Skip to main content
SpringerLink
Log in

Automatic calibration of dynamic and heterogeneous parameters in agent-based models

  • Published:
Autonomous Agents and Multi-Agent Systems Aims and scope Submit manuscript

Abstract

Simulation has been applied to diverse domains such as urban growth modeling and market dynamics modeling. Some of these applications may require validations, based on some real-world observations modeled in the simulation. This validation can be conducted as either qualitative face-validation or quantitative empirical validation; however, as the importance and accumulation of data grows, the importance of quantitative validation has been highlighted in recent studies. The key component of quantitative validation is finding a calibrated set of parameters to regenerate the real-world observations in the simulation models. While the parameter of interest to be calibrated has hitherto been fixed throughout simulation executions, we expand the static parameter calibration in two dimensions in this study, dynamically and heterogeneously. The dynamic calibration changes the parameter values over the simulation period by reflecting the simulation output trend, and the heterogeneous calibration changes the parameter values per simulated entity clusters by considering the similarities of the entity states. We experimented with the proposed calibrations on a hypothetical case and a real-world case. For the hypothetical scenario, we used the wealth distribution model to illustrate how our calibration works. For the real-world scenario, we selected the real estate market model. The models were selected, because of two reasons. First, they have heterogeneous entities, being agent-based models. Second, they are agent-based models exhibiting real-world trends over time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Notes

  1. https://github.com/Kim-Dongjun/Automatic-Calibration-of-Dynamic-and-Heterogeneous-Parameters-in-Agent-based-Models.

  2. Lease contract includes Jeonse and rental contract, where Jeonse is the lump-sum housing lease that is a Korean-specific residential form of living for two years; it is secured by paying a large amount of deposit at the initiation of the contract, which is returned at the end of the contract period, instead of paying rental fee monthly.

  3. Jeonse is the lump-sum housing lease form of living for two years. The tenant pay large amount of deposit, instead of paying monthly rental fee.

References

  1. Bae, J. W., Lee, S., Hong, J. H., & Moon, I. C. (2014). Simulation-based analyses of an evacuation from a metropolis during a bombardment. Simulation, 90(11), 1244–1267.

    Article  Google Scholar 

  2. Barde, S. (2017). A practical, accurate, information criterion for nth order Markov processes. Computational Economics, 50(2), 281–324.

    Article  Google Scholar 

  3. Barde, S., & van der Hoog, S. (2017). An empirical validation protocol for large-scale agent-based models. Technical report, School of Economics, University of Kent.

  4. Beisbart, C., & Saam, N. J. (2018). Computer simulation validation: Fundamental concepts, methodological frameworks, and philosophical perspectives. Berlin: Springer.

    MATH  Google Scholar 

  5. Bertsekas, D. P., Bertsekas, D. P., Bertsekas, D. P., & Bertsekas, D. P. (1995). Dynamic programming and optimal control (Vol. 1). Belmont, MA: Athena Scientific.

    MATH  Google Scholar 

  6. Bilmes, J. A., et al. (1998). A gentle tutorial of the EM algorithm and its application to parameter estimation for gaussian mixture and hidden Markov models. International Computer Science Institute, 4(510), 126.

    Google Scholar 

  7. Bishop, C. M. (2006). Pattern recognition and machine learning. Berlin: Springer.

    MATH  Google Scholar 

  8. Bodin, E., Kaiser, M., Kazlauskaite, I., Campbell, N. D., & Ek, C. H. (2019). Modulated bayesian optimization using latent gaussian process models. arXiv preprint arXiv:190611152

  9. Bonabeau, E. (2002). Agent-based modeling: Methods and techniques for simulating human systems. Proceedings of the National Academy of Sciences, 99(suppl 3), 7280–7287.

    Article  Google Scholar 

  10. Bracke, P. (2015). How much do investors pay for houses? Real Estate Economics, 49(S1), 41–73.

    Article  Google Scholar 

  11. Brischetto, A., Voss, G., et al. (1999). A structural vector autoregression model of monetary policy in Australia. Sydney, NSW: Reserve Bank of Australia Sydney.

    Google Scholar 

  12. Brochu, E., Cora, V. M., & De Freitas, N. (2010). A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. arXiv preprint arXiv:10122599

  13. Buigut, S. K., & Valev, N. T. (2005). Is the proposed east African monetary union an optimal currency area? A structural vector autoregression analysis. World Development, 33(12), 2119–2133.

    Article  Google Scholar 

  14. Bull, A. D. (2011). Convergence rates of efficient global optimization algorithms. Journal of Machine Learning Research, 12(Oct), 2879–2904.

  15. Byrne, H., & Drasdo, D. (2009). Individual-based and continuum models of growing cell populations: A comparison. Journal of Mathematical Biology, 58(4–5), 657.

    Article  MathSciNet  MATH  Google Scholar 

  16. Calvez, B., & Hutzler, G. (2005). Automatic tuning of agent-based models using genetic algorithms. In Proceedings of the 6th international conference on multi-agent-based simulation (pp. 41–57). Berlin, Heidelberg: Springer.

  17. Cares, J. R. (2002). The use of agent-based models in military concept development. In Proceedings of the winter simulation conference (Vol. 1, pp. 935–939). IEEE.

  18. Chen, Y., & Gutmann, M. U. (2019). Adaptive gaussian copula ABC. arXiv preprint arXiv:190210704.

  19. Dasgupta, S. (1999). Learning mixtures of gaussians. In 40th annual symposium on foundations of computer science (Cat. No. 99CB37039) (pp. 634–644). IEEE.

  20. Epstein, J. M. (2006). Generative social science: Studies in agent-based computational modeling. Princeton: Princeton University Press.

    MATH  Google Scholar 

  21. Ewens, W. J. (1990). Population genetics theory-the past and the future. In Mathematical and statistical developments of evolutionary theory (pp. 177–227). Dordrecht: Springer.

  22. Fehler, M., Klügl, F., & Puppe, F. (2004). Techniques for analysis and calibration of multi-agent simulations. In International workshop on engineering societies in the agents world (pp. 305–321). Berlin, Heidelberg: Springer.

  23. Forbes, F., & Wraith, D. (2014). A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweight: Application to robust clustering. Statistics and Computing, 24(6), 971–984.

    Article  MathSciNet  MATH  Google Scholar 

  24. Fox, E. B., Sudderth, E. B., Jordan, M. I., & Willsky, A. S. (2008). An HDP-HMM for systems with state persistence. In Proceedings of the 25th international conference on Machine learning (pp. 312–319). ACM.

  25. Frazier, P. I. (2018). A tutorial on Bayesian optimization. arXiv preprintarXiv:180702811

  26. Gini, C. (1936). On the measure of concentration with special reference to income and statistics. Colorado College Publication, General Series, 208, 73–79.

    Google Scholar 

  27. Grünewälder, S., Audibert, J. Y., Opper, M., & Shawe-Taylor, J. (2010). Regret bounds for gaussian process bandit problems. In Proceedings of the thirteenth international conference on artificial intelligence and statistics (pp. 273–280).

  28. Guerini, M., & Moneta, A. (2017). A method for agent-based models validation. Journal of Economic Dynamics and Control, 82, 125–141.

    Article  MathSciNet  MATH  Google Scholar 

  29. Gutmann, M. U., Dutta, R., Kaski, S., & Corander, J. (2014). Statistical inference of intractable generative models via classification. arXiv preprint arXiv:14074981

  30. Hamilton, J. D. (2016) Regime switching models. The new Palgrave dictionary of economics pp. 1–7

  31. Hansen, N., & Ostermeier, A. (2001). Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation, 9(2), 159–195.

    Article  Google Scholar 

  32. Hara, S., Kita, H., Ikeda, K., & Susukita, M. (2013). Configuring agents’ attributes with simulated annealing. In Agent-based approaches in economic and social complex systems VII (pp. 45–59). Tokyo: Springer.

  33. Heppenstall, A. J., Evans, A. J., & Birkin, M. H. (2007). Genetic algorithm optimisation of an agent-based model for simulating a retail market. Environment and Planning B: Planning and Design, 34(6), 1051–1070.

    Article  Google Scholar 

  34. Hoffman, M., Brochu, E., & de Freitas, N. (2011). Portfolio allocation for Bayesian optimization. In Proceedings of the twenty-seventh conference on uncertainty in artificial intelligence (pp. 327–336). AUAI Press.

  35. Hosseinali, F., Alesheikh, A. A., & Nourian, F. (2013). Agent-based modeling of urban land-use development, case study: Simulating future scenarios of Qazvin city. Cities, 31, 105–113.

    Article  Google Scholar 

  36. Jurafsky, D. (2000). Speech & language processing. London: Pearson Education India.

    Google Scholar 

  37. Kingma, D. P., & Welling, M. (2013). Auto-encoding variational Bayes. arXiv preprintarXiv:13126114.

  38. Kleijnen, J. P. (1995). Verification and validation of simulation models. European Journal of Operational Research, 82(1), 145–162.

    Article  MathSciNet  MATH  Google Scholar 

  39. Kosmidis, I., & Karlis, D. (2016). Model-based clustering using copulas with applications. Statistics and Computing, 26(5), 1079–1099.

    Article  MathSciNet  MATH  Google Scholar 

  40. Lamperti, F., Roventini, A., & Sani, A. (2018). Agent-based model calibration using machine learning surrogates. Journal of Economic Dynamics and Control, 90, 366–389.

    Article  MathSciNet  MATH  Google Scholar 

  41. Lewis DD, Gale WA (1994) A sequential algorithm for training text classiers. In: SIGIR'94, Springer, pp 3–12

  42. Lizotte, D. J. (2008). Practical Bayesian optimization. Alberta: University of Alberta.

    Google Scholar 

  43. Mahalanobis, P. C. (1936). On the generalized distance in statistics. New Delhi: National Institute of Science of India.

    MATH  Google Scholar 

  44. Malhotra, A. (2009). Agent-based modeling in defence. DRDO Science Spectrum., 60–65.

  45. Manson, S. (2003). Validation and verification of multi-agent models for ecosystem management. Complexity and ecosystem management: The theory and practice of multi-agent approaches. (pp. 63–74)

  46. Marjoram, P., Molitor, J., Plagnol, V., & Tavaré, S. (2003). Markov chain Monte Carlo without likelihoods. Proceedings of the National Academy of Sciences, 100(26), 15324–15328.

    Article  Google Scholar 

  47. Marks, R. E. (2013). Validation and model selection: Three similarity measures compared. Complexity Economics, 2(1), 41–61.

    Article  Google Scholar 

  48. Marks, R. E. (2019). Validation metrics: A case for pattern-based methods. In Computer simulation validation (pp. 319–338). Springer.

  49. Meeds, E., & Welling, M. (2014). GPS-ABC: Gaussian process surrogate approximate Bayesian computation. arXiv preprint arXiv:14012838

  50. Mockus, J. (2012). Bayesian approach to global optimization: Theory and applications. Berlin: Springer.

    MATH  Google Scholar 

  51. Moon, I. C., Kim, D., Yun, T. S., Bae, J. W., Kang, D. O., & Paik, E. (2018). Data-driven automatic calibration for validation of agent-based social simulations. In 2018 IEEE international conference on systems, man, and cybernetics (SMC) (pp. 1605–1610). IEEE.

  52. Moon, T. K. (1996). The expectation-maximization algorithm. IEEE Signal Processing Magazine, 13(6), 47–60.

    Article  Google Scholar 

  53. Morokoff, W. J., & Caflisch, R. E. (1994). Quasi-random sequences and their discrepancies. SIAM Journal on Scientific Computing, 15(6), 1251–1279.

    Article  MathSciNet  MATH  Google Scholar 

  54. Murphy, K. P. (2007). Conjugate Bayesian analysis of the gaussian distribution. def 1(22):16

  55. Murphy, K. P. (2012). Machine learning: A probabilistic perspective. Cambridge: MIT Press.

    MATH  Google Scholar 

  56. Naiem, A., Reda, M., El-Beltagy, M., & El-Khodary, I. (2010). An agent based approach for modeling traffic flow. In 2010 The 7th international conference on informatics and systems (INFOS) (pp. 1–6). IEEE.

  57. Nguyen, A. T., Reiter, S., & Rigo, P. (2014). A review on simulation-based optimization methods applied to building performance analysis. Applied Energy, 113, 1043–1058.

    Article  Google Scholar 

  58. Noel, M. M., & Jannett, T. C. (2004). Simulation of a new hybrid particle swarm optimization algorithm. In Proceedings of the Thirty-sixth southeastern symposium on system theory, 2004 (pp. 150–153). IEEE.

  59. Peel, D., & McLachlan, G. J. (2000). Robust mixture modelling using the t distribution. Statistics and Computing, 10(4), 339–348.

    Article  Google Scholar 

  60. Preuss, R., & von Toussaint, U. (2018). Global optimization employing gaussian process-based Bayesian surrogates. Entropy, 20(3), 201.

    Article  MATH  Google Scholar 

  61. Rabiner, L. R. (1989). A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE, 77(2), 257–286.

    Article  Google Scholar 

  62. Railsback, S. F., & Grimm, V. (2019). Agent-based and individual-based modeling: A practical introduction. Princeton: Princeton University Press.

    MATH  Google Scholar 

  63. Rasmussen, C., & Williams, C. (2006). Gaussian Processes for Machine Learning. Adaptive Computation and Machine Learning.

  64. Recchioni, M. C., Tedeschi, G., & Gallegati, M. (2015). A calibration procedure for analyzing stock price dynamics in an agent-based framework. Journal of Economic Dynamics and Control, 60, 1–25.

    Article  MathSciNet  MATH  Google Scholar 

  65. Ryzhov, I. O. (2016). On the convergence rates of expected improvement methods. Operations Research, 64(6), 1515–1528.

    Article  MathSciNet  MATH  Google Scholar 

  66. Sargent, R. G. (2010). Verification and validation of simulation models. In Proceedings of the 2010 winter simulation conference (pp. 166–183). IEEE.

  67. Sasena, M. J., Papalambros, P., & Goovaerts, P. (2002). Exploration of metamodeling sampling criteria for constrained global optimization. Engineering Optimization, 34(3), 263–278.

    Article  Google Scholar 

  68. Schonlau, M. (1997). Computer experiments and global optimization. PhD thesis, University of Waterloo, Waterloo, Ont., Canada, Canada, aAINQ22234.

  69. Scogings, C., & Hawick, K. (2012). An agent-based model of the battle of Isandlwana. In Proceedings of the 2012 winter simulation conference (WSC) (pp. 1–12). IEEE.

  70. Sethuraman, J. (1994). A constructive definition of dirichlet priors. Statistica Sinica, 4, 639–650.

    MathSciNet  MATH  Google Scholar 

  71. Silver, M., & Heravi, S. (2007). Why elementary price index number formulas differ: Evidence on price dispersion. Journal of Econometrics, 140(2), 874–883.

    Article  MathSciNet  MATH  Google Scholar 

  72. Sisson, S. A., Fan, Y., & Tanaka, M. M. (2007). Sequential Monte Carlo without likelihoods. Proceedings of the National Academy of Sciences, 104(6), 1760–1765.

    Article  MathSciNet  MATH  Google Scholar 

  73. Snoek, J., Larochelle, H., & Adams, R. P. (2012). Practical Bayesian optimization of machine learning algorithms. In Advances in neural information processing systems (pp. 2951–2959). Lake Tahoe: Harrahs and harveys.

  74. Sóbester, A., Leary, S. J., & Keane, A. J. (2005). On the design of optimization strategies based on global response surface approximation models. Journal of Global Optimization, 33(1), 31–59.

    Article  MathSciNet  MATH  Google Scholar 

  75. Stonedahl, F., & Wilensky, U. (2010a). Evolutionary robustness checking in the artificial anasazi model. In 2010 AAAI fall symposium series.

  76. Stonedahl, F., & Wilensky, U. (2010b). Finding forms of flocking: Evolutionary search in abm parameter-spaces. In International workshop on multi-agent systems and agent-based simulation (pp. 61–75). Berlin, Heidelberg: Springer.

  77. Suri, R. (1987). Infinitesimal perturbation analysis for general discrete event systems. Journal of the ACM (JACM), 34(3), 686–717.

    Article  MathSciNet  Google Scholar 

  78. Tavaré, S., Balding, D. J., Griffiths, R. C., & Donnelly, P. (1997). Inferring coalescence times from DNA sequence data. Genetics, 145(2), 505–518.

    Article  Google Scholar 

  79. Teh, Y. W. (2010). Dirichlet process. Encyclopedia of Machine Learning (pp 280–287).

  80. Tesfatsion, L. (2002). Agent-based computational economics: Growing economies from the bottom up. Artificial Life, 8(1), 55–82.

    Article  MathSciNet  Google Scholar 

  81. Tesfatsion, L. (2006). Agent-based computational economics: A constructive approach to economic theory. Handbook of Computational Economics, 2, 831–880.

    Article  Google Scholar 

  82. Thacker, B. H., Doebling, S. W., Hemez, F. M., Anderson, M. C., Pepin, J. E., & Rodriguez, E. A. (2004). Concepts of model verification and validation. Tech. rep., Los Alamos National Lab.

  83. Thiele, J. C., Kurth, W., & Grimm, V. (2014). Facilitating parameter estimation and sensitivity analysis of agent-based models: A cookbook using NetLogo and R. Journal of Artificial Societies and Social Simulation, 17(3), 11.

    Article  Google Scholar 

  84. Tresidder, E., Zhang, Y., & Forrester, A. (2012). Acceleration of building design optimisation through the use of kriging surrogate models. Proceedings of building simulation and optimization (pp. 1–8). Loughborough, UK.

  85. Valiant, L. (2013). Probably Approximately Correct: NatureÕs Algorithms for Learning and Prospering in a Complex World. Basic Books (AZ)

  86. Vazquez, E., & Bect, J. (2010). Convergence properties of the expected improvement algorithm with fixed mean and covariance functions. Journal of Statistical Planning and Inference, 140(11), 3088–3095.

    Article  MathSciNet  MATH  Google Scholar 

  87. Whittaker, G., Confesor, R., Di Luzio, M., Arnold, J., et al. (2010). Detection of overparameterization and overfitting in an automatic calibration of swat. Transactions of the ASABE, 53(5), 1487–1499.

    Article  Google Scholar 

  88. Wilensky, U. (1998). Netlogo wealth distribution model. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. https://ccl.northwestern.edu/netlogo/models/WealthDistribution.

  89. Willems, F. M., Shtarkov, Y. M., & Tjalkens, T. J. (1995). The context-tree weighting method: Basic properties. IEEE Transactions on Information Theory, 41(3), 653–664.

    Article  MATH  Google Scholar 

  90. Wilson, A., & Adams, R. (2013). Gaussian process kernels for pattern discovery and extrapolation. In International conference on machine learning (pp. 1067–1075).

  91. Wood, S. N. (2010). Statistical inference for noisy nonlinear ecological dynamic systems. Nature, 466(7310), 1102.

    Article  Google Scholar 

  92. Yun, T. S., Moon, I. C., et al. (2020). Housing market agent-based simulation with loan-to-value and debt-to-income. Journal of Artificial Societies and Social Simulation, 23(4), 1–5.

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by Institute of Information & Communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) (No.2018-0-00225).

Author information

Authors and Affiliations

  1. Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea

    Dongjun Kim, Tae-Sub Yun & Il-Chul Moon

  2. KOREATECH: Korea University of Technology and Education, Cheonan, Republic of Korea

    Jang Won Bae

Authors
  1. Dongjun Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tae-Sub Yun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Il-Chul Moon
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jang Won Bae
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jang Won Bae.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, D., Yun, TS., Moon, IC. et al. Automatic calibration of dynamic and heterogeneous parameters in agent-based models. Auton Agent Multi-Agent Syst 35, 46 (2021). https://doi.org/10.1007/s10458-021-09528-4

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10458-021-09528-4

Keywords

Search

Navigation