# An agent-oriented hierarchic strategy for solving inverse problems

Maciej Smołka; Robert Schaefer; Maciej Paszyński; David Pardo; Julen Álvarez-Aramberri

International Journal of Applied Mathematics and Computer Science (2015)

- Volume: 25, Issue: 3, page 483-498
- ISSN: 1641-876X

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topMaciej Smołka, et al. "An agent-oriented hierarchic strategy for solving inverse problems." International Journal of Applied Mathematics and Computer Science 25.3 (2015): 483-498. <http://eudml.org/doc/271762>.

@article{MaciejSmołka2015,

abstract = {The paper discusses the complex, agent-oriented hierarchic memetic strategy (HMS) dedicated to solving inverse parametric problems. The strategy goes beyond the idea of two-phase global optimization algorithms. The global search performed by a tree of dependent demes is dynamically alternated with local, steepest descent searches. The strategy offers exceptionally low computational costs, mainly because the direct solver accuracy (performed by the hp-adaptive finite element method) is dynamically adjusted for each inverse search step. The computational cost is further decreased by the strategy employed for solution inter-processing and fitness deterioration. The HMS efficiency is compared with the results of a standard evolutionary technique, as well as with the multi-start strategy on benchmarks that exhibit typical inverse problems' difficulties. Finally, an HMS application to a real-life engineering problem leading to the identification of oil deposits by inverting magnetotelluric measurements is presented. The HMS applicability to the inversion of magnetotelluric data is also mathematically verified.},

author = {Maciej Smołka, Robert Schaefer, Maciej Paszyński, David Pardo, Julen Álvarez-Aramberri},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {inverse problems; hybrid optimization methods; memetic algorithms; multi-agent systems; magnetotelluric data inversion},

language = {eng},

number = {3},

pages = {483-498},

title = {An agent-oriented hierarchic strategy for solving inverse problems},

url = {http://eudml.org/doc/271762},

volume = {25},

year = {2015},

}

TY - JOUR

AU - Maciej Smołka

AU - Robert Schaefer

AU - Maciej Paszyński

AU - David Pardo

AU - Julen Álvarez-Aramberri

TI - An agent-oriented hierarchic strategy for solving inverse problems

JO - International Journal of Applied Mathematics and Computer Science

PY - 2015

VL - 25

IS - 3

SP - 483

EP - 498

AB - The paper discusses the complex, agent-oriented hierarchic memetic strategy (HMS) dedicated to solving inverse parametric problems. The strategy goes beyond the idea of two-phase global optimization algorithms. The global search performed by a tree of dependent demes is dynamically alternated with local, steepest descent searches. The strategy offers exceptionally low computational costs, mainly because the direct solver accuracy (performed by the hp-adaptive finite element method) is dynamically adjusted for each inverse search step. The computational cost is further decreased by the strategy employed for solution inter-processing and fitness deterioration. The HMS efficiency is compared with the results of a standard evolutionary technique, as well as with the multi-start strategy on benchmarks that exhibit typical inverse problems' difficulties. Finally, an HMS application to a real-life engineering problem leading to the identification of oil deposits by inverting magnetotelluric measurements is presented. The HMS applicability to the inversion of magnetotelluric data is also mathematically verified.

LA - eng

KW - inverse problems; hybrid optimization methods; memetic algorithms; multi-agent systems; magnetotelluric data inversion

UR - http://eudml.org/doc/271762

ER -

## References

top- Álvarez-Aramberri, J., Pardo, D. and Barucq, H. (2013). Inversion of magnetotelluric measurements using multigoal oriented hp-adaptivity, Procedia Computer Science 18: 1564-1573.
- Barabasz, B., Gajda-Zagórska, E., Migórski, S., Paszyński, M., Schaefer, R. and Smołka, M. (2014). A hybrid algorithm for solving inverse problems in elasticity, International Journal of Applied Mathematics and Computer Science 24(4): 865-886, DOI: 10.2478/amcs-2014-0064. Zbl1309.49033
- Beasley, D., Bull, D.R. and Martin, R.R. (1993). A sequential niche technique for multimodal function optimization, Evolutionary Computation 1(2): 101-125.
- Berenger, J.-P. (1994). A perfectly matched layer for the absortion of electromagnetic waves, Journal of Computational Physics 114(2): 185-200. Zbl0814.65129
- Byrski, A., Schaefer, R., Smołka, M. and Cotta, C. (2013). Asymptotic guarantee of success for multi-agent memetic systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 61(1): 257-278.
- Cetnarowicz, K., Kisiel-Dorohinicki, M. and Nawarecki, E. (1996). The application of evolution process in multi-agent world (MAW) to the prediction system, in M. Tokoro (Ed.), Proceedings of the 2nd International Conference on Multiagent Systems (ICMAS-96), Menlo Park, CA, USA, pp. 26-32.
- Demkowicz, L. (2006). Computing with hp-Adaptive Finite Elements, Vol. 1: One and Two Dimensional Elliptic and Maxwell Problems, Chapman & Hall/CRC, Boca Raton, FL.
- Demkowicz, L., Kurtz, J., Pardo, D., Paszyński, M., Rachowicz, W. and Zdunek, A. (2007). Computing with hp-Adaptive Finite Elements, Vol. 2. Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications, Chapman & Hall/CRC, Boca Raton, FL. Zbl1148.65001
- Ester, M., Kriegel, H.-P., Sander, J. and Xu, X. (1996). A density-based algorithm for discovering clusters in large spatial databases with noise, Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining KDD-96, Portland, OR, USA, pp. 226-231.
- FIPA (2002). Foundation for Intelligent Physical Agents (FIPA) Specifications, www.fipa.org.
- Gajda-Zagórska, E., Schaefer, R., Smołka, M., Paszyński, M. and Pardo, D. (2015). A hybrid method for inversion of 3D DC resistivity logging measurements, Natural Computing 14(3): 355-374. DOI: 10.1007/s11047-014-9440-y.
- Grochowski, M., Smołka, M. and Schaefer, R. (2006). Architectural principles and scheduling strategies for computing agent systems, Fundamenta Informaticae 71(1): 15-26. Zbl1095.68006
- Jojczyk, P. and Schaefer, R. (2009). Global impact balancing in the hierarchic genetic search, Computing and Informatics 28(2): 181-193.
- Neri, F., Cotta, C. and Moscato, P. (Eds.) (2012). Handbook of Memetic Algorithms, Studies in Computational Intelligence, Vol. 379, Springer, Heidelberg.
- Obuchowicz, A. (1997). The evolutionary search with soft selection and deterioration of the objective function, Proceedings of the 6th International Conference on Intelligent Information Systems IIS'97, Zakopane, Poland, pp. 288-295.
- Pardo, D., Demkowicz, L., Torres-Verdín, C. and Tabarovsky, L. (2006). A goal-oriented hp-adaptive finite element method with electromagnetic applications, Part I: Electrostatics, International Journal for Numerical Methods in Engineering 65(8): 1269-1309. Zbl1118.78015
- Schaefer, R. and Kołodziej, J. (2003). Genetic search reinforced by the population hierarchy, in K.A. De Jong, R. Poli and J. Rowe (Eds.), Foundations of Genetic Algorithms 7, Morgan Kaufman, San Francisco, CA, pp. 383-399.
- Smołka, M., Gajda-Zagórska, E., Schaefer, R., Paszyński, M. and Pardo, D. (2015). A hybrid method for inversion of 3D AC logging measurements, Applied Soft Computing 36: 442-456.
- Smołka, M. and Schaefer, R. (2014). A memetic framework for solving difficult inverse problems, in A.I. Esparcia-Alcázar and A.M. Mora (Eds.), EvoApplications 2014, Lecture Notes in Computer Science, Vol. 8602, Springer, Berlin/Heidelberg, pp. 138-149.
- Vozoff, K. (1972). The magnetotelluric method in the exploration of sedimentary basins, Geophysics 37(1): 98-141.
- Wierzba, B., Semczuk, A., Kołodziej, J. and Schaefer, R. (2003). Hierarchical genetic strategy with real number encoding, Proceedings of the 6th Conference on Evolutionary Algorithms and Global Optimization, Łagów, Poland, pp. 231-237.
- Wolny, A. and Schaefer, R. (2011). Improving population-based algorithms with fitness deterioration, Journal of Telecommunications and Information Technology 4: 31-44.

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