniqueness theorems or smuggled ansätze. Ablation (Table VII) and the explicit sparsity limitation (Sec. V-B) are empirical, not circular. The derivation chain is therefore self-contained against external benchmarks.

Assumptions & free parameters 5 free parameters · 3 assumptions · 2 invented entities

Cosm is a heuristic whose performance claims rest on a small set of hand-chosen algorithmic parameters, standard Ising/Max-Cut definitions, and the empirical observation that bounded-degree sparsity keeps intra-sweep fluctuations moderate. No new physical entities are postulated; the free parameters are the usual annealing and perturbation knobs of a dynamical solver.

free parameters (5)
  • initial step size α0 = 14° (Gset) / 25° (tile-planted)
    Set to 14° for all Gset runs and 25° for tile-planted runs; linear ramp to zero. Chosen by hand to balance exploration and convergence.
  • DWT window width = 90 degrees
    Fixed at 90° (half the circle) after empirical testing; controls how many variables are twisted together.
  • DWT period and magnitude ratio = period 3–6, ratio 0.5–1.5
    Period 3–6 sweeps and ratio 0.5–1.5 of current αt, instance-dependent (Tables X–XI). Tuned for best success probability.
  • number of bisectors for binarization = 100
    100 equally spaced cuts of the circle; conservative choice to guarantee high-quality readout.
  • sweeps per trial = 0.2M–2M
    0.2 M–2 M depending on instance; chosen to keep success probability in a measurable range while minimizing wall-clock TTT.
assumptions (3)
  • domain assumption The Ising Hamiltonian (Eq. 1) and its Max-Cut equivalence correctly encode the combinatorial problems of interest.
    Standard; used throughout Sections I–II.
  • standard math A proper edge coloring of a bounded-degree graph can be obtained in polynomial time (greedy heuristic or lattice pattern) and yields conflict-free matchings.
    Invoked in Section II-C and Alg. 1; Vizing’s theorem guarantees chromatic index ≤ Δ+1.
  • ad hoc to paper For sparse bounded-degree graphs the cumulative angular displacement per sweep remains moderate, preserving the binary structure of the circular representation.
    Stated as a limitation in Section V-B; load-bearing for the claim that Cosm works on the tested instances but not on dense graphs.
invented entities (2)
  • Sequential Conflict-free Search (SCS)
    purpose: Replace simultaneous gradient steps by cyclic updates over edge-colored matchings so that forces never cancel inside a sub-sweep.
    Core algorithmic device introduced in Section II-C; no independent prior evidence outside this paper.
  • Dual Window Twist (DWT) perturbation
    purpose: Apply a coherent rotation to two diametrically opposite angular windows, promoting coordinated cluster motion while approximately preserving alignments.
    Novel correlated perturbation defined in Section II-D; ablation shows it is essential for reaching best-known cuts.

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Cite this review

Pith. "Pith review of Cosm: Collective Switched Motion for Fast and Accurate Sparse Ising Optimization." pith.science (2026). https://pith.science/paper/OIEHXE7K

@misc{pith2026260530355,
  author       = {Pith},
  title        = {Pith review of: Cosm: Collective Switched Motion for Fast and Accurate Sparse Ising Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OIEHXE7K}},
  note         = {Machine review of arXiv:2605.30355}
}
read the original abstract

We introduce Collective Switched Motion (Cosm), a dynamical system-based heuristic algorithm. Cosm combines locally interacting continuous circular variables with novel global coordination rules that facilitate collective dynamics. Pairwise interactions occur sequentially over a set of conflict-free edge partitions, resulting in an interaction network that switches periodically. Unlike conventional gradient-based approaches, Cosm employs structured, non-smooth switching dynamics with finite-magnitude interactions that sustain collective fluctuations and promote exploration beyond local minima. A correlated perturbation mechanism further promotes coordinated cluster motion in the circular phase space. On the three largest Ising problems from the Gset suite, which have 10,000-20,000 variables and represent 2D spin glasses, Cosm attains the optimal solutions (verified with an exact solver) heuristically for the first time. On two large bounded-degree non-lattice graph instances, Cosm reduces the state-of-the-art times-to-target from hundreds of hours to 36-303 s. Results on benchmark problems with tuned hardness suggest favorable scaling relative to previously characterized dynamical solvers. These results suggest that Cosm's synthesis of local interactions, structured switching dynamics, and global coordination provides an effective computational framework for sparse optimization.

Figures

Figures reproduced from arXiv: 2605.30355 by the authors.

Figure 1
Figure 1. Energy Functions for Ferromagnetic (FM) and Anti-Ferromagnetic [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Example of a Circular Conflict Trap. (top) Seemingly trivial 3-variable [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Example of Cosm’s Sequential Conflict-Free Search (SCS) Dynamics. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (5 more)
Figure 5
Figure 5. Figure 5: Visualization of Cosm Dynamics with a Dual Window Twist (DWT) [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: Example Cosm Dynamical System Evolution. a) Variables wrap around in the circular phase space. b) Example dynamics resulting from sequential [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: Spatial Layout of a Large Cluster of Variables (shaded) Representing [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 8
Figure 8. Figure 8: Example Energy Evolution for Cosm and Three Alternatives Tested [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: Additionally, we characterize Cosm scaling over a [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]

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Reference graph

Works this paper leans on

59 extracted references · 7 linked inside Pith · cited by 2 Pith papers

  1. [1]

    Combinatorial optimization with physics-inspired graph neural networks,

    M. J. Schuetz, J. K. Brubaker, and H. G. Katzgraber, “Combinatorial optimization with physics-inspired graph neural networks,”Nature Ma- chine Intelligence, vol. 4, no. 4, pp. 367–377, 2022

    2022

  2. [2]

    Industry applications of neutral-atom quantum computing solving independent set problems,

    J. Wurtz, P. L. Lopes, C. Gorgulla, N. Gemelke, A. Keesling, and S. Wang, “Industry applications of neutral-atom quantum computing solving independent set problems,”arXiv preprint arXiv:2205.08500, 2024

    arXiv 2024

  3. [3]

    Leveraging quantum comput- ing for accelerated classical algorithms in power systems optimization,

    R. Barrass, H. Nagarajan, and C. Coffrin, “Leveraging quantum comput- ing for accelerated classical algorithms in power systems optimization,” inIntegration of Constraint Programming, Artificial Intelligence, and Operations Research(G. Tack, ed.), (Cham), pp. 52–67, Springer Nature Switzerland, 2025

    2025

  4. [4]

    McSparse: Exact solutions of sparse maximum cut and sparse unconstrained binary quadratic optimization problems,

    J. Charfreitag, M. J ¨unger, S. Mallach, and P. Mutzel, “McSparse: Exact solutions of sparse maximum cut and sparse unconstrained binary quadratic optimization problems,” in2022 Proceedings of the Sympo- sium on Algorithm Engineering and Experiments (ALENEX), pp. 54–66, 2022

    2022

  5. [5]

    Faster exact solution of sparse MaxCut and QUBO problems,

    D. Rehfeldt, T. Koch, and Y . Shinano, “Faster exact solution of sparse MaxCut and QUBO problems,”Mathematical Programming Computa- tion, vol. 15, pp. 445–470, 2023

    2023

  6. [6]

    Solving sparse semidefinite programs using the dual scaling algorithm with an iterative solver,

    C. Choi and Y . Ye, “Solving sparse semidefinite programs using the dual scaling algorithm with an iterative solver,” tech. rep., Department of Management Sciences, University of Iowa, Iowa City, IA 52242, USA,

  7. [7]

    https://web.stanford.edu/ ∼yyye/yyye/cgsdp1.pdf

  8. [8]

    Efficient cluster algorithm for spin glasses in any space dimension,

    Z. Zhu, A. Ochoa, and H. Katzgraber, “Efficient cluster algorithm for spin glasses in any space dimension,”Physical Review Letters, vol. 115, p. 077201, 2015

    2015

Show all 59 references
  1. [9]

    High-performance combinatorial optimization based on classical mechanics,

    H. Gotoet al., “High-performance combinatorial optimization based on classical mechanics,”Science Advances, vol. 7, no. 6, 2021

    2021

  2. [10]

    Ising machines as hard- ware solvers of combinatorial optimization problems,

    N. Mohseni, P. McMahon, and T. Byrnes, “Ising machines as hard- ware solvers of combinatorial optimization problems,”Nature Reviews Physics, vol. 4, June 2022

    2022

  3. [11]

    Edge-of-chaos-enhanced quantum-inspired algorithm for combinatorial optimization,

    H. Goto, R. Hidaka, and K. Tatsumura, “Edge-of-chaos-enhanced quantum-inspired algorithm for combinatorial optimization,”Phys. Rev. Appl., vol. 25, p. 044011, Apr 2026

    2026

  4. [12]

    Direct comparison of stochastic driven nonlinear dynamical systems for combinatorial opti- mization,

    J. Hou, A. Barzegar, and H. G. Katzgraber, “Direct comparison of stochastic driven nonlinear dynamical systems for combinatorial opti- mization,”Physical Review E, vol. 112, no. 3, p. 035301, 2025

    2025

  5. [13]

    On the emerging potential of quantum annealing hardware for combinatorial optimization,

    B. Tasseff, T. Albash, Z. Morrell, M. Vuffray, A. Y . Lokhov, S. Misra, and C. Coffrin, “On the emerging potential of quantum annealing hardware for combinatorial optimization,”Journal of Heuristics, vol. 30, no. 5, pp. 325–358, 2024

    2024

  6. [14]

    Accuracy and performance evaluation of quantum, classical and hybrid solvers for the max-cut problem,

    J. V odeb, V . Erˇzen, T. Hrga, and J. Povh, “Accuracy and performance evaluation of quantum, classical and hybrid solvers for the max-cut problem,”arXiv preprint arXiv:2412.07460, 2024

    2024 arXiv

  7. [15]

    Performance of quantum an- nealing inspired algorithms for combinatorial optimization problems,

    Q.-G. Zeng, X.-P. Cui, B. Liu,et al., “Performance of quantum an- nealing inspired algorithms for combinatorial optimization problems,” Communications Physics, vol. 7, p. 249, 2024

    2024

  8. [16]

    Scaling advantage in approximate op- timization with quantum annealing,

    H. Munoz-Bauza and D. Lidar, “Scaling advantage in approximate op- timization with quantum annealing,”Physical Review Letters, vol. 134, 2025

    2025

  9. [17]

    Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware,

    J. Weidenfeller, L. C. Valor, J. Gacon, C. Tornow, L. Bello, S. Woerner, and D. J. Egger, “Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware,”Quantum, vol. 6, p. 870, 2022

    2022

  10. [18]

    A review on quantum approximate optimization algorithm and its variants,

    K. Blekos, D. Brand, A. Ceschini, C.-H. Chou, R.-H. Li, K. Pandya, and A. Summer, “A review on quantum approximate optimization algorithm and its variants,”Physics Reports, vol. 1068, pp. 1–66, 2024

    2024

  11. [19]

    Viewing vanilla quantum annealing through spin glasses,

    H. G. Katzgraber, “Viewing vanilla quantum annealing through spin glasses,”Quantum Science and Technology, vol. 3, no. 3, p. 030505, 2018

    2018

  12. [20]

    Giorgio Parisi – Facts – 2021

    Nobel Prize Outreach, “Giorgio Parisi – Facts – 2021.” https://www. nobelprize.org/prizes/physics/2021/parisi/facts/, 2026. Accessed: 2026- 04-10. 13

    2021

  13. [21]

    Spin-glass dynamics: Experiment, theory, and simulation,

    E. Dahlberg, I. Gonz ´alez-Adalid Pemart ´ın, E. Marinari, G. Parisi, F. Ricci-Tersenghi, V . Martin-Mayor, J. Moreno-Gordo, R. Orbach, I. Paga, J. Ruiz-Lorenzo,et al., “Spin-glass dynamics: Experiment, theory, and simulation,”Reviews of Modern Physics, vol. 97, no. 4, p. 045005, 2025

    2025

  14. [22]

    OIM: Oscillator-based Ising machines for solving combinatorial optimisation problems,

    T. Wang and J. Roychowdhury, “OIM: Oscillator-based Ising machines for solving combinatorial optimisation problems,” inInternational Con- ference on Unconventional Computation and Natural Computation, pp. 232–256, Springer, 2019

    2019

  15. [23]

    Coupled oscillators for computing: A review and perspective,

    G. Csaba and W. Porod, “Coupled oscillators for computing: A review and perspective,”Applied physics reviews, vol. 7, no. 1, 2020

    2020

  16. [24]

    Ring oscillator-based Ising machine system,

    K. M. Zick, “Ring oscillator-based Ising machine system,” January 2023. US Patent US11545963B1

    2023

  17. [25]

    Programmable and reconfigurable photonic simulator for classical XY models,

    J. Ouyang, Y . Liao, X. Feng, Y . Li, K. Cui, F. Liu, H. Sun, W. Zhang, and Y . Huang, “Programmable and reconfigurable photonic simulator for classical XY models,”Physical Review Applied, vol. 22, no. 2, p. L021001, 2024

    2024

  18. [26]

    Non-binary dynamical Ising machines for combinatorial optimization,

    A. Shukla, M. Erementchouk, and P. Mazumder, “Non-binary dynamical Ising machines for combinatorial optimization,”Physica D: Nonlinear Phenomena, vol. 481, p. 134809, 2025

    2025

  19. [27]

    A novel oscillator Ising ma- chine coupling scheme for high-quality optimization,

    S. Sreedhara and J. Roychowdhury, “A novel oscillator Ising ma- chine coupling scheme for high-quality optimization,” inInternational Conference on Unconventional Computation and Natural Computation, pp. 203–218, Springer, 2024

    2024

  20. [28]

    Rank-two relaxation heuristics for MAX CUT and other binary quadratic programs,

    S. Burer, R. D. C. Monteiro, and Y . Zhang, “Rank-two relaxation heuristics for MAX CUT and other binary quadratic programs,”SIAM Journal on Optimization, vol. 12, pp. 503–521, 2002

    2002

  21. [29]

    A cluster Monte Carlo algorithm for 2-dimensional spin glasses,

    J. Houdayer, “A cluster Monte Carlo algorithm for 2-dimensional spin glasses,”The European Physical Journal B-Condensed Matter and Complex Systems, vol. 22, no. 4, pp. 479–484, 2001

    2001

  22. [30]

    Record acceleration of the two-dimensional Ising model using a high-performance wafer-scale engine,

    D. Van Essendelft, H. Almolyki, W. Shi, T. Jordan, M.-Y . Wang, and W. A. Saidi, “Record acceleration of the two-dimensional Ising model using a high-performance wafer-scale engine,”Computer Physics Communications, vol. 315, p. 109734, 2025

    2025

  23. [31]

    Gset benchmark problems

    “Gset benchmark problems.” https://web.stanford.edu/ ∼yyye/yyye/Gset/. Retrieved April 2025

    2025

  24. [32]

    Mixed linear and semidefinite pro- gramming for combinatorial and quadratic optimization,

    S. J. Benson, Y . Ye, and X. Zhang, “Mixed linear and semidefinite pro- gramming for combinatorial and quadratic optimization,”Optimization Methods and Software, vol. 11, no. 1–4, pp. 515–544, 1999

    1999

  25. [33]

    On the computational complexity of Ising spin glass models,

    F. Barahona, “On the computational complexity of Ising spin glass models,”Journal of Physics A: Mathematical and General, vol. 15, no. 10, pp. 3241–3253, 1982

    1982

  26. [34]

    Domain-wall excitations in the two- dimensional Ising spin glass,

    H. Khoshbakht and M. Weigel, “Domain-wall excitations in the two- dimensional Ising spin glass,”Physical Review B, vol. 97, no. 6, p. 064410, 2018

    2018

  27. [35]

    Improved Sparse Ising Optimization,

    K. M. Zick, “Improved Sparse Ising Optimization,”arXiv preprint arXiv:2311.09275, 2023

    2023 arXiv

  28. [36]

    Performance report of heuristic algorithm that cracked the largest Gset Ising problems (G81 cut=14060),

    K. M. Zick, “Performance report of heuristic algorithm that cracked the largest Gset Ising problems (G81 cut=14060),”arXiv preprint arXiv:2505.18508, 2025

    2025 arXiv

  29. [37]

    Analog optical computer for AI inference and combinatorial optimization,

    K. P. Kalinin, J. Gladrow, J. Chu, J. H. Clegg, D. Cletheroe, D. J. Kelly, B. Rahmani, G. Brennan, B. Canakci, F. Falck,et al., “Analog optical computer for AI inference and combinatorial optimization,”Nature, vol. 645, no. 8080, pp. 354–361, 2025

    2025

  30. [38]

    Teams of global equilibrium search algorithms for solving the weighted maximum cut problem in parallel,

    V . Shyloet al., “Teams of global equilibrium search algorithms for solving the weighted maximum cut problem in parallel,”Cybernetics and Systems Analysis, vol. 51, pp. 16–24, 2015

    2015

  31. [39]

    Algorithm portfolios and teams in parallel optimization,

    V . P. Shylo and O. V . Shylo, “Algorithm portfolios and teams in parallel optimization,” inOptimization Methods and Applications(S. Butenko, P. Pardalos, and V . Shylo, eds.), vol. 130 ofSpringer Optimization and Its Applications, Cham: Springer, 2017

    2017

  32. [40]

    Systems and method for solving spin glasses and other sparse Ising problems,

    K. M. Zick, “Systems and method for solving spin glasses and other sparse Ising problems,” February 2024. US Patent application US20250258886A1

    2024

  33. [41]

    A large population island framework for the unconstrained binary quadratic problem,

    O. Goudet, A. Go ¨effon, and J.-K. Hao, “A large population island framework for the unconstrained binary quadratic problem,”Computers & Operations Research, vol. 168, p. 106684, 2024

    2024

  34. [42]

    Monte Carlo policy gradi- ent method for binary optimization,

    C. Chen, R. Chen, T. Li, R. Ao, and Z. Wen, “Monte Carlo policy gradi- ent method for binary optimization,”arXiv preprint arXiv:2307.00783, 2023

    2023 arXiv

  35. [43]

    A Monte Carlo policy gradient method with local search for binary optimization: C. chen et al.,

    C. Chen, R. Chen, T. Li, R. Ao, and Z. Wen, “A Monte Carlo policy gradient method with local search for binary optimization: C. chen et al.,”Mathematical Programming, pp. 1–57, 2025

    2025

  36. [44]

    API Reference - Fixstars Am- plify Annealing Engine

    Fixstars Amplify Corporation, “API Reference - Fixstars Am- plify Annealing Engine.” https://amplify.fixstars.com/en/docs/amplify/ v1/amplify ae.html, 2025

    2025

  37. [45]

    Enhanced open-source scatter search algorithm for solving quadratic unconstrained binary optimization problems,

    D. Liu, W. Yang, H. Wang, Y . Du, Y . Wang, Z. L ¨u, and J.-K. Hao, “Enhanced open-source scatter search algorithm for solving quadratic unconstrained binary optimization problems,”Computers & Operations Research, vol. 182, p. 107137, 2025

    2025

  38. [46]

    Breakout Local Search for the Max-Cut problem,

    U. Benlic and J.-K. Hao, “Breakout Local Search for the Max-Cut problem,”Engineering Applications of Artificial Intelligence, vol. 26, Mar. 2013

    2013

  39. [47]

    Chook–a comprehensive suite for generating binary optimization problems with planted solutions,

    D. Perera, I. Akpabio, F. Hamze, S. Mandra, N. Rose, M. Aramon, and H. G. Katzgraber, “Chook–a comprehensive suite for generating binary optimization problems with planted solutions,”arXiv preprint arXiv:2005.14344, 2020

    2005 arXiv

  40. [48]

    Computational hardness of spin-glass problems with tile-planted solu- tions,

    D. Perera, F. Hamze, J. Raymond, M. Weigel, and H. G. Katzgraber, “Computational hardness of spin-glass problems with tile-planted solu- tions,”Physical Review E, vol. 101, no. 2, p. 023316, 2020

    2020

  41. [49]

    Direct comparison of stochastic driven nonlinear dynamical systems for combinatorial opti- mization,

    J. Hou, A. Barzegar, and H. G. Katzgraber, “Direct comparison of stochastic driven nonlinear dynamical systems for combinatorial opti- mization,”arXiv preprint arXiv:2503.15427, 2025

    2025 arXiv

  42. [50]

    Pushing the boundary of quantum advantage in hard combinato- rial optimization with probabilistic computers,

    S. Chowdhury, N. A. Aadit, A. Grimaldi, E. Raimondo, A. Raut, P. A. Lott, J. H. Mentink, M. M. Rams, F. Ricci-Tersenghi, M. Chiappini, et al., “Pushing the boundary of quantum advantage in hard combinato- rial optimization with probabilistic computers,”Nature Communications, v...

    2025

  43. [51]

    Searching for spin glass ground states through deep reinforcement learning,

    C. Fan, M. Shen, Z. Nussinov, Z. Liu, Y . Sun, and Y .-Y . Liu, “Searching for spin glass ground states through deep reinforcement learning,”Nature communications, vol. 14, no. 1, p. 725, 2023

    2023

  44. [52]

    Guiding the self-organization of cyber-physical sys- tems,

    C. Gershenson, “Guiding the self-organization of cyber-physical sys- tems,”Frontiers in Robotics and AI, vol. 7, p. 41, 2020

    2020

  45. [53]

    Dynamic neighbourhood cellular automata,

    S. Dantchev, “Dynamic neighbourhood cellular automata,”The Com- puter Journal, vol. 54, no. 1, pp. 26–30, 2011

    2011

  46. [54]

    Blinking model and synchronization in small-world networks with a time-varying coupling,

    I. V . Belykh, V . N. Belykh, and M. Hasler, “Blinking model and synchronization in small-world networks with a time-varying coupling,” Physica D: Nonlinear Phenomena, vol. 195, no. 1-2, pp. 188–206, 2004

    2004

  47. [55]

    Frequency-dependent synchro- nization in blinking networks: insights from Hindmarsh–Rose, Lorenz, and R ¨ossler systems,

    X. Wang, Z. Wang, S. Dang, and J. Dai, “Frequency-dependent synchro- nization in blinking networks: insights from Hindmarsh–Rose, Lorenz, and R ¨ossler systems,”The European Physical Journal B, vol. 98, no. 8, p. 163, 2025

    2025

  48. [56]

    Chaotic chattering in sliding mode control systems,

    A. Rehan, I. Boiko, and Y . Zweiri, “Chaotic chattering in sliding mode control systems,”IEEE Transactions on Automatic Control, vol. 69, no. 11, pp. 7925–7931, 2024

    2024

  49. [57]

    Quadratic unconstrained binary optimi- sation for training and regularisation of binary neural networks,

    J. C. Villumsen and Y . Sugita, “Quadratic unconstrained binary optimi- sation for training and regularisation of binary neural networks,”arXiv preprint arXiv:2601.00449, 2026

    2026

  50. [58]

    Co-design of free-space metasurface optical neuromorphic classifiers for high performance,

    F. L ´eonard, A. S. Backer, E. J. Fuller, C. Teeter, and C. M. Vineyard, “Co-design of free-space metasurface optical neuromorphic classifiers for high performance,”ACS Photonics, vol. 8, no. 7, pp. 2103–2111, 2021

    2021

  51. [59]

    Energy landscapes of combinatorial optimization in Ising machines,

    D. Dobrynin, A. Renaudineau, M. Hizzani, D. Strukov, M. Mohseni, and J. P. Strachan, “Energy landscapes of combinatorial optimization in Ising machines,”Physical Review E, vol. 110, no. 4, p. 045308, 2024. BIOGRAPHYSECTION Kenneth M. Zick, Ph.D.is the Research Director of Tran...

    2024

Pith tools

Reviewed July 12, 2026 · model on record in the stance chip above.