Top

Soft Computing

Published in:

01-08-2011 | Original Paper

Use of the q-Gaussian mutation in evolutionary algorithms

Authors: Renato Tinós, Shengxiang Yang

Published in: Soft Computing | Issue 8/2011

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This paper proposes the use of the q-Gaussian mutation with self-adaptation of the shape of the mutation distribution in evolutionary algorithms. The shape of the q-Gaussian mutation distribution is controlled by a real parameter q. In the proposed method, the real parameter q of the q-Gaussian mutation is encoded in the chromosome of individuals and hence is allowed to evolve during the evolutionary process. In order to test the new mutation operator, evolution strategy and evolutionary programming algorithms with self-adapted q-Gaussian mutation generated from anisotropic and isotropic distributions are presented. The theoretical analysis of the q-Gaussian mutation is also provided. In the experimental study, the q-Gaussian mutation is compared to Gaussian and Cauchy mutations in the optimization of a set of test functions. Experimental results show the efficiency of the proposed method of self-adapting the mutation distribution in evolutionary algorithms.

previous article Numerical solution of fully fuzzy linear systems by fuzzy neural network

next article Genetic programming with one-point crossover and subtree mutation for effective problem solving and bloat control

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Tables with the results and other relevant information about the Real Parameter Optimization Competition of the 2005 IEEE Congress on Evolutionary Computation can be found at http://sci2s.ugr.es/EAMHCO/.

Auger A, Hansen N (2005a) A restart CMA evolution strategy with increasing population size. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 1769–1776

Auger A, Hansen N (2005b) Performance evaluation of an advanced local search evolutionary algorithm. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 1777–1784

Bäck T (2000) Self-adaptation. In: Bäck T, Fogel DB, Michalewicz Z (eds) Evolutionary computation 2: advanced algorithms and operators. Institute of Physics Publishing, Bristol

Ballester PJ, Stephenson J, Carter JN, Gallagher K (2005) Real-parameter optimization performance study on the CEC-2005 benchmark with SPC-PNX. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 498–505

Beyer H-G, Schwefel HS (2002) Evolution strategies: a comprehensive introduction. Nat Comput 1(1):3–52MATHCrossRefMathSciNet

Das S, Abraham A, Chakraborty UK, Konar A (2009) Differential evolution using a neighborhood-based mutation operator. IEEE Trans Evol Comput 13(3):526–553CrossRef

Davis MW (1994) The natural formation of gaussian mutation strategies in evolutionary programming. In: Proceedings of the 3rd annual Conf. on evolutionary programming. World Scientific, Singapore

Dong H, He J, Huang H, Hou W (2007) Evolutionary programming using a mixed mutation strategy. Inform Sci177(1):312–327MATHCrossRefMathSciNet

Eiben AE, Hinterding R, Michalewicz Z (1999) Parameter control in evolutionary algorithms. IEEE Trans Evol Comput 3(2):124–141CrossRef

García-Martínez C, Lozano M (2005) Hybrid real-coded genetic algorithms with female and male differentiation. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 896–903

García-Martínez C, Lozano M, Herrera F, Molina D, Sánchez AM (2008) Global and local real-coded genetic algorithms based on parent-centric crossover operators. Eur J Oper Res 185(3):1088–1113MATHCrossRef

García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 Special Session on Real Parameter Optimization. J Heuristics 15:617–644MATHCrossRef

Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evol Comput 9(2):159–195CrossRef

Hansen N, Gemperle F, Auger A, Koumoutsakos P (2006) When do heavy-tail distributions help? In: Proceedings 9th Int. Conf. on parallel problem solving from nature. Lecture Notes in Computer Science, vol 4193, pp 62–71

Hansen N (2008) Adaptive encoding: how to render search coordinate system invariant. In: Proceedings of 10th Int. Conf. on on parallel problem solving from nature. Lecture Notes in Computer Science, vol 5199, pp 205–214

Herrera F, Lozano M, Verdegay JL (1998) Tackling real-coded genetic algorithms: operators and tools for the behavioral analysis. Artif Intell Rev 12(4):265–319MATHCrossRef

Iwamatsu M (2002) Generalized evolutionary programming with levy-type mutation. Comput Phys Commun 147(1–2):729–732MATHCrossRef

Lee CY, Yao X (2004) Evolutionary programming using mutations based on the levy probability distribution. IEEE Trans Evol Comput 8(1):1–13CrossRef

Liang JJ, Suganthan PN (2005) Dynamic multi-swarm particle swarm optimizer with local search. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 522–528

Lozano M, Herrera F, Krasnogor N, Molina D (2004) Real-coded memetic algorithms with crossover hill-climbing. Evol Comput 12(3):273–302CrossRef

Molina D, Herrera F, Lozano M (2005) Adaptive local search parameters for real-coded memetic algorithms. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 888–895

Mezura-Montes E, Coello CAC (2004) An improved diversity mechanism for solving constrained optimization problems using a multimembered evolution strategy. In: Proceedings of the 2004 Genetic and Evol. Comput. Conf. (GECCO-2004), pp 700–712

Moret MA, Pascutti PG, Bisch PM, Mundim MSP, Mundim KC (2006) Classical and quantum conformational analysis using generalized genetic algorithm. Phys A Stat Mech Appl 363(2):260–268CrossRef

Nguyen QH, Ong YS, Lim MH (2009) A probabilistic memetic framework. IEEE Trans Evol Comput 13(3):604–623CrossRef

Noman N, Iba H (2008) Accelerating differential evolution using an adaptive local search. IEEE Trans Evol Comput 12(1):107–125CrossRef

Obuchowicz A (2003) Multidimensional mutations in evolutionary algorithms based on real-valued representation. Int J Syst Sci 34(7):469–483MATHCrossRefMathSciNet

Price KV, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization. Springer, Berlin

Pošík P (2005) Real-parameter optimization using the mutation step co-evolution. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 872–879

Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 1785–1791

Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):298–417CrossRef

Rathie PN, Da Silva S (2008) Shannon, Lévy, and Tsallis: a note. Appl Math Sci 2(28):1359–1363

Rönkkönen J, Kukkonen S, Price KV (2005) Real-parameter optimization with differential evolution. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 506–513

Sinha A, Tiwari S, Deb K (2005) A population-based, steady-state procedure for real-parameter optimization. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 514–521

Souza AMC, Tsallis C (1997) Student’s t- and r-distributions: unified derivation from an entropic variational principle. Phys A Stat Mech Appl 236(1–2):52–57CrossRef

Suganthan PN, Hansen N, Liang JJ, Deb K, Chen YP, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real parameter optimization. Technical Report, Nanyang Technological University

Thistleton W, Marsh JA, Nelson K, Tsallis C (2007) Generalized Box–Muller method for generating q-Gaussian random deviates. IEEE Trans Inform Theory 53(12):4805–4810CrossRefMathSciNet

Tinós R, Carvalho ACPLF (2006) Use of gene dependent mutation probability in evolutionary neural networks for non-stationary problems. Neurocomputing 70(1–3):44–54CrossRef

Tinós R, Yang S (2007) Self-organizing random immigrants genetic algorithm for dynamic optimization problems. Genetic Program Evol Mach 8(3):255–286CrossRef

Tsallis C (1988) Possible generalization of Boltzmann–Gibbs statistics. J Statist Phys 52:479–487MATHCrossRefMathSciNet

Tsallis C, Stariolo DA (1996) Generalized simulated annealing. Phys A 233(1–2):395–406CrossRef

Umarov S, Tsallis C, Steinberg S (2008) On a q-central limit theorem consistent with nonextensive statistical mechanics. Milan J Math 76(1):307–328MATHCrossRefMathSciNet

Vrugt JA, Robinson BA, Hyman JM (2009) Self-adaptive multimethod search for global optimization in real-parameter spaces. IEEE Trans Evol Comput 13(2):243–259CrossRef

Wang H, Yang S, Ip WH, Wang D (2009) Adaptive primal-dual genetic algorithms in dynamic environments. IEEE Transon Syst Man Cybern Part B Cybern 39(6):1348–1361CrossRef

Yao X, Liu Y (1997) Fast evolution strategies. Control Cybern 26(3):467–496MATHMathSciNet

Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82–102CrossRef

Yuan B, Gallagher M (2005) Experimental results for the special session on real-parameter optimization at CEC 2005: a simple, continuous EDA. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 1792–1799

Title: Use of the q-Gaussian mutation in evolutionary algorithms
Authors: Renato Tinós
Shengxiang Yang
Publication date: 01-08-2011
Publisher: Springer-Verlag
Published in: Soft Computing / Issue 8/2011
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-010-0686-8

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Other articles of this Issue 8/2011

Analysis of alternative objective functions for attribute reduction in complete decision tables

Automatic summarisation and annotation of microarray data

Clustering of protein expression data: a benchmark of statistical and neural approaches

β-Interval attribute reduction in variable precision rough set model

Graphics processing units and genetic programming: an overview

A fuzzy-rule-based driving architecture for non-player characters in a car racing game

Premium Partner