Symbolic regression by uniform random global search
This work describes a novel algorithm for symbolic regression, namely symbolic regression by uniform random global search (SRURGS). SRURGS has only one tuning parameter and is very simple conceptually. The method produces random equations, which is useful for the generation of symbolic regression be...
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| Published in | SN applied sciences Vol. 2; no. 1; p. 34 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.01.2020
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2523-3963 2523-3971 2523-3971 |
| DOI | 10.1007/s42452-019-1734-3 |
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| Abstract | This work describes a novel algorithm for symbolic regression, namely symbolic regression by uniform random global search (SRURGS). SRURGS has only one tuning parameter and is very simple conceptually. The method produces random equations, which is useful for the generation of symbolic regression benchmark problems. We have released well documented and open-source python code which passed a formal peer-review, so that interested researchers can deploy the tool in practice. We conduct experiments comparing SRURGS with symbolic regression by genetic programming (SRGP) using 100 randomly generated equations. Our results suggest that SRGP is faster than SRURGS in producing equations with good
R
2
for simple problems. However, our experiments suggest that SRURGS is more robust than SRGP, able to produce good output in more challenging problems. |
|---|---|
| AbstractList | This work describes a novel algorithm for symbolic regression, namely symbolic regression by uniform random global search (SRURGS). SRURGS has only one tuning parameter and is very simple conceptually. The method produces random equations, which is useful for the generation of symbolic regression benchmark problems. We have released well documented and open-source python code which passed a formal peer-review, so that interested researchers can deploy the tool in practice. We conduct experiments comparing SRURGS with symbolic regression by genetic programming (SRGP) using 100 randomly generated equations. Our results suggest that SRGP is faster than SRURGS in producing equations with good R2 for simple problems. However, our experiments suggest that SRURGS is more robust than SRGP, able to produce good output in more challenging problems. This work describes a novel algorithm for symbolic regression, namely symbolic regression by uniform random global search (SRURGS). SRURGS has only one tuning parameter and is very simple conceptually. The method produces random equations, which is useful for the generation of symbolic regression benchmark problems. We have released well documented and open-source python code which passed a formal peer-review, so that interested researchers can deploy the tool in practice. We conduct experiments comparing SRURGS with symbolic regression by genetic programming (SRGP) using 100 randomly generated equations. Our results suggest that SRGP is faster than SRURGS in producing equations with good R 2 for simple problems. However, our experiments suggest that SRURGS is more robust than SRGP, able to produce good output in more challenging problems. |
| ArticleNumber | 34 |
| Author | Towfighi, Sohrab |
| Author_xml | – sequence: 1 givenname: Sohrab orcidid: 0000-0002-3050-8943 surname: Towfighi fullname: Towfighi, Sohrab email: sohrab.towfighi@mail.utoronto.ca organization: Faculty of Medicine, University of Toronto |
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| Keywords | Symbolic regression Tree enumeration Evolutionary algorithm Genetic programming 62-07 Uniform random global search Pure random search 05C05 |
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| References | Ghodrat MA, Givargis T, Nicolau A (2005) Equivalence checking of arithmetic expressions using fast evaluation. In: Proceedings of the 2005 international conference on compilers, architectures and synthesis for embedded systems, ACM, New York, NY, USA, CASES’05, pp 147–156. https://doi.org/10.1145/1086297.1086317 McDermott J, White DR, Luke S, Manzoni L, Castelli M, Vanneschi L, Jaskowski W, Krawiec K, Harper R, De Jong K, O’Reilly UM (2012) Genetic programming needs better benchmarks. In: Proceedings of the 14th annual conference on genetic and evolutionary computation, ACM, New York, GECCO ’12, pp 791–798. https://doi.org/10.1145/2330163.2330273 Amaral JN, Neto ATC, Dias AV (1997) Genetic algorithms in optimization: Better than random search? In: International conference on engineering and informatics, pp 320–326 ZabinskyZBRandom search algorithmsWiley Encyclopedia of Operations Research and Management Science201110.1002/9780470400531.eorms0704 WoodwardJRNeilJRRyanCSouleTKeijzerMTsangEPoliRCostaENo free lunch, program induction and combinatorial problemsGenetic programming2003BerlinSpringer47548410.1007/3-540-36599-0_45 TowfighiSpySRURGS - a python package for symbolic regression by uniform random global searchJ Op Source Softw2019441167510.21105/joss.01675 de FrançaFOA greedy search tree heuristic for symbolic regressionInform Sci2018442–4431832377180310.1016/j.ins.2018.02.040 WolpertDHMacreadyWGNo free lunch theorems for optimizationIEEE Trans Evol Comput199711678210.1109/4235.585893 ZabinskyZBPure random search and pure adaptive searchStochastic adaptive search for global optimization2003Boston, MASpringer255410.1007/978-1-4419-9182-9_21044.90001 McConaghyTRioloRVladislavlevaEMooreJFFX: fast, scalable, deterministic symbolic regression technologyGenetic programming theory and practice IX2011New YorkSpringer23526010.1007/978-1-4614-1770-5_13 Fortin FA, De Rainville FM, Gardner MA, Parizeau M, Gagné C (2012) DEAP: evolutionary algorithms made easy. J Mach Learn Res 13:2171–2175. http://www.jmlr.org/papers/volume13/fortin12a/fortin12a.pdf UyNQHoaiNXO’NeillMMckayRIGalván-LópezESemantically-based crossover in genetic programming: application to real-valued symbolic regressionGenetic Program Evol Mach20111229111910.1007/s10710-010-9121-2 CozadASahinidisNVA global MINLP approach to symbolic regressionMath Program2018170197119381655910.1007/s10107-018-1289-x1402.90092 Tychonievich L (2013) Enumerating trees. https://www.cs.virginia.edu/~lat7h/blog/posts/434.html RothlaufFOetzelMColletPTomassiniMEbnerMGustafsonSEkártAOn the locality of grammatical evolutionGenetic programming2006BerlinSpringer32033010.1007/11729976_29 SolisFJWetsRJBMinimization by random search techniquesMath Oper Res198161193061896110.1287/moor.6.1.190502.90070 ShamshiriSRojasJMGazzolaLFraserGMcMinnPMarianiLArcuriARandom or evolutionary search for object-oriented test suite generation?Softw Test Verif Reliab2018284e166010.1002/stvr.1660 Galván-López E, McDermott J, O’Neill M, Brabazon A (2010) Defining locality in genetic programming to predict performance. In: IEEE congress on evolutionary computation, Barcelona, Spain, pp 1–8. https://doi.org/10.1109/CEC.2010.5586095 SipperMFuWAhujaKMooreJHInvestigating the parameter space of evolutionary algorithmsBioData Min2018111210.1186/s13040-018-0164-x StreeterMJTwo broad classes of functions for which a no free lunch result does not holdProceedings of the 2003 international conference on genetic and evolutionary computation2003BerlinSpringer1418143010.1007/3-540-45110-2_151038.68880 WormTChiuKPrioritized grammar enumeration: symbolic regression by dynamic programmingProceedings of the 15th annual conference on genetic and evolutionary computation2013New York, NY, USAACM1021102810.1145/2463372.2463486 d Melo VV, Fowler B, Banzhaf W (2015) Evaluating methods for constant optimization of symbolic regression benchmark problems. In: 2015 Brazilian conference on intelligent systems (BRACIS), pp 25–30. https://doi.org/10.1109/BRACIS.2015.55 WhiteDRMcDermottJCastelliMManzoniLGoldmanBWKronbergerGJaśkowskiWO’ReillyUMLukeSBetter GP benchmarks: community survey results and proposalsGenet Program Evolvable Mach201314132910.1007/s10710-012-9177-2 ChenSHNavetNFailure of genetic-programming induced trading strategies: distinguishing between efficient markets and inefficient algorithmsComputational intelligence in economics and finance2007BerlinSpringer16918210.1007/978-3-540-72821-4_11 Qi Y, Mao X, Lei Y, Dai Z, Wang C (2014) The strength of random search on automated program repair. In: Jalote P, Briand L, VanderHoek A (eds) 36th international conference on software engineering (ICSE 2014), Association for Computing Machinery, New York, NY, USA, pp 254–265. https://doi.org/10.1145/2568225.2568254 WolpertDHMacreadyWGCoevolutionary free lunchesIEEE Trans Evol Comput20059672173510.1109/TEVC.2005.856205 KommendaMAffenzellerMKronbergerGWinklerSMMoreno-DíazRPichlerFQuesada-ArencibiaANonlinear least squares optimization of constants in symbolic regressionComputer aided systems theory—EUROCAST 20132013BerlinSpringer42042710.1007/978-3-642-53856-8_53 Kommenda M, Kronberger G, Winkler S, Affenzeller M, Wagner S (2013b) Effects of constant optimization by nonlinear least squares minimization in symbolic regression. In: Proceedings of the 15th annual conference companion on genetic and evolutionary computation, ACM, New York, GECCO ’13 Companion, pp 1121–1128. https://doi.org/10.1145/2464576.2482691 KornsMFAccuracy in symbolic regressionGenetic programming theory and practice IX2011New YorkSpringer12915110.1007/978-1-4614-1770-5_8 BoulesteixALStierleVHapfelmeierAPublication bias in methodological computational researchCancer Inform201514(S5)111910.4137/CIN.S30747 Arnaldo I, O’Reilly UM, Veeramachaneni K (2015) Building predictive models via feature synthesis. In: Proceedings of the 2015 annual conference on genetic and evolutionary computation, ACM, New York, NY, USA, GECCO’15, pp 983–990. https://doi.org/10.1145/2739480.2754693 KozaJRGenetic programming as a means for programming computers by natural selectionStat Comput1994428711210.1007/BF00175355 MeurerASmithCPPaprockiMČertíkOKirpichevSBRocklinMKumarAIvanovSMooreJKSinghSRathnayakeTVigSGrangerBEMullerRPBonazziFGuptaHVatsSJohanssonFPedregosaFCurryMJTerrelARRoučkavSabooAFernandoIKulalSCimrmanRScopatzASymPy: symbolic computing in PythonPeerJ Comput Sci20173e10310.7717/peerj-cs.103 KozakMComparison of random search method and genetic algorithm for stratificationCommun Stat Simul Comput2014432249253320096710.1080/03610918.2012.7003641361.62007 KronbergerGKammererLBurlacuBWinklerSMKommendaMAffenzellerMBanzhafWSpectorLShenemanLCluster analysis of a symbolic regression search spaceGenetic programming theory and practice XVI2019ChamSpringer8510210.1007/978-3-030-04735-1_5 NissenSBMagidsonTGrossKBergstromCTResearch: publication bias and the canonization of false factsELife20165e2145110.7554/eLife.21451 FJ Solis (1734_CR25) 1981; 6 M Kommenda (1734_CR10) 2013 JR Woodward (1734_CR33) 2003 ZB Zabinsky (1734_CR35) 2003 M Kozak (1734_CR14) 2014; 43 1734_CR28 NQ Uy (1734_CR29) 2011; 12 S Towfighi (1734_CR27) 2019; 4 1734_CR21 1734_CR1 DH Wolpert (1734_CR32) 2005; 9 1734_CR2 1734_CR6 1734_CR7 1734_CR9 AL Boulesteix (1734_CR3) 2015; 14 A Meurer (1734_CR19) 2017; 3 M Sipper (1734_CR24) 2018; 11 1734_CR18 FO de França (1734_CR8) 2018; 442–443 JR Koza (1734_CR13) 1994; 4 1734_CR17 SB Nissen (1734_CR20) 2016; 5 1734_CR11 T Worm (1734_CR34) 2013 F Rothlauf (1734_CR22) 2006 A Cozad (1734_CR5) 2018; 170 DH Wolpert (1734_CR31) 1997; 1 SH Chen (1734_CR4) 2007 S Shamshiri (1734_CR23) 2018; 28 MJ Streeter (1734_CR26) 2003 MF Korns (1734_CR12) 2011 G Kronberger (1734_CR15) 2019 DR White (1734_CR30) 2013; 14 ZB Zabinsky (1734_CR36) 2011 T McConaghy (1734_CR16) 2011 |
| References_xml | – reference: Qi Y, Mao X, Lei Y, Dai Z, Wang C (2014) The strength of random search on automated program repair. In: Jalote P, Briand L, VanderHoek A (eds) 36th international conference on software engineering (ICSE 2014), Association for Computing Machinery, New York, NY, USA, pp 254–265. https://doi.org/10.1145/2568225.2568254 – reference: ShamshiriSRojasJMGazzolaLFraserGMcMinnPMarianiLArcuriARandom or evolutionary search for object-oriented test suite generation?Softw Test Verif Reliab2018284e166010.1002/stvr.1660 – reference: WolpertDHMacreadyWGCoevolutionary free lunchesIEEE Trans Evol Comput20059672173510.1109/TEVC.2005.856205 – reference: CozadASahinidisNVA global MINLP approach to symbolic regressionMath Program2018170197119381655910.1007/s10107-018-1289-x1402.90092 – reference: TowfighiSpySRURGS - a python package for symbolic regression by uniform random global searchJ Op Source Softw2019441167510.21105/joss.01675 – reference: Galván-López E, McDermott J, O’Neill M, Brabazon A (2010) Defining locality in genetic programming to predict performance. In: IEEE congress on evolutionary computation, Barcelona, Spain, pp 1–8. https://doi.org/10.1109/CEC.2010.5586095 – reference: ZabinskyZBRandom search algorithmsWiley Encyclopedia of Operations Research and Management Science201110.1002/9780470400531.eorms0704 – reference: KommendaMAffenzellerMKronbergerGWinklerSMMoreno-DíazRPichlerFQuesada-ArencibiaANonlinear least squares optimization of constants in symbolic regressionComputer aided systems theory—EUROCAST 20132013BerlinSpringer42042710.1007/978-3-642-53856-8_53 – reference: StreeterMJTwo broad classes of functions for which a no free lunch result does not holdProceedings of the 2003 international conference on genetic and evolutionary computation2003BerlinSpringer1418143010.1007/3-540-45110-2_151038.68880 – reference: Amaral JN, Neto ATC, Dias AV (1997) Genetic algorithms in optimization: Better than random search? In: International conference on engineering and informatics, pp 320–326 – reference: RothlaufFOetzelMColletPTomassiniMEbnerMGustafsonSEkártAOn the locality of grammatical evolutionGenetic programming2006BerlinSpringer32033010.1007/11729976_29 – reference: d Melo VV, Fowler B, Banzhaf W (2015) Evaluating methods for constant optimization of symbolic regression benchmark problems. In: 2015 Brazilian conference on intelligent systems (BRACIS), pp 25–30. https://doi.org/10.1109/BRACIS.2015.55 – reference: WormTChiuKPrioritized grammar enumeration: symbolic regression by dynamic programmingProceedings of the 15th annual conference on genetic and evolutionary computation2013New York, NY, USAACM1021102810.1145/2463372.2463486 – reference: ZabinskyZBPure random search and pure adaptive searchStochastic adaptive search for global optimization2003Boston, MASpringer255410.1007/978-1-4419-9182-9_21044.90001 – reference: MeurerASmithCPPaprockiMČertíkOKirpichevSBRocklinMKumarAIvanovSMooreJKSinghSRathnayakeTVigSGrangerBEMullerRPBonazziFGuptaHVatsSJohanssonFPedregosaFCurryMJTerrelARRoučkavSabooAFernandoIKulalSCimrmanRScopatzASymPy: symbolic computing in PythonPeerJ Comput Sci20173e10310.7717/peerj-cs.103 – reference: SipperMFuWAhujaKMooreJHInvestigating the parameter space of evolutionary algorithmsBioData Min2018111210.1186/s13040-018-0164-x – reference: Fortin FA, De Rainville FM, Gardner MA, Parizeau M, Gagné C (2012) DEAP: evolutionary algorithms made easy. J Mach Learn Res 13:2171–2175. http://www.jmlr.org/papers/volume13/fortin12a/fortin12a.pdf – reference: Kommenda M, Kronberger G, Winkler S, Affenzeller M, Wagner S (2013b) Effects of constant optimization by nonlinear least squares minimization in symbolic regression. In: Proceedings of the 15th annual conference companion on genetic and evolutionary computation, ACM, New York, GECCO ’13 Companion, pp 1121–1128. https://doi.org/10.1145/2464576.2482691 – reference: de FrançaFOA greedy search tree heuristic for symbolic regressionInform Sci2018442–4431832377180310.1016/j.ins.2018.02.040 – reference: McConaghyTRioloRVladislavlevaEMooreJFFX: fast, scalable, deterministic symbolic regression technologyGenetic programming theory and practice IX2011New YorkSpringer23526010.1007/978-1-4614-1770-5_13 – reference: UyNQHoaiNXO’NeillMMckayRIGalván-LópezESemantically-based crossover in genetic programming: application to real-valued symbolic regressionGenetic Program Evol Mach20111229111910.1007/s10710-010-9121-2 – reference: ChenSHNavetNFailure of genetic-programming induced trading strategies: distinguishing between efficient markets and inefficient algorithmsComputational intelligence in economics and finance2007BerlinSpringer16918210.1007/978-3-540-72821-4_11 – reference: Arnaldo I, O’Reilly UM, Veeramachaneni K (2015) Building predictive models via feature synthesis. 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| Title | Symbolic regression by uniform random global search |
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