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arxiv: 2604.21961 · v1 · submitted 2026-04-23 · 💻 cs.LO · cs.AI· cs.SC

Recognition: unknown

A general optimization solver based on OP-to-MaxSAT reduction

Yuxin Zhao , Han Huang , Zhifeng Hao
Authors on Pith no claims yet

Pith reviewed 2026-05-08 13:45 UTC · model grok-4.3

classification 💻 cs.LO cs.AIcs.SC
keywords optimizationMaxSATreductiongeneral solverGOREDautomated methodsolution quality
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0 comments X

The pith

An automated reduction to MaxSAT instances allows a single solver to address many types of optimization problems.

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

The paper proposes an automated OP-to-MaxSAT reduction that converts optimization problems into MaxSAT problems in polynomial time. This enables the GORED solver to use existing MaxSAT technology to solve a variety of optimization problems that previously required specialized algorithms. Experiments across 136 instances from 11 problem types show that the solutions match the quality of traditional methods without significant differences. The work aims to replace the need for custom solvers with a unified reduction-based approach.

Core claim

We introduce an automated reduction method from optimization problems to MaxSAT and build the GORED solver on it. GORED reduces optimization problems to MaxSAT instances in polynomial time and solves them with a state-of-the-art MaxSAT solver. Validation on 136 instances across 11 optimization problem types shows successful solving with solution quality comparable to existing specialized methods, with no statistically significant differences.

What carries the argument

The automated OP-to-MaxSAT reduction, which transforms arbitrary optimization problems into MaxSAT instances while running in polynomial time and preserving solution optimality.

If this is right

  • Multiple optimization problem types can be solved using one general solver instead of separate specialized ones.
  • Improvements to MaxSAT solvers will automatically improve performance on a broad range of optimization tasks.
  • The focus of optimization research can shift toward better reduction methods and MaxSAT algorithms.
  • New optimization problems can be addressed by developing the reduction rather than a full new solver.

Where Pith is reading between the lines

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

  • Developers in fields like engineering or economics could apply optimization more easily without expertise in custom algorithms.
  • This reduction approach might extend to other constraint satisfaction solvers beyond MaxSAT.
  • Testing on more problem types could reveal limits or further generalizations of the method.

Load-bearing premise

That an automated reduction from any optimization problem type to MaxSAT can be constructed in polynomial time and that the resulting MaxSAT instances can be solved efficiently to yield optimal or near-optimal solutions.

What would settle it

A counterexample optimization problem where either no polynomial-time automated reduction to MaxSAT exists, or the MaxSAT solver returns solutions that are provably far from optimal for that problem.

read the original abstract

Optimization problems are fundamental in diverse fields, such as engineering, economics, and scientific computing. However, current algorithms are mostly designed for specific problem types and exhibit limited generality in solving multiple types of optimization problems. To enhance generality, we propose an automated reduction method named OP-to-MaxSAT reduction and a general optimization solver based on OP-to-MaxSAT reduction (GORED). GORED unifies the solving of multiple types of optimization problems by reducing the problems from optimization problems to MaxSAT instances in polynomial time and solving them using the state-of-the-art MaxSAT solver. The generality and solution quality of GORED are validated through experiments on 136 instances across 11 types of optimization problems. Experimental results demonstrate that GORED not only successfully solves a wide range of optimization problems but also yields solutions comparable in quality to those from existing methods, with no statistically significant differences observed. By introducing automated reduction, this work shifts the paradigm of optimization solvers from designing specialized algorithms for each problem type to employing a single algorithm for diverse problems. As a result, advances in this single algorithm can now drive progress in a wide range of optimization problems across various domains.

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 / 1 minor

Summary. The paper proposes GORED, a general optimization solver that performs an automated reduction from arbitrary optimization problems (OP) to MaxSAT instances in polynomial time, solves the resulting instances with a state-of-the-art MaxSAT solver, and maps solutions back to the original OP. It validates generality and solution quality via experiments on 136 instances across 11 optimization problem types, claiming no statistically significant quality differences versus existing specialized methods.

Significance. If the automated OP-to-MaxSAT reduction is correct, general across arbitrary problem types, polynomial-time, and solution-preserving, the work would offer a genuine unification of optimization solving under a single algorithmic paradigm, allowing MaxSAT advances to propagate to many domains. The reported experimental coverage of 11 distinct problem types would be a positive indicator of breadth, though the absence of the reduction construction itself prevents assessment of whether this potential is realized.

major comments (2)
  1. [Abstract] Abstract: the central claim that an automated OP-to-MaxSAT reduction exists which applies to arbitrary optimization problem types, runs in polynomial time, correctly encodes objectives and constraints, and produces MaxSAT instances tractable for current solvers is load-bearing for the entire contribution, yet the manuscript supplies no reduction construction, encoding scheme, complexity argument, or correctness proof.
  2. [Experimental validation] Experimental validation (implied section reporting results on 136 instances): the claim of comparable solution quality with 'no statistically significant differences' is unsupported because no baseline solvers, statistical test procedure, p-value thresholds, or per-problem-type reduction details are provided, making it impossible to evaluate whether the reduction preserves optimality or near-optimality as asserted.
minor comments (1)
  1. [Abstract] Abstract: the sentence 'reducing the problems from optimization problems to MaxSAT instances' contains redundant phrasing that should be tightened for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. We address each major comment below and will revise the manuscript to strengthen the presentation of the core technical contributions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that an automated OP-to-MaxSAT reduction exists which applies to arbitrary optimization problem types, runs in polynomial time, correctly encodes objectives and constraints, and produces MaxSAT instances tractable for current solvers is load-bearing for the entire contribution, yet the manuscript supplies no reduction construction, encoding scheme, complexity argument, or correctness proof.

    Authors: We agree that a self-contained description of the reduction is required to substantiate the central claim. The current manuscript focuses on the overall framework and experimental outcomes; we will add a new section that formally defines the OP-to-MaxSAT encoding for arbitrary optimization problems, proves that the reduction runs in polynomial time, establishes correctness (solution preservation), and discusses tractability under current MaxSAT solvers. revision: yes

  2. Referee: [Experimental validation] Experimental validation (implied section reporting results on 136 instances): the claim of comparable solution quality with 'no statistically significant differences' is unsupported because no baseline solvers, statistical test procedure, p-value thresholds, or per-problem-type reduction details are provided, making it impossible to evaluate whether the reduction preserves optimality or near-optimality as asserted.

    Authors: We accept that the experimental section must be expanded for reproducibility and statistical rigor. In the revision we will list the exact baseline solvers and versions, specify the statistical procedure (Wilcoxon signed-rank test at p < 0.05), report all p-values per problem type, and include per-instance reduction details together with optimality-gap tables so that readers can directly verify that solution quality is preserved. revision: yes

Circularity Check

0 steps flagged

No circularity: new reduction method with external validation

full rationale

The paper introduces a novel automated OP-to-MaxSAT reduction as its core technical contribution, then applies an existing MaxSAT solver and validates generality via experiments on 136 instances from 11 distinct problem types. No step equates the claimed reduction or its polynomial-time guarantee to a fitted parameter, self-citation, or definitional loop; the reduction is presented as a constructive method whose correctness is checked empirically rather than assumed by construction. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; it contains no explicit free parameters, axioms, or invented entities. The reduction is asserted to exist and to run in polynomial time, but no supporting definitions or assumptions are stated.

pith-pipeline@v0.9.0 · 5500 in / 1277 out tokens · 64422 ms · 2026-05-08T13:45:44.155354+00:00 · methodology

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Reference graph

Works this paper leans on

76 extracted references · 2 canonical work pages

  1. [1]

    & Hao, Z

    Huang, H., Yang, S., Li, X. & Hao, Z. An embedded hamiltonian graph-guided heuristic algorithm for two-echelon vehicle routing problem.IEEE Transactions on Cybernetics52, 5695–5707 (2022)

    2022

  2. [2]

    Wang, H.et al.A hybrid fuzzy C-means heuristic approach for two-echelon vehicle routing with simultaneous pickup and delivery of multicommodity.IEEE Transactions on Fuzzy Systems 33, 218–230 (2025)

    2025

  3. [3]

    Zou, Y., Hao, J.-K. & Wu, Q. A two-individual evolutionary algorithm for cumulative capac- itated vehicle routing with single and multiple depots.IEEE Transactions on Evolutionary Computation29, 505–518 (2025)

    2025

  4. [4]

    K., Gupta, P., Khaitan, A

    Mehlawat, M. K., Gupta, P., Khaitan, A. & Pedrycz, W. A hybrid intelligent approach to integrated fuzzy multiple depot capacitated green vehicle routing problem with split delivery and vehicle selection.IEEE Transactions on Fuzzy Systems28, 1155–1166 (2020)

    2020

  5. [5]

    Feng, L.et al.Solving generalized vehicle routing problem with occasional drivers via evolutionary multitasking.IEEE Transactions on Cybernetics51, 3171–3184 (2021)

    2021

  6. [6]

    & Martin, S

    Bertsimas, D., Delarue, A. & Martin, S. Optimizing schools’ start time and bus routes. Proceedings of the National Academy of Sciences116, 5943–5948 (2019)

    2019

  7. [7]

    & Chen, Z

    Xing, Q., Xu, Y. & Chen, Z. A bilevel graph reinforcement learning method for electric vehicle fleet charging guidance.IEEE Transactions on Smart Grid14, 3309–3312 (2023)

    2023

  8. [8]

    & Zhao, Y

    Yin, F. & Zhao, Y. Wasserstein distributionally robust equilibrium optimization under random fuzzy environment for the electric vehicle routing problem.IEEE Transactions on Fuzzy Systems33, 1120–1132 (2025)

    2025

  9. [9]

    & Zhang, L

    An, Y., Chen, X., Gao, K., Li, Y. & Zhang, L. Multiobjective flexible job-shop reschedul- ing with new job insertion and machine preventive maintenance.IEEE Transactions on Cybernetics53, 3101–3113 (2023)

    2023

  10. [10]

    & Hao, Z

    Su, J., Huang, H., Li, G., Li, X. & Hao, Z. Self-organizing neural scheduler for the flexible job shop problem with periodic maintenance and mandatory outsourcing constraints.IEEE Transactions on Cybernetics53, 5533–5544 (2023)

    2023

  11. [11]

    & Dong, C

    Li, R., Gong, W., Wang, L., Lu, C. & Dong, C. Co-evolution with deep reinforcement learning for energy-aware distributed heterogeneous flexible job shop scheduling.IEEE Transactions on Systems, Man, and Cybernetics: Systems54, 201–211 (2024). 16

    2024

  12. [12]

    & Wang, L

    Pan, Z., Lei, D. & Wang, L. A Bi-population evolutionary algorithm with feedback for energy-efficient fuzzy flexible job shop scheduling.IEEE Transactions on Systems, Man, and Cybernetics: Systems52, 5295–5307 (2022)

    2022

  13. [13]

    & Weng, P.-H

    Liu, C.-L., Tseng, C.-J. & Weng, P.-H. Dynamic job-shop scheduling via graph attention networks and deep reinforcement learning.IEEE Transactions on Industrial Informatics20, 8662–8672 (2024)

    2024

  14. [14]

    Lei, K.et al.Large-Scale Dynamic Scheduling for Flexible Job-Shop With Random Arrivals of New Jobs by Hierarchical Reinforcement Learning.IEEE Transactions on Industrial Informatics20, 1007–1018 (2024)

    2024

  15. [15]

    Kuang, Y.et al.Accelerate presolve in large-scale linear programming via reinforcement learning.IEEE Transactions on Pattern Analysis and Machine Intelligence47, 6660–6672 (2025)

    2025

  16. [16]

    Mo, P.et al.Energy-efficient train scheduling and rolling stock circulation planning in a metro line: A linear programming approach.IEEE Transactions on Intelligent Transportation Systems21, 3621–3633 (2020)

    2020

  17. [17]

    & Wen, Z

    Wang, R., Zhang, C., Pu, S., Gao, J. & Wen, Z. A customized augmented lagrangian method for block-structured integer programming.IEEE Transactions on Pattern Analysis and Machine Intelligence46, 9439–9455 (2024)

    2024

  18. [18]

    & Sodhi, B

    Dash, S., Sodhi, R. & Sodhi, B. An appliance load disaggregation scheme using automatic state detection enabled enhanced integer programming.IEEE Transactions on Industrial Informatics17, 1176–1185 (2021)

    2021

  19. [19]

    Shen, Z.-S.et al.Free-energy machine for combinatorial optimization.Nature Computational Science5, 322–332 (2025)

    2025

  20. [20]

    Lam, B. S. Y. & Liew, A. W.-C. A fast binary quadratic programming solver based on stochas- tic neighborhood search.IEEE Transactions on Pattern Analysis and Machine Intelligence 44, 32–49 (2022)

    2022

  21. [21]

    Shir, O. M. & Emmerich, M. Multiobjective mixed-integer quadratic models: A study on math- ematical programming and evolutionary computation.IEEE Transactions on Evolutionary Computation29, 661–675 (2025)

    2025

  22. [22]

    & Yen, G

    Duan, J., He, Z. & Yen, G. G. Robust multiobjective optimization for vehicle routing problem with time windows.IEEE Transactions on Cybernetics52, 8300–8314 (2022)

    2022

  23. [23]

    & Abdalhaq, B

    Awad, A., Hawash, A. & Abdalhaq, B. A genetic algorithm (GA) and swarm-based binary deci- sion diagram (BDD) reordering optimizer reinforced with recent operators.IEEE Transactions on Evolutionary Computation27, 535–549 (2023)

    2023

  24. [24]

    & Wang, R

    Li, J., Liu, R. & Wang, R. Elastic strategy-based adaptive genetic algorithm for solving dynamic vehicle routing problem with time windows.IEEE Transactions on Intelligent Transportation Systems24, 13930–13947 (2023)

    2023

  25. [25]

    & Sierpinski, G

    Krol, A. & Sierpinski, G. Application of a genetic algorithm with a fuzzy objective function for optimized siting of electric vehicle charging devices in urban road networks.IEEE Transactions on Intelligent Transportation Systems23, 8680–8691 (2022)

    2022

  26. [26]

    Liu, S.-C.et al.Many-objective job-shop scheduling: A multiple populations for multiple objectives-based genetic algorithm approach.IEEE Transactions on Cybernetics53, 1460– 1474 (2023)

    2023

  27. [27]

    He, L.et al.Multiobjective optimization of energy-efficient JOB-shop scheduling with dynamic reference point-based fuzzy relative entropy.IEEE Transactions on Industrial Informatics 18, 600–610 (2022). 17

    2022

  28. [28]

    & Zhou, A

    Li, B., Zhang, Y., Yang, P., Yao, X. & Zhou, A. A two-population algorithm for large- scale multiobjective optimization based on fitness-aware operator and adaptive environmental selection.IEEE Transactions on Evolutionary Computation29, 631–645 (2025)

    2025

  29. [29]

    & Hao, Z

    Huang, H., Xu, Y., Xiang, Y. & Hao, Z. Correlation-based dynamic allocation scheme of fitness evaluations for constrained evolutionary optimization.IEEE Transactions on Evolutionary Computation28, 1250–1264 (2024)

    2024

  30. [30]

    & Hao, Z

    Yang, S., Huang, H., Luo, F., Xu, Y. & Hao, Z. Local-diversity evaluation assignment strat- egy for decomposition-based multiobjective evolutionary algorithm.IEEE Transactions on Systems, Man, and Cybernetics: Systems53, 1697–1709 (2023)

    2023

  31. [31]

    A., Z˘ avoianu, A.-C

    Han, K., Christie, L. A., Z˘ avoianu, A.-C. & McCall, J. A. W. Exploring representations for optimizing connected autonomous vehicle routes in multi-modal transport networks using evolutionary algorithms.IEEE Transactions on Intelligent Transportation Systems25, 10790– 10801 (2024)

    2024

  32. [32]

    & Pedrycz, W

    Gao, D., Wang, G.-G. & Pedrycz, W. Solving fuzzy job-shop scheduling problem using DE algorithm improved by a selection mechanism.IEEE Transactions on Fuzzy Systems28, 3265–3275 (2020)

    2020

  33. [33]

    & Bartczuk, L

    Dziwinski, P. & Bartczuk, L. A new hybrid particle swarm optimization and genetic algorithm method controlled by fuzzy logic.IEEE Transactions on Fuzzy Systems28, 1140–1154 (2020)

    2020

  34. [34]

    & Yang, Q

    Dai, S.-H., Jia, Y.-H., Chen, W.-N., Mei, Y. & Yang, Q. Multistage particle swarm opti- mization for heterogeneous multipoint dynamic aggregation.IEEE Transactions on Systems, Man, and Cybernetics: Systems55, 4614–4628 (2025)

    2025

  35. [35]

    & Wang, J.-J

    Han, H.-G., Xu, Z.-A. & Wang, J.-J. A novel set-based discrete particle swarm optimization for wastewater treatment process effluent scheduling.IEEE Transactions on Cybernetics54, 5394–5406 (2024)

    2024

  36. [36]

    Zouari, M.et al.PSO-based adaptive hierarchical interval type-2 fuzzy knowledge representa- tion system (PSO-AHIT2FKRS) for travel route guidance.IEEE Transactions on Intelligent Transportation Systems23, 804–818 (2022)

    2022

  37. [37]

    & Wang, L

    Zhang, L., Oh, S.-K., Pedrycz, W., Yang, B. & Wang, L. A promotive particle swarm optimizer with double hierarchical structures.IEEE Transactions on Cybernetics52, 13308–13322 (2022)

    2022

  38. [38]

    & Cai, S.Solving set cover and dominating set via maximum satisfiability

    Lei, Z. & Cai, S.Solving set cover and dominating set via maximum satisfiability. In Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 34, 1569–1576 (2020)

    2020

  39. [39]

    & Meel, K

    Ciampiconi, L., Ghosh, B., Scarlett, J. & Meel, K. S.A MaxSAT-based framework for group testing. In Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 34, 10144–10152 (2020)

    2020

  40. [40]

    Qubit mapping and routing via MaxSAT

    Molavi, A.et al. Qubit mapping and routing via MaxSAT. In 2022 55th IEEE/ACM International Symposium on Microarchitecture (MICRO), 1078–1091 (2022)

    2022

  41. [41]

    Beasley, J. E. Or-library: Distributing test problems by electronic mail.Journal of the Operational Research Society41, 1069–1072 (1990)

    1990

  42. [42]

    Tsplib—a traveling salesman problem library.ORSA Journal on Computing3, 376–384 (1991)

    Reinelt, G. Tsplib—a traveling salesman problem library.ORSA Journal on Computing3, 376–384 (1991)

    1991

  43. [43]

    European Journal of Operational Research257, 845–858 (2017)

    Uchoa, E.et al.New benchmark instances for the capacitated vehicle routing problem. European Journal of Operational Research257, 845–858 (2017)

    2017

  44. [44]

    Benchmarks for basic scheduling problems.European Journal of Operational Research64, 278–285 (1993)

    Taillard, E. Benchmarks for basic scheduling problems.European Journal of Operational Research64, 278–285 (1993). 18

    1993

  45. [45]

    & Rendl, F

    Burkard, R., Karisch, S. & Rendl, F. Qaplib-a quadratic assignment problem library.European Journal of Operational Research55, 115–119 (1991)

    1991

  46. [46]

    Suganthan, P.et al.Problem definitions and evaluation criteria for the cec 2005 special session on real-parameter optimization.Natural Computing341-357(2005)

    2005

  47. [47]

    M., Le Bodic, P

    Kazachkov, A. M., Le Bodic, P. & Sankaranarayanan, S. An abstract model for branch and cut.Mathematical Programming206, 175–202 (2024)

    2024

  48. [48]

    Galias, Z. Deterministic branch and cut algorithm for multiobjective optimization of protective device allocation in radial distribution systems.IEEE Transactions on Industrial Informatics 21, 2344–2353 (2025)

    2025

  49. [49]

    B., Coelho, L

    Castellucci, P. B., Coelho, L. C. & Darvish, M. A new branch-and-benders-cut algorithm for the time-dependent vehicle routing problem.Expert Systems with Applications265, 125996 (2025)

    2025

  50. [50]

    & Dai, F.-A

    Zhang, Z., Zhao, Q. & Dai, F.-A. A warm-start strategy in interior point methods for shrinking horizon model predictive control with variable discretization step.IEEE Transactions on Automatic Control68, 3830–3837 (2023)

    2023

  51. [51]

    Lu, W., Liu, M., Lin, S. & Li, L. Fully decentralized optimal power flow of multi-area inter- connected power systems based on distributed interior point method.IEEE Transactions on Power Systems33, 901–910 (2018)

    2018

  52. [52]

    & Chen, J

    Huang, M. & Chen, J. Proactive mobility load balancing through interior-point policy opti- mization for open radio access networks.IEEE Transactions on Mobile Computing24, 500–506 (2025)

    2025

  53. [53]

    & Staudigl, M

    Dvurechensky, P. & Staudigl, M. Hessian barrier algorithms for non-convex conic optimization. Mathematical Programming209, 171–229 (2025)

    2025

  54. [54]

    J., Kokkolaras, M

    Dzahini, K. J., Kokkolaras, M. & Le Digabel, S. Constrained stochastic blackbox optimization using a progressive barrier and probabilistic estimates.Mathematical Programming198, 675–732 (2023)

    2023

  55. [55]

    & Freund, R

    Zhao, R. & Freund, R. M. Analysis of the frank–wolfe method for convex composite opti- mization involving a logarithmically-homogeneous barrier.Mathematical Programming199, 123–163 (2023)

    2023

  56. [56]

    & Seada, H

    Blank, J., Deb, K., Dhebar, Y., Bandaru, S. & Seada, H. Generating well-spaced points on a unit simplex for evolutionary many-objective optimization.IEEE Transactions on Evolutionary Computation25, 48–60 (2021)

    2021

  57. [57]

    Xu, J.et al.Scaled simplex representation for subspace clustering.IEEE Transactions on Cybernetics51, 1493–1505 (2021)

    2021

  58. [58]

    IBM ILOG CPLEX Optimization Studio 22 (2024)

    IBM. IBM ILOG CPLEX Optimization Studio 22 (2024). https://www.ibm.com/products/ ilog-cplex-optimization-studio. Accessed 15 July 2025

    2024

  59. [59]

    Gurobi 12.0 (2025)

    Gurobi Optimization. Gurobi 12.0 (2025). https://docs.gurobi.com/12.0/. Accessed 15 July 2025

    2025

  60. [60]

    https://optimization-online

    Suresh Bolusaniet al.The SCIP optimization suite 9.0 (2024). https://optimization-online. org/?p=25734. Accessed 15 July 2025

    2024

  61. [61]

    A., Nekoukar, V., Garcia, C

    Davari, S. A., Nekoukar, V., Garcia, C. & Rodriguez, J. Online weighting factor optimization by simplified simulated annealing for finite set predictive control.IEEE Transactions on Industrial Informatics17, 31–40 (2021)

    2021

  62. [62]

    Onizawa, N., Katsuki, K., Shin, D., Gross, W. J. & Hanyu, T. Fast-converging simulated annealing for ising models based on integral stochastic computing.IEEE Transactions on Neural Networks and Learning Systems34, 10999–11005 (2023). 19

    2023

  63. [63]

    & Wang, X

    Han, C., Gu, Y., Wu, G. & Wang, X. Simulated annealing-based heuristic for multiple agile satellites scheduling under cloud coverage uncertainty.IEEE Transactions on Systems, Man, and Cybernetics: Systems53, 2863–2874 (2023)

    2023

  64. [64]

    & Jin, Y

    Ming, F., Gong, W., Wang, L. & Jin, Y. Constrained multi-objective optimization with deep reinforcement learning assisted operator selection.IEEE/CAA Journal of Automatica Sinica 11, 919–931 (2024)

    2024

  65. [65]

    DOI:10.1109/tevc.2025.3584207

    Peng, C.et al.Learning-based temporal sequence of constrained handling selection for constrained multi-objective evolutionary optimization.IEEE Transactions on Evolutionary Computation(2025). DOI:10.1109/tevc.2025.3584207

    work page doi:10.1109/tevc.2025.3584207 2025

  66. [66]

    & Cheng, R

    Yuan, Z., Li, G., Wang, Z., Sun, J. & Cheng, R. RL-CSL: A combinatorial optimization method using reinforcement learning and contrastive self-supervised learning.IEEE Transactions on Emerging Topics in Computational Intelligence7, 1010–1024 (2023)

    2023

  67. [67]

    & Wang, J

    Zhang, Z., Wu, Z., Zhang, H. & Wang, J. Meta-learning-based deep reinforcement learning for multiobjective optimization problems.IEEE Transactions on Neural Networks and Learning Systems34, 7978–7991 (2023)

    2023

  68. [68]

    & Buehler, M

    Ghafarollahi, A. & Buehler, M. J. Modeling protein motions through reinforcement learning. Proceedings of the National Academy of Sciences121, e2422180121 (2024)

    2024

  69. [69]

    & Precup, D

    Barreto, A., Hou, S., Borsa, D., Silver, D. & Precup, D. Fast reinforcement learning with generalized policy updates.Proceedings of the National Academy of Sciences117, 30079– 30087 (2020)

    2020

  70. [70]

    & Koushanfar, F

    Heydaribeni, N., Zhan, X., Zhang, R., Eliassi-Rad, T. & Koushanfar, F. Distributed con- strained combinatorial optimization leveraging hypergraph neural networks.Nature Machine Intelligence6, 664–672 (2024)

    2024

  71. [71]

    Schuetz, M. J. A., Brubaker, J. K. & Katzgraber, H. G. Combinatorial optimization with physics-inspired graph neural networks.Nature Machine Intelligence4, 367 (2022)

    2022

  72. [72]

    Akiba, T., Shing, M., Tang, Y., Sun, Q. & Ha, D. Evolutionary optimization of model merging recipes.Nature Machine Intelligence7, 195–204 (2025)

    2025

  73. [73]

    http://hdl.handle.net/ 10138/584878

    MaxSAT evaluation 2024 : Solver and benchmark descriptions (2024). http://hdl.handle.net/ 10138/584878. Accessed 15 July 2025

    2024

  74. [74]

    Certifying Without Loss of Generality Reasoning in Solution-Improving Maxi- mum Satisfiability

    Berg, J.et al. Certifying Without Loss of Generality Reasoning in Solution-Improving Maxi- mum Satisfiability. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024), Vol. 307, 4:1–4:28 (2024)

    2024

  75. [75]

    & Kjellerstrand, H.Optimizing SAT encodings for arithmetic constraints

    Zhou, N.-F. & Kjellerstrand, H.Optimizing SAT encodings for arithmetic constraints. In Principles and Practice of Constraint Programming, Vol. 10416, 671–686 (2017). 20 Appendices A Grammar of Unified Modeling Language The grammar of the proposed modeling language is described below using Extended Backus-Naur Form (ISO/IEC 14977). 1model = { ’\ begin { al...

    2017

  76. [76]

    am+n ∨ ¬ai ∨a ′ i i= 0,

    The clauses generated by this rule are shown in Formula 114. am+n ∨ ¬ai ∨a ′ i i= 0, . . . , m+n−1 am+n ∨a i ∨ ¬a′ i i= 0, . . . , m+n−1 am+n ∨ ¬a′ m+n ¬am+n ∨d 0 ¬am+n ∨Half Adder(¬a i, di, a′ i, di+1)i= 0, . . . , m+n−1 ¬am+n ∨d m+n ∨a ′ m+n ¬am+n ∨ ¬dm+n ∨ ¬a′ m+nWm+n−1 i=0 a′ i ∨ ¬a′ m+n (114) whered 0 tod m+n are intermediate Boolean variables. This ...

    work page arXiv 2085