Abstract
We describe an approach to utilize a broader spectrum of domain knowledge to model magnetization curves for high magnetic field strengths \(0 \le H \le 10^{6}\) with access to data points far below the saturation polarization. Thereby, we extend the implementation of Shape-Constrained Symbolic Regression. The extension allows the modification of model estimates by a given expression to apply additional sets of constraints. We apply the given expression of an Extended Constraint row-by-row and compare the minimum and maximum outputs with the target interval. Furthermore, we introduce regions and thresholds as additional tools for constraint description and soft constraint evaluation. Our achieved results demonstrate the positive impact of such additional knowledge. The logical downside is the dependence on that knowledge to describe applicable constraints. Nevertheless, the approach is a promising way to reduce the human calculation effort for extrapolating magnetization curves. For future work, we plan to combine soft and hard constraint evaluation as well as the utilization of structure template GP.
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References
Affenzeller, M., Wagner, S.: Offspring selection: a new self-adaptive selection scheme for genetic algorithms. In: Ribeiro, B., Albrecht, R.F., Dobnikar, A., Pearson, D.W., Steele, N.C. (eds.) Adaptive and Natural Computing Algorithms, pp. 218–221. Springer, Vienna (2005). https://doi.org/10.1007/3-211-27389-1_52
Affenzeller, M., Wagner, S., Winkler, S., Beham, A.: Genetic Algorithms and Genetic Programming: Modern Concepts and Practical Applications. CRC Press (2009)
Bladek, I., Krawiec, K.: Solving symbolic regression problems with formal constraints. In: Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2019, pp. 977–984. Association for Computing Machinery, New York (2019)
Haider, C., de França, F.O., Burlacu, B., Kronberger, G.: Using shape constraints for improving symbolic regression models. arXiv preprint arXiv:2107.09458 (2021)
Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. MIT Press (1992)
Hornby, G.S.: ALPS: the age-layered population structure for reducing the problem of premature convergence, GECCO 2006, pp. 815–822. Association for Computing Machinery, New York (2006)
Kommenda, M., Kronberger, G., Wagner, S., Winkler, S., Affenzeller, M.: On the architecture and implementation of tree-based genetic programming in heuristicLab, GECCO 2012, pp. 101–108. Association for Computing Machinery, New York (2012)
Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection, vol. 1. MIT Press (1992)
Kronberger, G., de França, F.O., Burlacu, B., Haider, C., Kommenda, M.: Shape-constrained symbolic regression-improving extrapolation with prior knowledge. Evol. Comput. 30(1), 75–98 (2022)
Labridis, D., Dokopoulos, P.: Calculation of eddy current losses in nonlinear ferromagnetic materials. IEEE Trans. Magn. 25(3), 2665–2669 (1989)
Pechstein, C., Jüttler, B.: Monotonicity-preserving interproximation of B-H-curves. J. Comput. Appl. Math. 196(1), 45–57 (2006)
Skarlatos, A., Theodoulidis, T.: A modal approach for the solution of the non-linear induction problem in ferromagnetic media. IEEE Trans. Magn. 52(2), 1–11 (2016)
Szewczyk, R.: Technical BH saturation magnetization curve models for spice, fem and mom simulations. J. Autom. Mob. Rob. Intell. Syst. 10(2), 3–7 (2016)
Wagner, S., Affenzeller, M.: HeuristicLab: a generic and extensible optimization environment. In: Ribeiro, B., Albrecht, R.F., Dobnikar, A., Pearson, D.W., Steele, N.C. (eds.) Adaptive and Natural Computing Algorithms, pp. 538–541. Springer Vienna, Vienna (2005). https://doi.org/10.1007/3-211-27389-1_130
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This work has been supported by the LCM - K2 Center within the framework of the Austrian COMET-K2 program.
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Piringer, D., Wagner, S., Haider, C., Fohler, A., Silber, S., Affenzeller, M. (2022). Improving the Flexibility of Shape-Constrained Symbolic Regression with Extended Constraints. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2022. EUROCAST 2022. Lecture Notes in Computer Science, vol 13789. Springer, Cham. https://doi.org/10.1007/978-3-031-25312-6_18
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