Soft Computing

, Volume 16, Issue 3, pp 527–561 | Cite as

Metaheuristic optimization frameworks: a survey and benchmarking

  • José Antonio Parejo
  • Antonio Ruiz-Cortés
  • Sebastián Lozano
  • Pablo Fernandez
Original Paper

Abstract

This paper performs an unprecedented comparative study of Metaheuristic optimization frameworks. As criteria for comparison a set of 271 features grouped in 30 characteristics and 6 areas has been selected. These features include the different metaheuristic techniques covered, mechanisms for solution encoding, constraint handling, neighborhood specification, hybridization, parallel and distributed computation, software engineering best practices, documentation and user interface, etc. A metric has been defined for each feature so that the scores obtained by a framework are averaged within each group of features, leading to a final average score for each framework. Out of 33 frameworks ten have been selected from the literature using well-defined filtering criteria, and the results of the comparison are analyzed with the aim of identifying improvement areas and gaps in specific frameworks and the whole set. Generally speaking, a significant lack of support has been found for hyper-heuristics, and parallel and distributed computing capabilities. It is also desirable to have a wider implementation of some Software Engineering best practices. Finally, a wider support for some metaheuristics and hybridization capabilities is needed.

Keywords

Graphical User Interface Mutation Operator Crossover Operator Variable Neighborhood Search Artificial Immune System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

We would like to thank Stefan Wagner, Andreas Schaerf, Sebastián Ventura, Sean Luke, Marcel Kronfeld and David L. Woodruff for their helpful comments in earlier versions of this article. We are thankful to David Benavides and Sergio Segura for providing us their inspirational work Benavides et al. (2009), and Ana Galan for her linguistic support. This work has been partially funded by the European Commission (FEDER) and Spanish Government under CICYT project SETI (TIN2009-07366) and the Andalusian Government projects ISABEL (TIC-2533) and THEOS (TIC-5906).

References

  1. Aarts E, Lenstra J (1997) Local search in combinatorial optimization. WileyGoogle Scholar
  2. Ackley DH (1987) A connectionist machine for genetic hillclimbing. Kluwer Academic Publishers, Norwell, MA, USACrossRefGoogle Scholar
  3. Alba E, Luque G, García-Nieto J, Ordonez G, Leguizamon G (2007) Mallba: a software library to design efficient optimisation algorithms. Int J Innov Comput Appl 1:74–85. doi: 10.1504/IJICA.2007.013403, http://portal.acm.org/citation.cfm?id=1359342.1359349 Google Scholar
  4. Andresen B, Gordon JM (1994) Constant thermodynamic speed for minimizing entropy production in thermodynamic processes and simulated annealing. Phys Rev E 50(6):4346–4351. doi: 10.1103/PhysRevE.50.4346 CrossRefGoogle Scholar
  5. Angeline PJ, Fogel DB, Fogel LJ (1996) A comparison of self-adaptation methods for finite state machines in a dynamic environment. In: Proc. 5th Ann. Conf. on Evolutionary Programming, pp 441–450Google Scholar
  6. Arabas J, Michalewicz Z, Mulawka J (1994) Gavaps-a genetic algorithm with varying population size. Evolutionary Computation. In: Proceedings of the First IEEE Conference on Computational Intelligence, vol 1, pp 73–78. doi: 10.1109/ICEC.1994.350039
  7. Back T, Fogel DB, Michalewicz Z (eds) (1997) Handbook of evolutionary computation. IOP Publishing Ltd., Bristol. http://portal.acm.org/citation.cfm?id=548530
  8. Baker J (1987) Reducing bias and inefficiency in the selection algorithm. In: Proceedings of the Second International Conference on Genetic Algorithms, pp 14–21Google Scholar
  9. Benavides D, Segura S, Ruiz-Cortès A (2009) Automated analysis of feature models after 20 years: a literature review. (Information Systems Accepted for publication)Google Scholar
  10. Birgmeier M (1996) Evolutionary programming for the optimization of trellis-coded modulation schemes. In: Proc. 5th Ann. Conf. on Evolutionary ProgrammingGoogle Scholar
  11. Blanton JL Jr., Wainwright RL (1993) Multiple vehicle routing with time and capacity constraints using genetic algorithms. In: Proceedings of the 5th International Conference on Genetic Algorithms, Morgan Kaufmann Publishers Inc., San Francisco, pp 452–459Google Scholar
  12. Brindle A (1981) Genetic algorithms for function optimization. Ph.D. thesis, University of Alberta, EdmontonGoogle Scholar
  13. Brown AW, Wallnau KC (1996) A framework for evaluating software technology. IEEE Softw 13(5):39–49. doi: 10.1109/52.536457 Google Scholar
  14. Brownlee J (2007) Oat: the optimization algorithm toolkit. Tech. rep., Complex Intelligent Systems Laboratory, Swinburne University of TechnologyGoogle Scholar
  15. Cahon S, Melab N, Talbi EG (2004) Paradiseo: a framework for the reusable design of parallel and distributed metaheuristics. J Heuristics 10(3):357–380. doi: 10.1023/B:HEUR.0000026900.92269.ec Google Scholar
  16. Chakhlevitch K, Cowling P (2008) Hyperheuristics: recent developments. In: Adaptive and multilevel metaheuristics, pp 3–29Google Scholar
  17. Chatterjee A, Siarry P (2006) Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization. Comput Oper Res 33(3):859–871. doi: 10.1016/j.cor.2004.08.012, http://www.sciencedirect.com/science/article/B6VC5-4DBJG28-2/2/57210fee165fec156db017ff5e59aa5f
  18. Clerc M (2006) Particle swarm optimization. ISTE Publishing CompanyGoogle Scholar
  19. Corne D, Knowles JD, Oates MJ (2000) The pareto envelope-based selection algorithm for multi-objective optimisation. In: Proceedings of the 6th International Conference on Parallel Problem Solving from Nature (PPSN VI), Springer, London, pp 839–848Google Scholar
  20. Cowling PI, Kendall G, Soubeiga E (2002) Hyperheuristics: a tool for rapid prototyping in scheduling and optimisation. In: Proceedings of the Applications of Evolutionary Computing on EvoWorkshops 2002, Springer, London, pp 1–10Google Scholar
  21. Cramer NL (1985) A representation for the adaptive generation of simple sequential programs. In: Proceedings of the 1st International Conference on Genetic Algorithms, L. Erlbaum Associates Inc., Hillsdale, pp 183–187Google Scholar
  22. Davis L (1985) Applying adaptive algorithms to epistatic domains. In: Proceedings of the 9th international joint conference on Artificial intelligence (IJCAI’85). Morgan Kaufmann Publishers Inc., San Francisco, pp 162–164Google Scholar
  23. Davis L (1989) Adapting operator probabilities in genetic algorithms. In: Proceedings of the third international conference on Genetic algorithms. Morgan Kaufmann Publishers Inc., San Francisco pp 61–69Google Scholar
  24. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans Evol Comput 6:182–197CrossRefGoogle Scholar
  25. de Castro L, Von Zuben F (2002) Learning and optimization using the clonal selection principle. IEEE Trans Evol Comput 6(3):239–251Google Scholar
  26. Di Gaspero L, Schaerf A (2003) Easylocal++: An object-oriented framework for flexible design of local search algorithms. Softw Pract Exp 33(8):733–765. doi: 10.1002/spe.524 CrossRefGoogle Scholar
  27. Dorigo M, Gambardella L (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evol Comput 1(1):53–66. doi: 10.1109/4235.585892 CrossRefGoogle Scholar
  28. Dreo, Pétrowski A, Siarry P, Taillard E (2005) Metaheuristics for hard optimization: methods and case studies. SpringerGoogle Scholar
  29. Eiben AE, Raué PE, Ruttkay Z (1994) Genetic algorithms with multi-parent recombination. In: Proceedings of the International Conference on Evolutionary Computation. The Third Conference on Parallel Problem Solving from Nature (PPSN III), Springer, London, pp 78–87Google Scholar
  30. Eshelman LJ (1991) The chc adaptive search algorithm: how to have safe search when engaging in nontraditional genetic recombination. Foundations of Genetic Algorithms pp 265–283. http://ci.nii.ac.jp/naid/10000024547/en/
  31. Eshelman LJ, Schaffer JD (1993) Real-coded genetic algorithms and interval-schemata. In: Whitley DL (ed) Foundation of Genetic Algorithms 2, Morgan Kaufmann., San Mateo, pp 187–202Google Scholar
  32. Eshelman LJ, Caruana RA, Schaffer JD (1989) Biases in the crossover landscape. In: Proceedings of the third international conference on Genetic algorithms, Morgan Kaufmann Publishers Inc., San Francisco, pp 10–19Google Scholar
  33. Feo T, Resende M (1989) A probabilistic heuristic for a computationally difficult set covering problem. Oper Res Lett 8:67–71MathSciNetMATHCrossRefGoogle Scholar
  34. Feo TA, Resende MG (1995) Greedy randomized adaptive search procedures. J Glob Optim 6:109–133MathSciNetMATHCrossRefGoogle Scholar
  35. Fogarty TC (1989) Varying the probability of mutation in the genetic algorithm. In: Proceedings of the 3rd International Conference on Genetic Algorithms, Morgan Kaufmann Publishers Inc., San Francisco, pp 104–109Google Scholar
  36. Fogel D, Fogel L, Atmar J (1991) Meta-evolutionary programming, vol 1. In: Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems and Computers, 1991. pp 540–545. doi: 10.1109/ACSSC.1991.186507
  37. Fogel LJ (1964) On the organization of intellect. Ph.D. thesis, UCLAGoogle Scholar
  38. Fogel LJ, Fogel DB (1986) Artificial intelligence through evolutionary programming. Tech. rep., Final Report for US Army Research Institute, contract no PO-9-X56-1102C-1Google Scholar
  39. Fogel LJ, Owens AJ, Walsh MJ (1966) Artificial intelligence through simulated evolution. WileyGoogle Scholar
  40. Fonseca CM, Fleming PJ (1993) Genetic algorithms for multiobjective optimization: Formulationdiscussion and generalization. In: Proceedings of the 5th International Conference on Genetic Algorithms, Morgan Kaufmann Publishers Inc., San Francisco, pp 416–423Google Scholar
  41. Fontoura M, Lucena C, Andreatta A, Carvalho S, Ribeiro C (2001) Using uml-f to enhance framework development: a case study in the local search heuristics domain. J Syst Softw 57(3):201–206Google Scholar
  42. Fowler M (2004) Inversion of control containers and the dependency injection pattern. http://www.martinfowler.com/articles/injection.html
  43. Gagnè C, Parizeau M (2006) Genericity in evolutionary computation software tools: principles and case-study. Int J Artif Intell Tools 15(2):173–194CrossRefGoogle Scholar
  44. Gamma E, Helm R, Johnson R, Vlissides J (1994) Design patterns: elements of reusable object-oriented software, illustrated edition. Addison-Wesley ProfessionalGoogle Scholar
  45. García-Nieto J, Alba E, Chicano F (2007) Using metaheuristic algorithms remotely via ros. In: Proceedings of the 9th annual conference on Genetic and evolutionary computation (GECCO ’07), ACM, New York, pp 1510–1510. doi:  10.1145/1276958.1277239
  46. Geman S, Geman D (1987) Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. Readings in computer vision: issues, problems, principles, and paradigms, pp 564–584Google Scholar
  47. Glover F (1977) Heuristics for integer programming using surrogate constraints. Decis Sci 8(1):156–166. doi: 10.1111/j.1540-5915.1977.tb01074.x Google Scholar
  48. Glover F (1989) Tabu search—part i. ORSA J Comput 1:190–206MathSciNetMATHGoogle Scholar
  49. Glover F, Kochenberger GA (2002) Handbook of metaheuristic. Kluwer Academic PublishersGoogle Scholar
  50. Goldberg D, Lingle R (1985) Alleles loci and the traveling salesman problem. In: Proc. 1st Int. Conf. on Genetic Algorithms and their Applications, pp 154–159Google Scholar
  51. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley.Google Scholar
  52. Goldberg DE (1990) A note on boltzmann tournament selection for genetic algorithms and population-oriented simulated annealing. Complex Syst 4(4):445–460MATHGoogle Scholar
  53. Goldberg DE, Smith RE (1987) Nonstationary function optimization using genetic algorithm with dominance and diploidy. In: Proceedings of the Second International Conference on Genetic Algorithms on Genetic algorithms and their application, L. Erlbaum Associates Inc., Hillsdale, pp 59–68Google Scholar
  54. Hansen P, Mladenović N, Perez-Britos D (2001) Variable neighborhood decomposition search. J Heuristics 7(4):335–350. doi: 10.1023/A:1011336210885 Google Scholar
  55. Ho YC, Pepyne DL (2002) Simple explanation of the no-free-lunch theorem and its implications. J Optim Theory Appl 115(3):549–570. http://www.ingentaconnect.com/content/klu/jota/2002/00000115/00000003/00450394
  56. Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. University of Michigan PressGoogle Scholar
  57. Holland JH (1992) Adaptation in natural and artificial systems. MIT Press, CambridgeGoogle Scholar
  58. Horn J, Nafpliotis N, Goldberg D (1994) A niched pareto genetic algorithm for multiobjective optimization. In: Proceedings of the First IEEE Conference on Evolutionary Computation, 1994, vol 1, pp 82–87. doi: 10.1109/ICEC.1994.350037
  59. Iredi S, Merkle D, Middendorf M (2001) Bi-criterion optimization with multi colony ant algorithms. In: Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization (EMO ’01), Springer, London, pp 359–372Google Scholar
  60. Jong KAD (1975) An analysis of the behavior of a class of genetic adaptive systems. Ph.D. thesis, University of MichiganGoogle Scholar
  61. Kennedy J, Eberhart R (1995) Particle swarm optimization, vol 4. In: Proceedings., IEEE International Conference on Neural Networks, 1995. pp 1942–1948. doi: 10.1109/ICNN.1995.488968.
  62. Kennedy J, Mendes R (2002) Population structure and particle swarm performance. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC)Google Scholar
  63. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680. http://www.jstor.org/stable/1690046 Google Scholar
  64. Kitchenham BA (2004) Procedures for undertaking systematic reviews. Tech. rep., Computer Science Department, Keele UniversityGoogle Scholar
  65. Knowles JD, Corne DW (2000) Approximating the nondominated front using the pareto archived evolution strategy. Evol Comput 8(2):149–172. doi: 10.1162/106365600568167 Google Scholar
  66. Koza JR (1992) Genetic programming: on the programming of computers by natural selection. MIT PressGoogle Scholar
  67. Kronfeld M, Planatscher H, Zell A (2010) The EvA2 optimization framework. In: Blum C, Battiti R (eds) Learning and Intelligent Optimization Conference, Special Session on Software for Optimization (LION-SWOP), Springer, Venice, no. 6073 in Lecture Notes in Computer Science, LNCS, pp 247–250. http://www.ra.cs.uni-tuebingen.de/publikationen/2010/Kron10EvA2Short.pdf
  68. Luke S, Panait L, Balan G, Paus S, Skolicki Z, Popovici E, Sullivan K, Harrison J, Bassett J, Hubley R, Chircop A, Compton J, Haddon W, Donnelly S, Jamil B, O’Beirne J (2009) Ecj: A java-based evolutionary computation research system. http://cs.gmu.edu/eclab/projects/ecj/
  69. Martin Lukasiewycz FR Michael Glaβ, Helwig S (2009) Opt4j—the optimization framework for java. http://www.opt4j.org
  70. Meffert K (2006) JUnit Profi-Tips. Entwickler PressGoogle Scholar
  71. Michalewicz Z (1994) Genetic algorithms plus data structures equals evolution programs. Springer, New YorkGoogle Scholar
  72. Michalewicz Z, Fogel DB (2004) How to solve it: modern heuristics. SpringerGoogle Scholar
  73. Mladenović N (1995) A variable neighborhood search algorithm - a new metaheuristic for combinatorial optimization. Abstracts of papers published at Optimization Week, p 112Google Scholar
  74. Monmarchè N, Venturini G, Slimane M (2000) On how pachycondyla apicalis ants suggest a new search algorithm. Futur Gener Comput Syst 16(9):937–946CrossRefGoogle Scholar
  75. Montana DJ (1995) Strongly typed genetic programming. Evol Comput 3(2):199–230. doi: 10.1162/evco.1995.3.2.199 Google Scholar
  76. Montana DJ, Davis L (1989) Training feedforward neural networks using genetic algorithms. In: Proceedings of the 11th international joint conference on Artificial intelligence (IJCAI’ 89). Morgan Kaufmann Publishers Inc., San Francisco, pp 762–767Google Scholar
  77. Muhlenbein H (1991) Evolution on time and space-the parallel genetic glgorithm. Foundations of Genetic Algorithms. http://ci.nii.ac.jp/naid/10016718767/en/
  78. Nossal GJV, Lederberg J (1958) Antibody production by single cells. Nature 181(4620):1419–1420. doi: 10.1038/1811419a0 Google Scholar
  79. Nulton JD, Salamon P (1988) Statistical mechanics of combinatorial optimization. Phys Rev A 37(4):1351–1356. doi: 10.1103/PhysRevA.37.1351 MathSciNetCrossRefGoogle Scholar
  80. Oliver IM, Smith DJ, Holland JRC (1987) A study of permutation crossover operators on the traveling salesman problem. In: Proceedings of the Second International Conference on Genetic Algorithms on Genetic algorithms and their application, L. Erlbaum Associates Inc., Hillsdale, pp 224–230Google Scholar
  81. Parejo JA, Racero J, Guerrero F, Kwok T, Smith K (2003) Fom: A framework for metaheuristic optimization. Computational Science ICCS 2003 Lecture Notes in Computer Science 2660:886–895, no-indexadaGoogle Scholar
  82. Parsopoulos K, Vrahatis M (2002a) Recent approaches to global optimization problems through particle swarm optimization. Nat Comput 1(2):235–306MathSciNetMATHCrossRefGoogle Scholar
  83. Parsopoulos KE, Vrahatis MN (2002b) Particle swarm optimization method in multiobjective problems. In: Proceedings of the 2002 ACM symposium on Applied computing (SAC ’02), ACM, New York, pp 603–607. doi: 10.1145/508791.508907
  84. Price KV, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization. Natural Computing Series, Springer, Berlin. http://www.springer.com/west/home/computer/foundations?SGWID=4-156-22-32104365-0&teaserId=68063&CENTER_ID=69103
  85. Radcliffe NJ (1991) Forma analysis and random respectful recombination. In: In Foundations of Genetic Algorithms, pp 222–229Google Scholar
  86. Rahman I, Das AK, Mankar RB, Kulkarni BD (2009) Evaluation of repulsive particle swarm method for phase equilibrium and phase stability problems. Fluid Phase Equilibria. doi: 10.1016/j.fluid.2009.04.014
  87. Raidl GR (2006) Hybrid metaheuristics. Springer, chap a unified view on hybrid metaheuristics, pp 1–12Google Scholar
  88. Rechenberg I (1965) Cybernetic solution path of an experimental problem. Royal Aircraft Establishment Library Translation 1122, FarnboroughGoogle Scholar
  89. Renders JM, Bersini H (1994) Hybridizing genetic algorithms with hill-climbing methods for global optimization: two possible ways. In: Proceedings of the First IEEE Conference on Computational Intelligence, vol 1, pp 312–317. doi: 10.1109/ICEC.1994.349948
  90. Roli A, Blum C (2008) Hybrid metaheuristics: an introduction. In: Hybrid metaheuristics, SpringerGoogle Scholar
  91. Rothlauf F (2006) Representations for genetic and evolutionary algorithms, 2nd edn. SpringerGoogle Scholar
  92. Sasaki D (2005) Armoga: an efficient multi-objective genetic algorithm. Tech. rep.Google Scholar
  93. Schaffer JD, Morishima A (1987) An adaptive crossover distribution mechanism for genetic algorithms. In: Proceedings of the Second International Conference on Genetic Algorithms on Genetic algorithms and their application, L. Erlbaum Associates Inc., Hillsdale, pp 36–40Google Scholar
  94. Schwefel HP (1981) Numerical optimization of computer models. Wiley, New YorkMATHGoogle Scholar
  95. Sloane NJA, Hardin RH (1991–2003) Gosset: a general-purpose program for designing experiments. http://www.research.att.com/njas/gosset/index.html
  96. de Souza MC, Martins P (2008) Skewed vns enclosing second order algorithm for the degree constrained minimum spanning tree problem. Eur J Oper Res 191(3):677–690. doi: 10.1016/j.ejor.2006.12.061, http://www.sciencedirect.com/science/article/B6VCT-4N2KTC4-7/2/7799160d76fbba32ad42f719ee72bbf9 Google Scholar
  97. Stutzle T, Hoos H (1997) Max–min ant system and local search for the traveling salesman problem. In: EEE International Conference on Evolutionary Computation, 1997, pp 309–314. doi: 10.1109/ICEC.1997.592327.
  98. Suganthan PN (1999) Particle swarm optimiser with neighbourhood operator. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC), pp 1958–1962Google Scholar
  99. Suresh R, Mohanasundaram K (2004) Pareto archived simulated annealing for permutation flow shop scheduling with multiple objectives, vol 2. In: IEEE Conference on Cybernetics and Intelligent Systems, 2004, pp 712–717. doi: 10.1109/ICCIS.2004.1460675
  100. Syswerda G (1991) Foundations of genetic algorithms. Morgan Kaufmann, chap a study of reproduction in generational and steady-state genetic algorithmsGoogle Scholar
  101. Talbi EG (2002) A taxonomy of hybrid metaheuristics. J Heuristics 8(5):541–564CrossRefGoogle Scholar
  102. Ulungu E, Teghem J, Fortemps P, Tuyttens D (1999) Mosa method: a tool for solving multiobjective combinatorial optimization problems. J Multi Criter Decis Anal 8(4):221–236MATHCrossRefGoogle Scholar
  103. Van Veldhuizen DA, Lamont GB (2000) Multiobjective optimization with messy genetic algorithms. In: Proceedings of the 2000 ACM symposium on Applied computing (SAC ’00), ACM, New York, pp 470–476. doi: 10.1145/335603.335914
  104. Ventura S, Romero C, Zafra A, Delgado J, Hervás C (2008) Jclec: a java framework for evolutionary computation. Soft computing—a fusion of foundations, methodologies and applications 12(4):381–392.  10.1007/s00500-007-0172-0
  105. Vesterstrm JS, Riget J (2002) Particle swarms: extensions for improved local, multi-modal, and dynamic search in numerical optimization. Ph.D. thesis, Dept. of Computer Science, University of AarhusGoogle Scholar
  106. Voß S (2001) Meta-heuristics: the state of the art. pp 1–23Google Scholar
  107. Voß S (2002) Optimization software class libraries. Kluwer Academic PublishersGoogle Scholar
  108. Wagner S (2009) Heuristic optimization software systemsm odeling of heuristic optimization algorithms in the heuristic lab software environment. Ph.D. thesis, Johannes Kepler University, LinzGoogle Scholar
  109. Whitley D (1989) The genitor algorithim and selection pressure: Why rank-based allocation of reproductive trials is best. In: Proceedings of the Third International Conference on Genetic Algorithms, pp 116–121Google Scholar
  110. Whitley D, Rana S, Heckendorn RB (1999) The island model genetic algorithm: on separability, population size and convergence. CIT J Comput Inf Technol 7(1):33–47Google Scholar
  111. Wilke DN, Kok S, Groenwold AA (2007) Comparison of linear and classical velocity update rules in particle swarm optimization: notes on diversity. International. Int J Numer Methods Eng 70(8):962–984MathSciNetMATHCrossRefGoogle Scholar
  112. Wilson GC, Mc Intyre A, Heywood MI (2004) Resource review: Three open source systems for evolving programs–lilgp, ecj and grammatical evolution. Genet Program Evolv Mach 5(1):103–105. doi: 10.1023/B:GENP.0000017053.10351.dc
  113. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82. doi: 10.1109/4235.585893. Google Scholar
  114. Wright AH (1994) Genetic algorithms for real parameter optimization. In: Foundations of genetic algorithms, Morgan Kaufmann, pp 205–218Google Scholar
  115. Yao X, Liu Y (1996) Fast evolutionary programming. In: Proc. 5th Ann. Conf. on Evolutionary ProgrammingGoogle Scholar
  116. Zhou H, Grefenstette JJ (1986) Induction of finite automata by genetic algorithms. In: Proceedings of the 1986 IEEE International Conference on Systems, Man, and Cybernetics, pp 170–174Google Scholar
  117. Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans Evol Computation 3(4):257–271CrossRefGoogle Scholar
  118. Zitzler E, Laumanns M, Thiele L (2001) Spea2: Improving the strength pareto evolutionary algorithm. Tech. rep., Computer Engineering and Networks Laboratory (TIK). Department of Electrical Engineering. Swiss Federal Institute of Technology (ETH)Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • José Antonio Parejo
    • 1
  • Antonio Ruiz-Cortés
    • 1
  • Sebastián Lozano
    • 1
  • Pablo Fernandez
    • 1
  1. 1.University of SevillaSevilleSpain

Personalised recommendations