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arxiv: 2604.22977 · v1 · submitted 2026-04-24 · 🧮 math.OC

A Reinforcement-learning-based Column Generation Algorithm for Integrated Operating Room Planning and Scheduling

Mahdi Dolatkhah , Hossein Hashemi Doulabi , Walter Rei , Michel Gendreau This is my paper

Pith reviewed 2026-05-08 11:01 UTC · model grok-4.3

classification 🧮 math.OC
keywords column generationreinforcement learninggenetic algorithmoperating room schedulingmixed integer programminghealthcare optimizationsurgery planningintegrated planning
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The pith

A reinforcement-learning column generation algorithm solves large integrated operating room planning and scheduling problems to within 1.5 percent of optimality.

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

This paper introduces a mixed-integer programming model that assigns elective and mandatory surgeries to operating rooms over multiple days while respecting surgeon daily limits and allowing overtime. To solve the resulting large-scale problems, the authors develop a column generation algorithm initialized by a hybrid reinforcement learning and genetic algorithm procedure. Tests on synthetic instances show an average optimality gap of 1.23 percent and on real-world hospital data 1.49 percent, with the method succeeding on scales where previous approaches find no feasible solution. Under uncertainty in surgery times, a 120-minute buffer time is shown to minimize overall cost, and emergency cases raise costs by only a few percent. Such a scalable solver matters for hospitals that must plan under tight resources and frequent disruptions.

Core claim

We propose a novel mixed integer programming model to formulate integrated operating room planning and scheduling problems, where several mandatory and elective surgeries are to be assigned and scheduled in operating rooms on different days. We consider both overtime in operating rooms and surgeons' daily availability limits. We propose a column generation algorithm to solve large-scale instances. In order to enhance the CG, we integrate the Reinforcement Learning Algorithm and the Genetic Algorithm and develop a hybrid algorithm to generate initial columns for the CG algorithm. Computational experiments demonstrate that our proposed model and methodology yields an average optimality gap of

What carries the argument

The hybrid reinforcement learning and genetic algorithm used to generate high-quality initial columns for the column generation solver of the mixed-integer operating room scheduling model.

If this is right

  • The approach obtains feasible high-quality solutions for large instances where other models and methods fail.
  • A 120-minute buffer time minimizes overall cost when surgery durations vary by 20 percent.
  • Inclusion of emergency surgeries increases total rescheduling cost by 4.13 percent on synthetic instances and 0.11 percent when priorities escalate in real cases.
  • The method outperforms prior solution methodologies in the literature on both optimality gap and scalability.

Where Pith is reading between the lines

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

  • The hybrid initialization approach may transfer to column generation formulations in other combinatorial healthcare problems such as radiotherapy scheduling or patient flow optimization.
  • Embedding the model in a daily re-optimization loop could support dynamic responses to new emergency arrivals without full re-solving from scratch.
  • Retraining the reinforcement learning agent on institution-specific historical patterns could further reduce the optimality gaps observed in the current tests.

Load-bearing premise

The hybrid reinforcement learning and genetic algorithm reliably produces high-quality initial columns that allow the column generation procedure to converge to near-optimal solutions within reasonable time for the tested instance sizes and variability levels.

What would settle it

On a large-scale instance known to be solvable to optimality by an exact method, check whether the column generation procedure returns a solution whose cost is more than 2 percent above the proven optimum or fails to produce any feasible solution within the allotted runtime.

Figures

Figures reproduced from arXiv: 2604.22977 by Hossein Hashemi Doulabi, Mahdi Dolatkhah, Michel Gendreau, Walter Rei.

Figure 1
Figure 1. Figure 1: Illustration of the sample surgery plan and schedule output view at source ↗
Figure 2
Figure 2. Figure 2: Flowchart of the column generation heuristic view at source ↗
Figure 3
Figure 3. Figure 3: Procedure of mutation operator selection by UCB in RGA view at source ↗
Figure 4
Figure 4. Figure 4: (a) GA operator selection’s frequency. (b) Normalized MCBOp To evaluate the performance of the RGA-CG algorithm, we implemented the four heuristic methods described by Lin and Chou [35], namely LPT+, SPT+, EDD+, and LPT/EDD+. LPT rule schedules surgeries in decreasing order of their expected durations. In contrast, the SPT rule prioritizes surgeries with the shortest durations. The EDD rule orders surgerie… view at source ↗
Figure 5
Figure 5. Figure 5: (a) GA operator selection’s frequency. (b) Normalized MCBOp 26 view at source ↗
Figure 6
Figure 6. Figure 6: Impact of buffer-time policies for Naples instances view at source ↗
Figure 7
Figure 7. Figure 7: The structure of the RGA chromosomes for Phase1 and Phase2 respectively view at source ↗
read the original abstract

In this paper, we propose a novel mixed integer programming model to formulate integrated operating room planning and scheduling problems, where several mandatory and elective surgeries are to be assigned and scheduled in operating rooms on different days. We consider both overtime in operating rooms and surgeons' daily availability limits. We propose a column generation (CG) algorithm to solve large-scale instances. In order to enhance the CG, we integrate the Reinforcement Learning Algorithm and the Genetic Algorithm and develop a hybrid algorithm to generate initial columns for the CG algorithm. For our analysis, we employed two sets of test instances: one consisting of synthetic data and the other based on real-world cases from a local hospital in Naples, Italy. Computational experiments demonstrate that our proposed model and methodology yields an average optimality gap of 1.23% for synthetic instances and 1.49% on real-world scenarios, significantly outperforming previous solution methodologies in the literature. Additionally, we demonstrate that the developed CG algorithm provides a high-quality solution for large-scale instances where other models and methods fail to obtain even a feasible solution. To further evaluate robustness under uncertainty, we examined scenarios with 20% variability in surgery durations. The results indicate that incorporating a 120-minute buffer time minimizes the overall cost. Moreover, we investigated the impact of emergency surgeries by either introducing additional cases or escalating surgical priorities. For synthetic instances, the inclusion of emergency surgeries increased the total rescheduling cost by 4.13%, whereas in the real-world Naples cases, priority escalation led to only a 0.11% increase.

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

4 major / 2 minor

Summary. The manuscript proposes a mixed-integer programming model for integrated operating room planning and scheduling that incorporates overtime costs and surgeon daily availability limits. It develops a column generation algorithm whose initial columns are generated by a hybrid reinforcement learning plus genetic algorithm procedure. Computational experiments on synthetic instances and real data from a Naples hospital report average optimality gaps of 1.23% and 1.49%, respectively, claim statistically significant outperformance over prior methods, and show that the approach finds high-quality solutions for large instances where competing formulations obtain no feasible solution. Additional experiments examine robustness under 20% surgery-duration variability and the effect of emergency cases.

Significance. If the performance claims hold, the work supplies a practical, scalable method for a high-stakes healthcare scheduling problem and demonstrates that a hybrid RL-GA initializer can make column generation viable on instances that defeat other MIP and heuristic approaches. The use of real hospital data strengthens external validity, and the reported ability to handle large-scale problems with modest gaps is potentially impactful for OR management under uncertainty.

major comments (4)
  1. [Abstract and Computational Experiments] Abstract and Computational Experiments section: the central claims of 1.23% and 1.49% average optimality gaps, outperformance, and success on large instances where other methods fail are presented without stating the number or sizes of instances, the precise RL/GA hyper-parameters, or any statistical significance tests on the gaps or run-time differences.
  2. [Section 5] Section 5 (Hybrid RL-GA initializer): the reinforcement-learning component is described only at a high level; no explicit definition is given for the state space, action space, reward function, training regime, or the precise integration protocol with the genetic algorithm. These omissions make it impossible to verify that the hybrid reliably supplies high-quality columns or to reproduce the reported gaps.
  3. [Computational Experiments] Computational Experiments section: no ablation study compares the hybrid RL-GA initialization against standard CG initializations (e.g., random feasible columns or greedy heuristics). Without such controls it is unclear whether the low gaps and large-instance feasibility are attributable to the hybrid or to the base CG formulation and solver settings.
  4. [Robustness Analysis] Robustness Analysis subsection: the 120-minute buffer time is reported to minimize cost under 20% duration variability, yet the paper does not indicate whether this value resulted from a systematic parameter sweep or was selected after inspecting results, leaving open the possibility of post-hoc tuning.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'significantly outperforming previous solution methodologies' is used without naming the specific prior methods or quantifying the improvement in gap or CPU time.
  2. [MIP Model] Notation in the MIP model section could be introduced with a compact table of indices, sets, and parameters to aid readers who are not specialists in OR scheduling.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment point by point below, indicating where revisions will be made to improve clarity, reproducibility, and evidential support.

read point-by-point responses

  1. Referee: [Abstract and Computational Experiments] Abstract and Computational Experiments section: the central claims of 1.23% and 1.49% average optimality gaps, outperformance, and success on large instances where other methods fail are presented without stating the number or sizes of instances, the precise RL/GA hyper-parameters, or any statistical significance tests on the gaps or run-time differences.

    Authors: We agree that these details should be stated explicitly. In the revised manuscript we will report the number and sizes of both the synthetic instances and the real Naples hospital cases, list the precise RL and GA hyper-parameters, and add statistical significance tests (e.g., paired t-tests or Wilcoxon tests) on the reported gaps and run-time differences to substantiate the outperformance claims. revision: yes

  2. Referee: [Section 5] Section 5 (Hybrid RL-GA initializer): the reinforcement-learning component is described only at a high level; no explicit definition is given for the state space, action space, reward function, training regime, or the precise integration protocol with the genetic algorithm. These omissions make it impossible to verify that the hybrid reliably supplies high-quality columns or to reproduce the reported gaps.

    Authors: We acknowledge that the current description is high-level. In the revision we will expand Section 5 to supply explicit definitions of the state space, action space, reward function, training regime, and the precise protocol by which RL-generated solutions are integrated with the genetic algorithm before seeding the column-generation master problem. These additions will enable verification and reproduction of the initializer. revision: yes

  3. Referee: [Computational Experiments] Computational Experiments section: no ablation study compares the hybrid RL-GA initialization against standard CG initializations (e.g., random feasible columns or greedy heuristics). Without such controls it is unclear whether the low gaps and large-instance feasibility are attributable to the hybrid or to the base CG formulation and solver settings.

    Authors: We agree that an explicit ablation would strengthen attribution of the results. In the revised Computational Experiments section we will add a controlled comparison of the hybrid RL-GA initializer against standard CG initializations using random feasible columns and a greedy heuristic, reporting the resulting optimality gaps and feasibility rates on the same instance sets. revision: yes

  4. Referee: [Robustness Analysis] Robustness Analysis subsection: the 120-minute buffer time is reported to minimize cost under 20% duration variability, yet the paper does not indicate whether this value resulted from a systematic parameter sweep or was selected after inspecting results, leaving open the possibility of post-hoc tuning.

    Authors: The 120-minute buffer was identified through a systematic parameter sweep. In the revision we will explicitly describe the sweep (including the range of buffer values tested and the selection criterion of lowest average cost) so that the choice is clearly documented and not open to the interpretation of post-hoc tuning. revision: yes

Circularity Check

0 steps flagged

No circularity: algorithmic pipeline validated on external benchmarks

full rationale

The paper defines a MIP model for OR planning/scheduling, applies standard column generation, and augments it with a hybrid RL+GA initializer. All reported results (1.23% and 1.49% gaps, large-instance feasibility) are obtained by running the algorithm on synthetic and real Naples instances and comparing against prior methods. No equation, parameter fit, or self-citation reduces these performance numbers to quantities defined inside the paper itself; the derivation chain consists of a conventional CG framework whose quality is measured externally. This is the normal, non-circular case for an algorithmic paper.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard MIP modeling assumptions plus the empirical effectiveness of the RL-GA hybrid; no new physical entities are postulated.

free parameters (1)
  • 120-minute buffer time
    Chosen after testing variability scenarios to minimize cost; functions as a tuned parameter for robustness analysis.
axioms (2)
  • domain assumption Surgeon daily availability limits and overtime costs are correctly captured by the MIP constraints.
    Invoked when formulating the integrated planning model.
  • standard math The column generation master problem plus pricing subproblem formulation is valid for the set-partitioning structure of OR schedules.
    Standard assumption for CG applied to scheduling problems.

pith-pipeline@v0.9.0 · 5591 in / 1505 out tokens · 30083 ms · 2026-05-08T11:01:08.192191+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

82 extracted references · 3 canonical work pages

  1. [1]

    Mixed-integer linear programming, constraint programming and column generation approaches for operating room planning under block strategy

    Ghandehari N and Kianfar K. Mixed-integer linear programming, constraint programming and column generation approaches for operating room planning under block strategy. Applied Mathematical Modelling 2022;105:438–53

    2022

  2. [2]

    Using reinforcement learning to forecast the spread of COVID-19 in France

    Khalilpourazari S and Doulabi HH. Using reinforcement learning to forecast the spread of COVID-19 in France. In:2021 IEEE international conference on autonomous systems (ICAS). IEEE. 2021:1–8

    2021

  3. [3]

    Basics of the US health care system

    Niles NJ. Basics of the US health care system. Jones & Bartlett Learning, 2023

    2023

  4. [4]

    The Boundaries of Medicare: Public Health Care Beyond the Canada Health Act

    Fierlbeck K and Marchildon GP. The Boundaries of Medicare: Public Health Care Beyond the Canada Health Act. Vol. 61. McGill-Queen’s Press-MQUP, 2023

    2023

  5. [5]

    Integrated consultation and chemotherapy scheduling with stochastic treatment times

    Haghi M, Hashemi Doulabi H, Contreras I, and Bhuiyan N. Integrated consultation and chemotherapy scheduling with stochastic treatment times. Journal of the Operational Research Society 2023;74:2012–27

    2023

  6. [6]

    Operating room planning with multiple downstream units

    Andam A and Doulabi HH. Operating room planning with multiple downstream units. In:2021 IEEE Interna- tional Conference on Prognostics and Health Management (ICPHM). IEEE. 2021:1–8

    2021

  7. [7]

    Solving operating room scheduling problems with surgical teams via answer set programming

    Dodaro C, Galat` a G, Khan MK, Maratea M, and Porro I. Solving operating room scheduling problems with surgical teams via answer set programming. In:International Conference of the Italian Association for Artificial Intelligence. Springer. 2020:204–20

    2020

  8. [8]

    Health Care 4.0: A vision for smart and connected health care

    Li J and Carayon P. Health Care 4.0: A vision for smart and connected health care. IISE Transactions on Healthcare Systems Engineering 2021;11:171–80

    2021

  9. [9]

    An integer programming approach to elective surgery scheduling: Analysis and comparison based on a real case

    Marques I, Captivo ME, and Vaz Pato M. An integer programming approach to elective surgery scheduling: Analysis and comparison based on a real case. OR spectrum 2012;34:407–27

    2012

  10. [10]

    Integrated operating room planning and scheduling: an ILP- Based off-line approach for emergency responsiveness at a local hospital in Naples

    Boccia M, Mancuso A, Masone A, and Sterle C. Integrated operating room planning and scheduling: an ILP- Based off-line approach for emergency responsiveness at a local hospital in Naples. Soft Computing 2024:1– 17

    2024

  11. [11]

    A constraint programming-based column generation ap- proach for operating room planning and scheduling

    Hashemi Doulabi SH, Rousseau LM, and Pesant G. A constraint programming-based column generation ap- proach for operating room planning and scheduling. In:International Conference on Integration of Constraint Programming, Artificial Intelligence, and Operations Research. Springer. 2014:455–63

    2014

  12. [12]

    A constraint-programming-based branch-and-price-and-cut approach for operating room planning and scheduling

    Hashemi Doulabi SH, Rousseau LM, and Pesant G. A constraint-programming-based branch-and-price-and-cut approach for operating room planning and scheduling. INFORMS Journal on Computing 2016;28:432–48

    2016

  13. [13]

    Solving integrated operating room planning and scheduling: Logic-based Benders decomposition versus Branch-Price-and-Cut

    Roshanaei V and Naderi B. Solving integrated operating room planning and scheduling: Logic-based Benders decomposition versus Branch-Price-and-Cut. European Journal of Operational Research 2021;293:65–78

    2021

  14. [14]

    The effect of few historical data on the performance of sample average approx- imation method for operating room scheduling

    Coban E, Kayı¸ s E, and Dexter F. The effect of few historical data on the performance of sample average approx- imation method for operating room scheduling. International transactions in operational research 2023;30:126– 50

    2023

  15. [15]

    Operating room planning and surgical case scheduling: a review of literature

    Zhu S, Fan W, Yang S, Pei J, and Pardalos PM. Operating room planning and surgical case scheduling: a review of literature. Journal of Combinatorial Optimization 2019;37:757–805. 38

    2019

  16. [16]

    Scheduling elective surgeries in a Portuguese hospital using a genetic heuristic

    Marques I, Captivo ME, and Pato MV. Scheduling elective surgeries in a Portuguese hospital using a genetic heuristic. Operations Research for Health Care 2014;3:59–72

    2014

  17. [17]

    A branch-and-price-and-cut algorithm for operating room scheduling under human resource constraints

    Bargetto R, Garaix T, and Xie X. A branch-and-price-and-cut algorithm for operating room scheduling under human resource constraints. Computers & Operations Research 2023;152:106136

    2023

  18. [18]

    Combining workload balance and patient priority maximisation in operating room planning through hierarchical multi-objective optimisation

    Aringhieri R, Duma D, Landa P, and Mancini S. Combining workload balance and patient priority maximisation in operating room planning through hierarchical multi-objective optimisation. European Journal of Operational Research 2022;298:627–43

    2022

  19. [19]

    The Operating Room Scheduling Problem Based on Patient Priority

    Mashkani O, Hwang F, and Salehipour A. The Operating Room Scheduling Problem Based on Patient Priority. In:Data and Decision Sciences in Action 2: Proceedings of the ASOR/DORS Conference 2018. Springer. 2021:155–66

    2018

  20. [20]

    An adaptive-learning-based genetic algorithm for collaborative scheduling of dis- tributed operating rooms

    Wang K, Yu C, and Qin H. An adaptive-learning-based genetic algorithm for collaborative scheduling of dis- tributed operating rooms. Applied Soft Computing 2022;131:109755

    2022

  21. [21]

    Machine learning based in- tegrated scheduling and rescheduling for elective and emergency patients in the operating theatre

    Eshghali M, Kannan D, Salmanzadeh-Meydani N, and Esmaieeli Sikaroudi AM. Machine learning based in- tegrated scheduling and rescheduling for elective and emergency patients in the operating theatre. Annals of Operations Research 2023:1–24

    2023

  22. [22]

    Surgery scheduling in flexible operating rooms by using a convex surrogate model of second-stage costs

    Almoghrabi MM and Sagnol G. Surgery scheduling in flexible operating rooms by using a convex surrogate model of second-stage costs. European Journal of Operational Research 2025;321:23–40

    2025

  23. [23]

    Scheduling of elective operations with coordinated utilization of hospital beds and operating rooms

    Li Z, Yu H, and Zhou Z. Scheduling of elective operations with coordinated utilization of hospital beds and operating rooms. Journal of Combinatorial Optimization 2024;47:75

    2024

  24. [24]

    Stochastic operating room scheduling: a new model for solving problem and an approach for determining the factors that affect operation time variations

    G¨ ur S ¸, Alaka¸ s HM, Pınarba¸ sı M, and Eren T. Stochastic operating room scheduling: a new model for solving problem and an approach for determining the factors that affect operation time variations. Soft Computing 2024;28:3987–4007

    2024

  25. [25]

    Surgical cases assignment problem using a multi-objective squirrel search algorithm

    Zhu L, Zhou Y, Jiang R, and Su Q. Surgical cases assignment problem using a multi-objective squirrel search algorithm. Expert Systems with Applications 2024;235:121217

    2024

  26. [26]

    Operating room planning with pooling downstream beds among specialties: A stochastic programming approach

    Andam A and Hashemi Doulabi H. Operating room planning with pooling downstream beds among specialties: A stochastic programming approach. arXiv preprint arXiv:2602.15269 2026

    work page arXiv 2026

  27. [27]

    Operating theatre optimization: A resource-constrained based solving approach

    Roland B, Di Martinelly C, and Riane F. Operating theatre optimization: A resource-constrained based solving approach. In:2006 International conference on service systems and service management. Vol. 1. IEEE. 2006:443– 8

    2006

  28. [28]

    Two-stage robust optimisation for surgery scheduling considering surgeon col- laboration

    Wang J, Guo H, and Tsui KL. Two-stage robust optimisation for surgery scheduling considering surgeon col- laboration. International Journal of Production Research 2020:1–14

    2020

  29. [29]

    A dual bin-packing approach to scheduling surgical cases at a publicly-funded hospital

    Vijayakumar B, Parikh PJ, Scott R, Barnes A, and Gallimore J. A dual bin-packing approach to scheduling surgical cases at a publicly-funded hospital. European Journal of Operational Research 2013;224:583–91

    2013

  30. [30]

    Adaptive operating rooms planning and scheduling: A rolling horizon approach

    Kamran MA, Karimi B, Dellaert N, and Demeulemeester E. Adaptive operating rooms planning and scheduling: A rolling horizon approach. Operations Research for Health Care 2019;22:100200

    2019

  31. [31]

    State-variable modeling for a class of two-stage stochastic optimization problems

    Hashemi Doulabi H, Ahmed S, and Nemhauser G. State-variable modeling for a class of two-stage stochastic optimization problems. INFORMS Journal on Computing 2022;34:354–69

    2022

  32. [32]

    Stochastic weekly operating room planning with an exponential number of scenarios

    Hashemi Doulabi H and Khalilpourazari S. Stochastic weekly operating room planning with an exponential number of scenarios. Annals of Operations Research 2023;328:643–64. 39

    2023

  33. [33]

    Vehicle routing problems with synchronized visits and stochastic travel and service times: Applications in healthcare

    Hashemi Doulabi H, Pesant G, and Rousseau LM. Vehicle routing problems with synchronized visits and stochastic travel and service times: Applications in healthcare. Transportation Science 2020;54:1053–72

    2020

  34. [34]

    An effective hybrid simulated annealing and two mixed integer linear formulations for just-in-time open shop scheduling problem

    Hashemi Doulabi SH, Avazbeigi M, Arab S, and Davoudpour H. An effective hybrid simulated annealing and two mixed integer linear formulations for just-in-time open shop scheduling problem. The International Journal of Advanced Manufacturing Technology 2012;59:1143–55

    2012

  35. [35]

    A hybrid genetic algorithm for operating room scheduling

    Lin YK and Chou YY. A hybrid genetic algorithm for operating room scheduling. Health care management science 2020;23:249–63

    2020

  36. [36]

    A dedicated branch-price-and-cut algorithm for advance patient planning and surgeon scheduling

    Akbarzadeh B and Maenhout B. A dedicated branch-price-and-cut algorithm for advance patient planning and surgeon scheduling. European Journal of Operational Research 2024

    2024

  37. [37]

    A two-layer heuristic for patient sequencing in the operating room theatre considering multiple resource phases

    Akbarzadeh B and Maenhout B. A two-layer heuristic for patient sequencing in the operating room theatre considering multiple resource phases. Computers & Operations Research 2024;170:106768

    2024

  38. [38]

    Incorporating machine learning and optimization techniques for assigning patients to operating rooms by considering fairness policies

    Ala A and Goli A. Incorporating machine learning and optimization techniques for assigning patients to operating rooms by considering fairness policies. Engineering Applications of Artificial Intelligence 2024;136:108980

    2024

  39. [39]

    Solving multi-depot electric vehicle scheduling problem by column generation and genetic algorithm

    Wang C, Guo C, and Zuo X. Solving multi-depot electric vehicle scheduling problem by column generation and genetic algorithm. Applied Soft Computing 2021;112:107774

    2021

  40. [40]

    Reinforcement learning: An introduction

    Sutton RS and Barto AG. Reinforcement learning: An introduction. MIT press, 2018

    2018

  41. [41]

    RL-GA: A reinforcement learning-based genetic al- gorithm for electromagnetic detection satellite scheduling problem

    Song Y, Wei L, Yang Q, Wu J, Xing L, and Chen Y. RL-GA: A reinforcement learning-based genetic al- gorithm for electromagnetic detection satellite scheduling problem. Swarm and Evolutionary Computation 2023;77:101236

    2023

  42. [42]

    Scheduling an operating theatre under human resource constraints

    Roland B, Di Martinelly C, Riane F, and Pochet Y. Scheduling an operating theatre under human resource constraints. Computers & Industrial Engineering 2010;58:212–20

    2010

  43. [43]

    Combinatorial optimization: theory and algorithms

    Korte B and Vygen J. Combinatorial optimization: theory and algorithms. Springer, 2008

    2008

  44. [44]

    Solving robust bin-packing problems with a branch-and-price approach

    Schepler X, Rossi A, Gurevsky E, and Dolgui A. Solving robust bin-packing problems with a branch-and-price approach. European Journal of Operational Research 2022;297:831–43

    2022

  45. [45]

    Drone-Aided Blood Collection Routing Problem: A Column Generation Approach

    Abbaszadeh A and Hashemi Doulabi H. Drone-Aided Blood Collection Routing Problem: A Column Generation Approach. arXiv preprint arXiv:2601.20693 2026

    work page arXiv 2026

  46. [46]

    Adaptive operator selection with dynamic multi-armed bandits

    DaCosta L, Fialho A, Schoenauer M, and Sebag M. Adaptive operator selection with dynamic multi-armed bandits. In:Proceedings of the 10th annual conference on Genetic and evolutionary computation. 2008:913–20

    2008

  47. [47]

    Reinforcement learning based recommender systems: A survey

    Afsar MM, Crump T, and Far B. Reinforcement learning based recommender systems: A survey. ACM Com- puting Surveys 2022;55:1–38

    2022

  48. [48]

    Near-optimal regret bounds for reinforcement learning

    Auer P, Jaksch T, and Ortner R. Near-optimal regret bounds for reinforcement learning. Advances in neural information processing systems 2008;21

    2008

  49. [49]

    Context-aware personalized POI sequence recommendation

    Chen J and Jiang W. Context-aware personalized POI sequence recommendation. In:Smart City and Informa- tization: 7th International Conference, iSCI 2019, Guangzhou, China, November 12–15, 2019, Proceedings 7. Springer. 2019:197–210

    2019

  50. [50]

    Assessment of operative times of multiple surgical specialties in a public university hospital

    Costa AdS. Assessment of operative times of multiple surgical specialties in a public university hospital. Einstein (Sao Paulo) 2017;15:200–5. 40

    2017

  51. [51]

    A machine learning approach to predicting case duration for robot-assisted surgery

    Zhao B, Waterman RS, Urman RD, and Gabriel RA. A machine learning approach to predicting case duration for robot-assisted surgery. Journal of medical systems 2019;43:1–8

    2019

  52. [52]

    Using machine learning to predict operating room case duration: A case study in otolaryngology

    Miller LE, Goedicke W, Crowson MG, Rathi VK, Naunheim MR, and Agarwala AV. Using machine learning to predict operating room case duration: A case study in otolaryngology. Otolaryngology–Head and Neck Surgery 2023;168:241–7

    2023

  53. [53]

    Solving a tactical operating room planning problem by a column-generation-based heuristic procedure with four criteria

    Fei H, Chu C, and Meskens N. Solving a tactical operating room planning problem by a column-generation-based heuristic procedure with four criteria. Annals of Operations Research 2009;166:91–108

    2009

  54. [54]

    Optimal allocation of surgery blocks to operating rooms under uncertainty

    Denton BT, Miller AJ, Balasubramanian HJ, and Huschka TR. Optimal allocation of surgery blocks to operating rooms under uncertainty. Operations research 2010;58:802–16

    2010

  55. [55]

    Boosted genetic algorithm using machine learning for traffic control optimization

    Mao T, Mih˘ ait˘ a AS, Chen F, and Vu HL. Boosted genetic algorithm using machine learning for traffic control optimization. IEEE Transactions on Intelligent Transportation Systems 2021;23:7112–41

    2021

  56. [56]

    Hyperparameter optimization

    Feurer M and Hutter F. Hyperparameter optimization. Automated machine learning: Methods, systems, chal- lenges 2019:3–33

    2019

  57. [57]

    Hyperparameter Tuning: The Art of Fine-Tuning Machine and Deep Learning Models to Improve Metric Results

    Ippolito PP. Hyperparameter Tuning: The Art of Fine-Tuning Machine and Deep Learning Models to Improve Metric Results. In:Applied data science in tourism: Interdisciplinary approaches, methodologies, and applica- tions. Springer, 2022:231–51

    2022

  58. [58]

    On hyperparameter optimization of machine learning algorithms: Theory and practice

    Yang L and Shami A. On hyperparameter optimization of machine learning algorithms: Theory and practice. Neurocomputing 2020;415:295–316

    2020

  59. [59]

    Dealing with categorical and integer-valued variables in bayesian optimization with gaussian processes

    Garrido-Merch´ an EC and Hern´ andez-Lobato D. Dealing with categorical and integer-valued variables in bayesian optimization with gaussian processes. Neurocomputing 2020;380:20–35

    2020

  60. [60]

    Bayesian optimization with application to computer experiments

    Pourmohamad T and Lee HK. Bayesian optimization with application to computer experiments. Springer, 2021

    2021

  61. [61]

    Bayesian Optimization: Theory and Practice Using Python

    Liu P. Bayesian Optimization: Theory and Practice Using Python. Springer, 2023

    2023

  62. [62]

    Bayesian Optimization: Open source constrained global optimization tool for Python

    Nogueira F. Bayesian Optimization: Open source constrained global optimization tool for Python. 2014.url: https://github.com/bayesian-optimization/BayesianOptimization

    2014

  63. [63]

    An adaptive parallel evolutionary algorithm for solving the uncapacitated facility location problem

    Sonu¸ c E and ¨Ozcan E. An adaptive parallel evolutionary algorithm for solving the uncapacitated facility location problem. Expert Systems with Applications 2023;224:119956

    2023

  64. [64]

    Differential evolution with an adaptive penalty coefficient mechanism and a search history exploitation mechanism

    Li J, Li G, Wang Z, and Cui L. Differential evolution with an adaptive penalty coefficient mechanism and a search history exploitation mechanism. Expert Systems with Applications 2023;230:120530

    2023

  65. [65]

    Introduction to evolutionary computing

    Eiben AE and Smith JE. Introduction to evolutionary computing. Springer, 2015

    2015

  66. [66]

    Evolutionary computation 1: Basic algorithms and operators

    B¨ ack T, Fogel DB, and Michalewicz Z. Evolutionary computation 1: Basic algorithms and operators. CRC press, 2018. 41 Appendix A Proof of Theorem 5.1 In explaining the proof of Theorem 5.1, we introduce a new set, a supplementary variable, and an alternative math- ematical model named APMIORPS. Denoted asT ′ i, the set encompasses time slots wherein surg...

    2018

  67. [67]

    Step 1: In this initial stage, we prove the APMIORPS model is a valid representation of the MIORPS model

  68. [68]

    # Vars” column, is more than eight times that of PMIORPS. Similarly, the average number of constraints, presented in the “# Cons

    Step 2: Subsequently, we demonstrate in the APMIORPS model that for any feasible solution ofx idt obtained from constraints (9) to (14), there always exists a feasible solution forx ′ idkt variables such that Constraints (29) to (31) are always satisfied. In the following, we provide the details of the above-mentioned two steps. Step1: As evidenced in the...

    work page arXiv

  69. [69]

    Read instance and calculatec it (a) Read instance data from the file (b) Calculatec it based on the formulation given in Table 1

  70. [70]

    Initialize GA parameters (nPop, nGen, pMu, Selection Method, Termination conditions) ii

    RGA Phase1 (a) Initialize parameters i. Initialize GA parameters (nPop, nGen, pMu, Selection Method, Termination conditions) ii. Initialize Reinforcement Learning parameters (RLA algorithm, L Reward, F Reward) (b) Initialize RGA Phase1 population i. Create random permutation of mandatory surgeries ii. Create random permutation of non-mandatory surgeries i...

  71. [71]

    Select the np-th individual from the population of the RGA Phase1 ii

    RGA Phase1 enhancement (a) For np=1 to nPop: i. Select the np-th individual from the population of the RGA Phase1 ii. Calculatex idt,y d,z i matrices according to the surgery lists of each individual iii. For d=1 to D: A. Createy ′ matrix wherey ′ =y B. Sety ′ d =y d −1 C. Calculate newx ′′ idt,y ′′ d,z ′′ i matrices consideringy ′ as an upper bound for t...

  72. [72]

    For np=1 to nPop: A

    RGA Phase2 (a) Initialize RGA Phase2 population i. For np=1 to nPop: A. Select the np-th individual from the population of the RGA Phase1 B. Create an integrated surgery list by joining mandatory and non-mandatory surgery lists together C. Add the individual to the RGA Phase2 population with the same fitness value (b) For Gen=1 to Gen= nGen: i. Terminate ...

  73. [73]

    Select the np-th individual from the population of the RGA Phase2 6 ii

    RGA Phase2 enhancement (a) For np=1 to nPop: i. Select the np-th individual from the population of the RGA Phase2 6 ii. Calculatex idt,y d,z i matrices according to the surgery lists of each individual iii. For d=1 to D: A. Createy ′ matrix wherey ′ =y B. Sety ′ d =y d −1 C. Calculate newx ′′ idt,y ′′ d,z ′′ i matrices consideringy ′ as an upper bound for...

  74. [74]

    Report thex B idt,y B d ,z B i and the corresponding fitness value as the best solution

  75. [75]

    Construct the relaxed M-CG wherex j ∈(0,1) and calculate the reduced cost

  76. [76]

    Iteratively solve the S-CG and M-CG until termination condition(s) met

  77. [77]

    Table 22 shows the new notation of the BCMIORPS

    Solve the M-CG with binaryx j ∈ {0,1}variables and report the solution as the best found upper bound of the problem C BCMIORPS mathematical model Like the IORPS, we modified the proposed Branch-and-Cut algorithm which is referred to as BCMIORPS to be compatible with the new cost minimization objective function. Table 22 shows the new notation of the BCMIO...

  78. [78]

    An optimal subproblem when ¯βd = ¯αd

  79. [79]

    A suboptimal subproblem when ¯βd >¯αd

  80. [80]

    An infeasible subproblem In the first scenario, which is the desirable scenario we expect to have for all subproblems, we do not need to add any cuts to the master problem. However, in the second and third scenarios, we must add optimality and feasibility cuts respectively to the master problem to transfer the achieved information on the proposed solution...

Showing first 80 references.