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2020 | OriginalPaper | Chapter

Fitness Landscape Analysis of Dimensionally-Aware Genetic Programming Featuring Feynman Equations

Authors : Marko Durasevic, Domagoj Jakobovic, Marcella Scoczynski Ribeiro Martins, Stjepan Picek, Markus Wagner

Published in: Parallel Problem Solving from Nature – PPSN XVI

Publisher: Springer International Publishing

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Abstract

Genetic programming is an often-used technique for symbolic regression: finding symbolic expressions that match data from an unknown function. To make the symbolic regression more efficient, one can also use dimensionally-aware genetic programming that constrains the physical units of the equation. Nevertheless, there is no formal analysis of how much dimensionality awareness helps in the regression process. In this paper, we conduct a fitness landscape analysis of dimensionally-aware genetic programming search spaces on a subset of equations from Richard Feynman’s well-known lectures. We define an initialisation procedure and an accompanying set of neighbourhood operators for conducting the local search within the physical unit constraints. Our experiments show that the added information about the variable dimensionality can efficiently guide the search algorithm. Still, further analysis of the differences between the dimensionally-aware and standard genetic programming landscapes is needed to help in the design of efficient evolutionary operators to be used in a dimensionally-aware regression.

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previous chapter On Stochastic Fitness Landscapes: Local Optimality and Fitness Landscape Analysis for Stochastic Search Operators

next chapter Global Landscape Structure and the Random MAX-SAT Phase Transition

We have experimented with a range of more open-ended bloat-control mechanism, e.g., lexicographic optimisation for fitness and size. However, we observed that even in our rather discrete setting, optimising I.8.14 or I.27.6 would result in trees of a size of over 256 nodes.

Evolutionary computation framework (2019). http://ecf.zemris.fer.hr/

Daolio, F., Verel, S., Ochoa, G., Tomassini, M.: Local optima networks and the performance of iterated local search. In: Genetic and Evolutionary Computation Conference (GECCO), pp. 369–376. ACM (2012)

Feynman, R.P., Leighton, R.B., Sands, M.: The Feynman Lectures on Physics, New millennium edn. Basic Books, New York (2010). https://cds.cern.ch/record/1494701. Originally published 1963–1965

Fitzsimmons, J., Moscato, P.: Symbolic regression modelling of drug responses. In: First IEEE Conference on Artificial Intelligence for Industries (2018)

Frade, M., de Vega, F.F., Cotta, C.: Breeding terrains with genetic terrain programming: the evolution of terrain generators. Comput. Games Technol. 2009, 125714:1–125714:13 (2009)

Graham, M.J., Djorgovski, S.G., Mahabal, A., Donalek, C., Drake, A., Longo, G.: Data challenges of time domain astronomy. Distrib. Parallel Databases 30(5), 371–384 (2012)CrossRef

Graham, M., Djorgovski, S., Mahabal, A., Donalek, C., Drake, A.: Machine-assisted discovery of relationships in astronomy. Mon. Not. R. Astron. Soc. 431(3), 2371–2384 (2013)CrossRef

Keijzer, M.: Improving symbolic regression with interval arithmetic and linear scaling. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 70–82. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36599-0_7CrossRef

Keijzer, M., Babovic, V.: Dimensionally aware genetic programming. In: 1st Annual Conference on Genetic and Evolutionary Computation (GECCO), vol. 2, pp. 1069–1076. Morgan Kaufmann Publishers Inc. (1999)

10.

Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)MATH

11.

McConaghy, T.: FFX: fast, scalable, deterministic symbolic regression technology. In: Riolo, R., Vladislavleva, E., Moore, J. (eds.) Genetic Programming Theory and Practice IX. GEVO, pp. 235–260. Springer, New York (2011). https://doi.org/10.1007/978-1-4614-1770-5_13CrossRef

12.

Moscato, P.: An introduction to population approaches for optimization and hierarchical objective functions: a discussion on the role of tabu search. Ann. Oper. Res. 41(2), 85–121 (1993)CrossRef

13.

Moscato, P., Fontanari, J.: Stochastic versus deterministic update in simulated annealing. Phys. Lett. A 146(4), 204–208 (1990)CrossRef

14.

Ochoa, G., Tomassini, M., Vérel, S., Darabos, C.: A study of NK landscapes’ basins and local optima networks. In: Genetic and Evolutionary Computation Conference (GECCO), pp. 555–562. ACM (2008)

15.

Richter, H., Engelbrecht, A.: Recent Advances in the Theory and Application of Fitness Landscapes. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-41888-4CrossRef

16.

Schmidt, M., Lipson, H.: Distilling free-form natural laws from experimental data. Science 324(5923), 81–85 (2009)CrossRef

17.

Udrescu, S.M., Tegmark, M.: Ai Feynman: a physics-inspired method for symbolic regression (2019)

18.

Udrescu, S.M., Tegmark, M.: The Feynman database for symbolic regression (2020). https://space.mit.edu/home/tegmark/aifeynman.html. Accessed 31 Jan 2020

19.

Verel, S., Daolio, F., Ochoa, G., Tomassini, M.: Sampling local optima networks of large combinatorial search spaces: the QAP case. In: Auger, A., Fonseca, C.M., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds.) PPSN 2018. LNCS, vol. 11102, pp. 257–268. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99259-4_21CrossRef

20.

Vladislavleva, E., Friedrich, T., Neumann, F., Wagner, M.: Predicting the energy output of wind farms based on weather data: important variables and their correlation. Renew. Energy 50, 236–243 (2013)CrossRef

21.

Worm, T., Chiu, K.: Prioritized grammar enumeration: symbolic regression by dynamic programming, pp. 1021–1028, July 2013. https://doi.org/10.1145/2463372.2463486

22.

Yafrani, M.E., et al.: A fitness landscape analysis of the travelling thief problem. In: Genetic and Evolutionary Computation Conference (GECCO), pp. 277–284 (2018)

Title: Fitness Landscape Analysis of Dimensionally-Aware Genetic Programming Featuring Feynman Equations
Authors: Marko Durasevic
Domagoj Jakobovic
Marcella Scoczynski Ribeiro Martins
Stjepan Picek
Markus Wagner
Publisher: Springer International Publishing
Book: Parallel Problem Solving from Nature – PPSN XVI
Print ISBN: 978-3-030-58114-5

Electronic ISBN: 978-3-030-58115-2

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-58115-2_8

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