Koopman Mode Analysis of agent-based models of logistics processes
Autoři:
James Hogg aff001; Maria Fonoberova aff001; Igor Mezić aff001; Ryan Mohr aff001
Působiště autorů:
Aimdyn, Inc., Santa Barbara, CA, United States of America
aff001; University of California Santa Barbara, Santa Barbara, CA, United States of America
aff002
Vyšlo v časopise:
PLoS ONE 14(9)
Kategorie:
Research Article
doi:
https://doi.org/10.1371/journal.pone.0222023
Souhrn
Modern logistics processes and systems can feature extremely complicated dynamics. Agent Based Modeling is emerging as a powerful modeling tool for design, analysis and control of such logistics systems. However, the complexity of the model itself can be overwhelming and mathematical meta-modeling tools are needed that aggregate information and enable fast and accurate decision making and control system design. Here we present Koopman Mode Analysis (KMA) as such a tool. KMA uncovers exponentially growing, decaying or oscillating collective patterns in dynamical data. We apply the methodology to two problems, both of which exhibit a bifurcation in dynamical behavior, but feature very different dynamics: Medical Treatment Facility (MTF) logistics and ship fueling (SF) logistics. The MTF problem features a transition between efficient operation at low casualty rates and inefficient operation beyond a critical casualty rate, while the SF problem features a transition between short mission life at low initial fuel levels and sustained mission beyond a critical initial fuel level. Both bifurcations are detected by analyzing the spectrum of the associated Koopman operator. Mathematical analysis is provided justifying the use of the Dynamic Mode Decomposition algorithm in punctuated linear decay dynamics that is featured in the SF problem.
Klíčová slova:
Physical sciences – Mathematics – Algebra – Linear algebra – Eigenvalues – Applied mathematics – Algorithms – Systems science – Agent-based modeling – Bifurcation theory – Materials science – Materials – Fuels – Chemistry – Chemical reactions – Decomposition – Engineering and technology – Energy and power – Research and analysis methods – Simulation and modeling – Computer and information sciences – Biology and life sciences – Psychology – Behavior – Social sciences
Zdroje
1. Abar S, Theodoropoulos GK, Lemarinier P, O’Hare GMP. Agent Based Modelling and Simulation tools: A review of the state-of-art software. Computer Science Review. 2017;24:13–33. https://doi.org/10.1016/j.cosrev.2017.03.001.
2. Epstein JM, Axtell R. Growing artificial societies: social science from the bottom up. Brookings Institution Press; 1996.
3. Auyang SY. Foundations of complex-system theories: in economics, evolutionary biology, and statistical physics. Cambridge University Press; 1999.
4. Epstein JM. Modeling civil violence: An agent-based computational approach. Proceedings of the National Academy of Sciences. 2002;99(suppl 3):7243–7250.
5. Makowsky M. An agent-based model of mortality shocks, intergenerational effects, and urban crime. Journal of Artificial Societies and Social Simulation. 2006;9(2).
6. Rauhut H, Junker M. Punishment deters crime because humans are bounded in their strategic decision-making. Journal of Artificial Societies and Social Simulation. 2009;12(3):1.
7. Bosse T, Gerritsen C. Social Simulation and Analysis of the Dynamics of Criminal Hot Spots. Journal of Artificial Societies and Social Simulation. 2010;13.
8. Fonoberova M, Fonoberov VA, Mezic I, Mezic J, Brantingham PJ. Nonlinear dynamics of crime and violence in urban settings. Journal of Artificial Societies and Social Simulation. 2012;15(1):2.
9. Fonoberova M, Mezić I, Mezić J, Mohr R. An agent-based model of urban insurgence: Effect of gathering sites and Koopman mode analysis. PloS one. 2018;13(10):e0205259.
10. LeBaron B. Empirical regularities from interacting long-and short-memory investors in an agent-based stock market. Ieee transactions on evolutionary computation. 2001;5(5):442–455.
11. Huang CC. Using intelligent agents to manage fuzzy business processes. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans. 2001;31(6):508–523.
12. Das R, Hanaoka S. An agent-based model for resource allocation during relief distribution. Journal of Humanitarian Logistics and Supply Chain Management. 2014.
13. Démare T, Bertelle C, Dutot A, Lévêque L. Modeling logistic systems with an agent-based model and dynamic graphs. Journal of Transport Geography. 2017;62:51–65. https://doi.org/10.1016/j.jtrangeo.2017.04.007.
14. Binmad R, Li M. Computational Models Based on Forgiveness Mechanism for Untrustworthy Agents. In: Lavangnananda K, Phon-Amnuaisuk S, Engchuan W, Chan JH, editors. Intelligent and Evolutionary Systems. Cham: Springer International Publishing; 2016. p. 29–42.
15. Stavash J, Chadha B, Wedgwood J, Welsh J, Parker M, Teitelbaum D. Agent Based Models for Logistics in Wargaming. In: Proceedings of the Fall 2003 SISO Simulation Interoperability Workshop; 2003.
16. Mezić I. Spectral Properties of Dynamical Systems, Model Reduction and Decompositions. Nonlinear Dynamics. 2005;41:309–325.
17. Mohr R, Mezić I. Construction of Eigenfunctions for Scalar-type Operators via Laplace Averages with Connections to the Koopman Operator. arXivorg. 2014; p. 1–25.
18. Mohr, R. M. Spectral Properties of the Koopman Operator in the Analysis of Nonstationary Dynamical Systems. Ph.D. thesis, University of California, Santa Barbara, Santa Barbara. 2014.
19. Korda M, Putinar M, Mezić I. Data-driven spectral analysis of the Koopman operator. arXiv. 2017;math.OC(1710.06532):1–18.
20. Schmid PJ, Sesterhenn J. Dynamic Mode Decomposition of Numerical and Experimental Data. In: Sixty-First Annual Meeting of the APS Division of Fluid Dynamics. San Antonio, Texas, USA; 2008.
21. Schmid PJ. Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics. 2010;656:5–28.
22. Kutz JN, Brunton SL, Brunton BW, Proctor JL. Dynamic Mode Decomposition. Philadelphia, PA: Society for Industrial and Applied Mathematics; 2016.
23. Drmač Z, Mezić I, Mohr R. Data Driven Modal Decompositions: Analysis and Enhancements. SIAM Journal on Scientific Computing. 2018;40(4):A2253–A2285.
24. Mauroy A, Mezić I. Global stability analysis using the eigenfunctions of the Koopman operator. IEEE Transactions on Automatic Control. 2016;61(11):3356–3369.
25. Crnjaric-Zic N, Macesic S, Mezic I. Koopman Operator Spectrum for Random Dynamical Systems. arXiv preprint arXiv:171103146. 2017.
26. Barbati M, Bruno G, Genovese A. Applications of agent-based models for optimization problems: A literature review. Expert Systems with Applications. 2012;39(5):6020–6028. https://doi.org/10.1016/j.eswa.2011.12.015.
27. Oremland M, Laubenbacher R. Optimization of Agent-Based Models: Scaling Methods and Heuristic Algorithms. Journal of Artificial Societies and Social Simulation. 2014;17(2):6.
28. Arvitrida NI. A review of agent-based modeling approach in the supply chain collaboration context. IOP Conference Series: Materials Science and Engineering. 2018;337:012015.
29. Fuller D, Martins Ferreira Filho VJ, Arruda EF. Oil industry value chain simulation with learning agents. Computers & Chemical Engineering. 2018;111:199–209.
30. Cabrera E, Taboada M, Iglesias ML, Epelde F, Luque E. Optimization of Healthcare Emergency Departments by Agent-Based Simulation. In: ICCS; 2011.
31. Weng S, Tsai B, Wang L, Chang C, Gotcher D. Using simulation and Data Envelopment Analysis in optimal healthcare efficiency allocations. In: Proceedings of the 2011 Winter Simulation Conference (WSC); 2011. p. 1295–1305.
32. Wong SY, Tsui KL, Chin KS, Xu M. A simulation study to achieve healthcare service quality improvement in accident emergency department (AED). In: 2011 IEEE International Conference on Quality and Reliability; 2011. p. 259–263.
33. Zeinali F, Mahootchi M, Sepehri MM. Resource planning in the emergency departments: A simulation-based metamodeling approach. Simulation Modelling Practice and Theory. 2015;53:123–138. https://doi.org/10.1016/j.simpat.2015.02.002.
34. Yousefi M, Yousefi M, Ferreira RPM, Kim JH, Fogliatto FS. Chaotic genetic algorithm and Adaboost ensemble metamodeling approach for optimum resource planning in emergency departments. Artificial Intelligence in Medicine. 2018;84:23–33. https://doi.org/10.1016/j.artmed.2017.10.002.
35. Korda M, Mezić I. Learning Koopman eigenfunctions for prediction and control: the transient case. arXiv e-prints. 2018; p. arXiv:1810.08733.
36. Lusch B, Kutz JN, Brunton SL. Deep learning for universal linear embeddings of nonlinear dynamics. Nature Communications. 2018;9.
37. Hogg J, Fonoberova M, Mezić I., Mohr R. Simulation results of two agent-based models of logistics systems. 2019. Available from: http://doi.org/10.5281/zenodo.2567599.
Článek vyšel v časopise
PLOS One
2019 Číslo 9
- Pomohou nám s detekcí karcinomu plic i včely?
- Duševní onemocnění se u teenagerů přenáší v rámci školní třídy
- Od kostiček k lidské kůži. Jak si postavit 3D biotiskárnu?
- Řekněte mi, co jíte, a já vám řeknu, jaká je úroveň vaší kognice
- Umělá inteligence v mozkovém implantátu pomáhá muži po mrtvici s dvojjazyčnou konverzací
Nejčtenější v tomto čísle
- Graviola (Annona muricata) attenuates behavioural alterations and testicular oxidative stress induced by streptozotocin in diabetic rats
- CH(II), a cerebroprotein hydrolysate, exhibits potential neuro-protective effect on Alzheimer’s disease
- Comparison between Aptima Assays (Hologic) and the Allplex STI Essential Assay (Seegene) for the diagnosis of Sexually transmitted infections
- Assessment of glucose-6-phosphate dehydrogenase activity using CareStart G6PD rapid diagnostic test and associated genetic variants in Plasmodium vivax malaria endemic setting in Mauritania
Zvyšte si kvalifikaci online z pohodlí domova
Všechny kurzy