The influence of population size in geometric semantic GP

Abstract In this work, we study the influence of the population size on the learning ability of Geometric Semantic Genetic Programming for the task of symbolic regression. A large set of experiments, considering different population size values on different regression problems, has been performed. Results show that, on real-life problems, having small populations results in a better training fitness with respect to the use of large populations after the same number of fitness evaluations. However, performance on the test instances varies among the different problems: in datasets with a high number of features, models obtained with large populations present a better performance on unseen data, while in datasets characterized by a relative small number of variables a better generalization ability is achieved by using small population size values. When synthetic problems are taken into account, large population size values represent the best option for achieving good quality solutions on both training and test instances.

[1]  I-Cheng Yeh.  Simulation of concrete slump using neural networks , 2009 .

[2]  Leonardo Vanneschi,et al.  Genetic programming needs better benchmarks , 2012, GECCO '12.

[3]  Riccardo Poli.  Recursive Conditional Schema Theorem, Convergence and Population Sizing in Genetic Algorithms , 2000, FOGA.

[4]  Thomas F. Brooks,et al.  Airfoil self-noise and prediction , 1989 .

[5]  John J. Grefenstette,et al.  Optimization of Control Parameters for Genetic Algorithms , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  Leonardo Vanneschi,et al.  Geometric Semantic Genetic Programming for Real Life Applications , 2013, GPTP.

[7]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[8]  Lawrence Davis,et al.  Adapting Operator Probabilities in Genetic Algorithms , 1989, ICGA.

[9]  Leonardo Vanneschi,et al.  Genetic programming for human oral bioavailability of drugs , 2006, GECCO.

[10]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[11]  Leonardo Vanneschi,et al.  Prediction of high performance concrete strength using Genetic Programming with geometric semantic genetic operators , 2013, Expert Syst. Appl..

[12]  Robert E. Smith,et al.  Adaptively Resizing Populations: Algorithm, Analysis, and First Results , 1993, Complex Syst..

[13]  Anabela Simões,et al.  The Influence of Population and Memory Sizes on the Evolutionary Algorithm's Performance for Dynamic Environments , 2009, EvoWorkshops.

[14]  Graham Kendall,et al.  Advanced Population Diversity Measures in Genetic Programming , 2002, PPSN.

[15]  Riccardo Poli,et al.  The impact of population size on code growth in GP: analysis and empirical validation , 2008, GECCO '08.

[16]  Leonardo Vanneschi,et al.  Semantic Search-Based Genetic Programming and the Effect of Intron Deletion , 2014, IEEE Transactions on Cybernetics.

[17]  Alberto Moraglio,et al.  Runtime analysis of mutation-based geometric semantic genetic programming for basis functions regression , 2013, GECCO '13.

[18]  Robert E. Smith,et al.  Adaptively Resizing Populations: An Algorithm and Analysis , 1993, ICGA.

[19]  Zbigniew Michalewicz,et al.  GAVaPS-a genetic algorithm with varying population size , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[20]  Leonardo Vanneschi,et al.  Measuring bloat, overfitting and functional complexity in genetic programming , 2010, GECCO '10.

[21]  M. Tomassini,et al.  Saving computational effort in genetic programming by means of plagues , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[22]  Maarten Keijzer,et al.  Improving Symbolic Regression with Interval Arithmetic and Linear Scaling , 2003, EuroGP.

[23]  Jim Smith,et al.  Self adaptation of mutation rates in a steady state genetic algorithm , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[24]  Leonardo Vanneschi,et al.  Parameter evaluation of geometric semantic genetic programming in pharmacokinetics , 2016, Int. J. Bio Inspired Comput..

[25]  Leonardo Vanneschi,et al.  A New Implementation of Geometric Semantic GP and Its Application to Problems in Pharmacokinetics , 2013, EuroGP.

[26]  Leonardo Vanneschi,et al.  Parameter tuning of evolutionary reactions systems , 2012, GECCO '12.

[27]  Carlos Alberto Conceição António,et al.  Self-adaptation in Genetic Algorithms applied to structural optimization , 2008 .

[28]  Leonardo Vanneschi,et al.  A C++ framework for geometric semantic genetic programming , 2014, Genetic Programming and Evolvable Machines.

[29]  Leonardo Vanneschi,et al.  Prediction of the Unified Parkinson's Disease Rating Scale assessment using a genetic programming system with geometric semantic genetic operators , 2014, Expert Syst. Appl..

[30]  Leonardo Vanneschi,et al.  Variable size population for dynamic optimization with genetic programming , 2009, GECCO.

[31]  Vipul K. Dabhi,et al.  Improving Generalization Ability of Genetic Programming: Comparative Study , 2013, ArXiv.

[32]  Thomas Bäck,et al.  Optimal Mutation Rates in Genetic Search , 1993, ICGA.

[33]  Leonardo Vanneschi,et al.  Genetic Programming and Other Machine Learning Approaches to Predict Median Oral Lethal Dose (LD50) and Plasma Protein Binding Levels (%PPB) of Drugs , 2007, EvoBIO.

[34]  Christopher R. Stephens,et al.  Self-Adaptation in Evolving Systems , 1997, Artificial Life.

[35]  Krzysztof Krawiec,et al.  Approximating geometric crossover in semantic space , 2009, GECCO.

[36]  David E. Goldberg,et al.  Sizing Populations for Serial and Parallel Genetic Algorithms , 1989, ICGA.

[37]  Dragan Cvetkovic,et al.  The Optimal Population Size for Uniform Crossover and Truncation Selection , 1994 .

[38]  Y. R. Tsoy,et al.  The influence of population size and search time limit on genetic algorithm , 2003, 7th Korea-Russia International Symposium on Science and Technology, Proceedings KORUS 2003. (IEEE Cat. No.03EX737).

[39]  Krzysztof Krawiec,et al.  Geometric Semantic Genetic Programming , 2012, PPSN.

[40]  Dick den Hertog,et al.  Order of Nonlinearity as a Complexity Measure for Models Generated by Symbolic Regression via Pareto Genetic Programming , 2009, IEEE Transactions on Evolutionary Computation.

[41]  R. Haupt.  Optimum population size and mutation rate for a simple real genetic algorithm that optimizes array factors , 2000, IEEE Antennas and Propagation Society International Symposium. Transmitting Waves of Progress to the Next Millennium. 2000 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (C.

[42]  Julian Togelius,et al.  Geometric Differential Evolution for Combinatorial and Programs Spaces , 2013, Evolutionary Computation.

[43]  Kenneth A. De Jong,et al.  An Analysis of the Interacting Roles of Population Size and Crossover in Genetic Algorithms , 1990, PPSN.

[44]  Leonardo Vanneschi,et al.  A survey of semantic methods in genetic programming , 2014, Genetic Programming and Evolvable Machines.

[45]  Leonardo Vanneschi,et al.  A new technique for dynamic size populations in genetic programming , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[46]  Leonardo Vanneschi,et al.  Self-tuning geometric semantic Genetic Programming , 2015, Genetic Programming and Evolvable Machines.