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A Tutorial on the Cross-Entropy Method

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Cited by:

  1. Futalef, Juan-Pablo & Di Maio, Francesco & Zio, Enrico, 2025. "A dynamic importance function for accidental scenarios generation by RESTART in the computational risk assessment of cyber-physical infrastructures," Reliability Engineering and System Safety, Elsevier, vol. 253(C).
  2. Daniel Berend & Shahar Golan & Yochai Twitto, 2022. "Using the method of conditional expectations to supply an improved starting point for CCLS," Journal of Combinatorial Optimization, Springer, vol. 44(5), pages 3711-3734, December.
  3. Enlu Zhou & Shalabh Bhatnagar, 2018. "Gradient-Based Adaptive Stochastic Search for Simulation Optimization Over Continuous Space," INFORMS Journal on Computing, INFORMS, vol. 30(1), pages 154-167, February.
  4. Xu, Hai-Yan & Kuo, Shyh-Hao & Li, Guoqi & Legara, Erika Fille T. & Zhao, Daxuan & Monterola, Christopher P., 2016. "Generalized Cross Entropy Method for estimating joint distribution from incomplete information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 162-172.
  5. Junran Wu & Ke Xu & Xueyuan Chen & Shangzhe Li & Jichang Zhao, 2021. "Price graphs: Utilizing the structural information of financial time series for stock prediction," Papers 2106.02522, arXiv.org, revised Nov 2021.
  6. A. Shibu & M. Reddy, 2014. "Optimal Design of Water Distribution Networks Considering Fuzzy Randomness of Demands Using Cross Entropy Optimization," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(12), pages 4075-4094, September.
  7. M Caserta & E Quiñonez Rico, 2009. "A cross entropy-based metaheuristic algorithm for large-scale capacitated facility location problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(10), pages 1439-1448, October.
  8. Chan, Jianpeng & Papaioannou, Iason & Straub, Daniel, 2024. "Bayesian improved cross entropy method with categorical mixture models for network reliability assessment," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
  9. Kailin Xie & Jianfei Yin & Hengyong Yu & Hong Fu & Ying Chu, 2024. "Passive Aggressive Ensemble for Online Portfolio Selection," Mathematics, MDPI, vol. 12(7), pages 1-19, March.
  10. Heath, Jeffrey W. & Fu, Michael C. & Jank, Wolfgang, 2009. "New global optimization algorithms for model-based clustering," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3999-4017, October.
  11. Tito Homem-de-Mello, 2007. "A Study on the Cross-Entropy Method for Rare-Event Probability Estimation," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 381-394, August.
  12. Casas-Ramírez, Martha-Selene & Camacho-Vallejo, José-Fernando & Martínez-Salazar, Iris-Abril, 2018. "Approximating solutions to a bilevel capacitated facility location problem with customer's patronization toward a list of preferences," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 369-386.
  13. Altiparmak, Fulya & Dengiz, Berna, 2009. "A cross entropy approach to design of reliable networks," European Journal of Operational Research, Elsevier, vol. 199(2), pages 542-552, December.
  14. Mattrand, C. & Bourinet, J.-M., 2014. "The cross-entropy method for reliability assessment of cracked structures subjected to random Markovian loads," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 171-182.
  15. Alibrandi, Umberto, 2014. "A response surface method for stochastic dynamic analysis," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 44-53.
  16. Nguyen, Hoa T.M. & Chow, Andy H.F. & Ying, Cheng-shuo, 2021. "Pareto routing and scheduling of dynamic urban rail transit services with multi-objective cross entropy method," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 156(C).
  17. R. Y. Rubinstein, 2005. "A Stochastic Minimum Cross-Entropy Method for Combinatorial Optimization and Rare-event Estimation," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 5-50, March.
  18. Kin-Ping Hui, 2011. "Cooperative Cross-Entropy method for generating entangled networks," Annals of Operations Research, Springer, vol. 189(1), pages 205-214, September.
  19. Mathieu Balesdent & Jérôme Morio & Loïc Brevault, 2016. "Rare Event Probability Estimation in the Presence of Epistemic Uncertainty on Input Probability Distribution Parameters," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 197-216, March.
  20. Alexander Weissman, 2013. "Optimizing information using the EM algorithm in item response theory," Annals of Operations Research, Springer, vol. 206(1), pages 627-646, July.
  21. Tai-Yu Ma & Jean-Patrick Lebacque, 2012. "Dynamic System Optimal Routing In Multimodal Transit Network," Working Papers hal-00740347, HAL.
  22. Tran, Cong Quoc & Keyvan-Ekbatani, Mehdi & Ngoduy, Dong & Watling, David, 2021. "Stochasticity and environmental cost inclusion for electric vehicles fast-charging facility deployment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 154(C).
  23. Xi Chen & Enlu Zhou, 2015. "Population model-based optimization," Journal of Global Optimization, Springer, vol. 63(1), pages 125-148, September.
  24. Kun Lin & Steven I. Marcus, 2016. "Cumulative weighting optimization," Journal of Global Optimization, Springer, vol. 65(3), pages 487-512, July.
  25. Jiang, Yubo & Zhu, Yunfang & Du, Xin & Jin, Tao, 2019. "The implicit network inferred from users’ residences and workplaces enhancing collaborative recommendation on smartphones," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
  26. Bismut, Elizabeth & Straub, Daniel, 2021. "Optimal adaptive inspection and maintenance planning for deteriorating structural systems," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
  27. Lvyang Qiu & Shuyu Li & Yunsick Sung, 2021. "3D-DCDAE: Unsupervised Music Latent Representations Learning Method Based on a Deep 3D Convolutional Denoising Autoencoder for Music Genre Classification," Mathematics, MDPI, vol. 9(18), pages 1-17, September.
  28. Ferdinand Bollwein & Stephan Westphal, 2022. "Oblique decision tree induction by cross-entropy optimization based on the von Mises–Fisher distribution," Computational Statistics, Springer, vol. 37(5), pages 2203-2229, November.
  29. Zhou, Yuekuan & Zheng, Siqian, 2020. "Climate adaptive optimal design of an aerogel glazing system with the integration of a heuristic teaching-learning-based algorithm in machine learning-based optimization," Renewable Energy, Elsevier, vol. 153(C), pages 375-391.
  30. Zheng Peng & Donghua Wu & Wenxing Zhu, 2016. "The robust constant and its applications in random global search for unconstrained global optimization," Journal of Global Optimization, Springer, vol. 64(3), pages 469-482, March.
  31. Akimoto, Youhei & Auger, Anne & Hansen, Nikolaus, 2022. "An ODE method to prove the geometric convergence of adaptive stochastic algorithms," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 269-307.
  32. Anastasia Spiliopoulou & Ioannis Papamichail & Markos Papageorgiou & Yannis Tyrinopoulos & John Chrysoulakis, 2017. "Macroscopic traffic flow model calibration using different optimization algorithms," Operational Research, Springer, vol. 17(1), pages 145-164, April.
  33. Xiaojiang Tang & Wenhao Zhao & Junwei Guo & Baoxia Li & Xin Liu & Yuan Wang & Feng Huang, 2023. "Recognition of Plasma-Treated Rice Based on 3D Deep Residual Network with Attention Mechanism," Mathematics, MDPI, vol. 11(7), pages 1-18, March.
  34. Huang, Zhenzhen & Kwok, Yue Kuen & Xu, Ziqing, 2024. "Efficient algorithms for calculating risk measures and risk contributions in copula credit risk models," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 132-150.
  35. M. Bayat & F. Hooshmand & S. A. MirHassani, 2024. "Scenario-based stochastic model and efficient cross-entropy algorithm for the risk-budgeting problem," Annals of Operations Research, Springer, vol. 341(2), pages 731-755, October.
  36. Marco Caserta & Stefan Voß, 2016. "A corridor method based hybrid algorithm for redundancy allocation," Journal of Heuristics, Springer, vol. 22(4), pages 405-429, August.
  37. Deng, Xiangtian & Zhang, Yi & Jiang, Yi & Zhang, Yi & Qi, He, 2024. "A novel operation method for renewable building by combining distributed DC energy system and deep reinforcement learning," Applied Energy, Elsevier, vol. 353(PB).
  38. Hao Su & Qun Niu & Zhile Yang, 2023. "Optimal Power Flow Using Improved Cross-Entropy Method," Energies, MDPI, vol. 16(14), pages 1-33, July.
  39. Zhang, Yali & Shang, Pengjian, 2019. "Multivariate multiscale distribution entropy of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 72-80.
  40. Dirk P. Kroese & Sergey Porotsky & Reuven Y. Rubinstein, 2006. "The Cross-Entropy Method for Continuous Multi-Extremal Optimization," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 383-407, September.
  41. Ali Kadhem, Athraa & Abdul Wahab, Noor Izzri & Aris, Ishak & Jasni, Jasronita & Abdalla, Ahmed N., 2017. "Computational techniques for assessing the reliability and sustainability of electrical power systems: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 80(C), pages 1175-1186.
  42. Erik Hintz & Marius Hofert & Christiane Lemieux & Yoshihiro Taniguchi, 2022. "Single-Index Importance Sampling with Stratification," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3049-3073, December.
  43. Jiyuan Qiu & Chen Jiang, 2025. "Enhancing Mirror and Glass Detection in Multimodal Images Based on Mathematical and Physical Methods," Mathematics, MDPI, vol. 13(5), pages 1-31, February.
  44. Chen, Siliang & Chen, Kang & Zhu, Xu & Jin, Xinqiao & Du, Zhimin, 2022. "Deep learning-based image recognition method for on-demand defrosting control to save energy in commercial energy systems," Applied Energy, Elsevier, vol. 324(C).
  45. Caserta, Marco & Reiners, Torsten, 2016. "A pool-based pattern generation algorithm for logical analysis of data with automatic fine-tuning," European Journal of Operational Research, Elsevier, vol. 248(2), pages 593-606.
  46. A. Gouda & T. Szántai, 2008. "Rare event probabilities in stochastic networks," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(4), pages 441-461, December.
  47. Zichong Wang & Weiyuan Cui & Chenjia Huang & Yuhao Zhou & Zihan Zhao & Yuchen Yue & Xinrui Dong & Chunli Lv, 2025. "Framework for Apple Phenotype Feature Extraction Using Instance Segmentation and Edge Attention Mechanism," Agriculture, MDPI, vol. 15(3), pages 1-23, January.
  48. John Efromson & Roger Lawrie & Thomas Jedidiah Jenks Doman & Matthew Bertone & Aurélien Bègue & Mark Harfouche & Dominic Reisig & R. Michael Roe, 2022. "Species Identification of Caterpillar Eggs by Machine Learning Using a Convolutional Neural Network and Massively Parallelized Microscope," Agriculture, MDPI, vol. 12(9), pages 1-11, September.
  49. Wada, Kentaro & Usui, Kento & Takigawa, Tsubasa & Kuwahara, Masao, 2018. "An optimization modeling of coordinated traffic signal control based on the variational theory and its stochastic extension," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 907-925.
  50. Jiaqiao Hu & Michael C. Fu & Steven I. Marcus, 2007. "A Model Reference Adaptive Search Method for Global Optimization," Operations Research, INFORMS, vol. 55(3), pages 549-568, June.
  51. Liang Huang & Juanjuan Zhu & Mulan Qiu & Xiaoxiang Li & Shasha Zhu, 2022. "CA-BASNet: A Building Extraction Network in High Spatial Resolution Remote Sensing Images," Sustainability, MDPI, vol. 14(18), pages 1-15, September.
  52. Jessica Pesantez-Narvaez & Montserrat Guillen & Manuela Alcañiz, 2019. "Predicting Motor Insurance Claims Using Telematics Data—XGBoost versus Logistic Regression," Risks, MDPI, vol. 7(2), pages 1-16, June.
  53. Reuven Y. Rubinstein, 2006. "How Many Needles are in a Haystack, or How to Solve #P-Complete Counting Problems Fast," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 5-51, March.
  54. Ad Ridder & Bruno Tuffin, 2012. "Probabilistic Bounded Relative Error Property for Learning Rare Event Simulation Techniques," Tinbergen Institute Discussion Papers 12-103/III, Tinbergen Institute.
  55. Wyean Chan & Ger Koole & Pierre L'Ecuyer, 2014. "Dynamic Call Center Routing Policies Using Call Waiting and Agent Idle Times," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 544-560, October.
  56. Sahar Abbas & Fahimeh Moosavi, 2012. "Finding shortest path in static networks: using a modified algorithm," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 1(1), pages 29-34, January.
  57. Zheng Peng & Donghua Wu & Quan Zheng, 2013. "A Level-Value Estimation Method and Stochastic Implementation for Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 493-523, February.
  58. Mehni, Moien Barkhori & Mehni, Mohammad Barkhori, 2023. "Reliability analysis with cross-entropy based adaptive Markov chain importance sampling and control variates," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
  59. Papaioannou, Iason & Geyer, Sebastian & Straub, Daniel, 2019. "Improved cross entropy-based importance sampling with a flexible mixture model," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
  60. Wu, Xin & Nie, Lei & Xu, Meng, 2017. "Robust fuzzy quality function deployment based on the mean-end-chain concept: Service station evaluation problem for rail catering services," European Journal of Operational Research, Elsevier, vol. 263(3), pages 974-995.
  61. Enlu Zhou & Xi Chen, 2013. "Sequential Monte Carlo simulated annealing," Journal of Global Optimization, Springer, vol. 55(1), pages 101-124, January.
  62. Xianmin Wang & Xinlong Zhang & Jia Bi & Xudong Zhang & Shiqiang Deng & Zhiwei Liu & Lizhe Wang & Haixiang Guo, 2022. "Landslide Susceptibility Evaluation Based on Potential Disaster Identification and Ensemble Learning," IJERPH, MDPI, vol. 19(21), pages 1-26, October.
  63. Thirunavukkarasu, M. & Sawle, Yashwant & Lala, Himadri, 2023. "A comprehensive review on optimization of hybrid renewable energy systems using various optimization techniques," Renewable and Sustainable Energy Reviews, Elsevier, vol. 176(C).
  64. Turati, Pietro & Pedroni, Nicola & Zio, Enrico, 2016. "Advanced RESTART method for the estimation of the probability of failure of highly reliable hybrid dynamic systems," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 117-126.
  65. Price, David J. & Bean, Nigel G. & Ross, Joshua V. & Tuke, Jonathan, 2018. "An induced natural selection heuristic for finding optimal Bayesian experimental designs," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 112-124.
  66. Bohteh Loh, Boris-Edmond & Nfah, Eustace Mbaka, 2024. "Techno – economic and environmental design of a three – phase hybrid renewable energy system for UNVDA Ndop Cameroon using meta-heuristic and analytical approaches," Renewable Energy, Elsevier, vol. 237(PA).
  67. Bin Liu, 2017. "Posterior exploration based sequential Monte Carlo for global optimization," Journal of Global Optimization, Springer, vol. 69(4), pages 847-868, December.
  68. Simon L. Dürr & Andrea Levy & Ursula Rothlisberger, 2023. "Metal3D: a general deep learning framework for accurate metal ion location prediction in proteins," Nature Communications, Nature, vol. 14(1), pages 1-14, December.
  69. Da, Fang & Kou, Gang & Peng, Yi, 2022. "Deep learning based dual encoder retrieval model for citation recommendation," Technological Forecasting and Social Change, Elsevier, vol. 177(C).
  70. Rishang Long & Jianhua Zhang, 2016. "Risk Assessment Method of UHV AC/DC Power System under Serious Disasters," Energies, MDPI, vol. 10(1), pages 1-13, December.
  71. El Masri, Maxime & Morio, Jérôme & Simatos, Florian, 2021. "Improvement of the cross-entropy method in high dimension for failure probability estimation through a one-dimensional projection without gradient estimation," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
  72. Alexander L Krall & Michael E Kuhl & Shanchieh J Yang, 2022. "Estimation of cyber network risk using rare event simulation," The Journal of Defense Modeling and Simulation, , vol. 19(1), pages 37-55, January.
  73. Satyajith Amaran & Nikolaos V. Sahinidis & Bikram Sharda & Scott J. Bury, 2016. "Simulation optimization: a review of algorithms and applications," Annals of Operations Research, Springer, vol. 240(1), pages 351-380, May.
  74. Caballero, Rafael & Hernández-Díaz, Alfredo G. & Laguna, Manuel & Molina, Julián, 2015. "Cross entropy for multiobjective combinatorial optimization problems with linear relaxations," European Journal of Operational Research, Elsevier, vol. 243(2), pages 362-368.
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