Extended Forma: Analysis and an Operator Exploiting it

  • C. Dharmani Bhaveshkumar
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 201)


There exists a long discussion over the issue of whether minimal alphabet or maximal alphabet gives maximum schemata. The article generalizes the concept of schemata to dependency relation based ‘extended formae’. Further, it proves that theoretical maximum schemata could be achieved through an operator exploiting extended formae and using maximal alphabet. It shows that the previous conclusion of minimal alphabet giving maximum schemata is also true for some operators. It is known that maximum schemata is advantageous to achieve maximum implicit parallelism. The article raises a discussion over the requirement of availing maximum schemata by showing some disadvantages also. As a conclusion, it suggests to use an intermediate level alphabet for representation, balancing maximal alphabet to avail maximum schemata and minimal alphabet to overcome the disadvantages due to maximum schemata.


Genetic algorithm (GA) Schema Schemata Forma Formae Implicit parallelism dependency relation Extended forma Extended formae P-schemata  Diploidy 


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  1. Antonisse., J.: A new interpretation of schema notation that overturns the binary coding constraint. In: Proceedings of the Third International Conference on Genetic Algorithms. pp. 86-91. Morgan Kaufmann (San Mateo) (1989).Google Scholar
  2. Eiben, A., Raué, P., Ruttkay, Z.: Genetic algorithms with multi-parent recombination. Parallel Problem Solving from NaturePPSN III pp. 78-87 (1994).Google Scholar
  3. Eshelman, L.: Real-coded genetic algorithms and interval-schemata. Foundations of genetic algorithms 2, 187-202 (1993).Google Scholar
  4. Goldberg, D.E.: Zen and the art of genetic algorithms. In: Proceedings of the third international conference on Genetic algorithms. pp. 80-85. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1989).Google Scholar
  5. Goldberg, D.: Genetic algorithms in search, optimization, and machine learning. Addison-wesley (1989).Google Scholar
  6. Goldberg, D.: Real-coded genetic algorithms, virtual alphabets, and blocking. Complex Systems 5, 139-167 (1991).Google Scholar
  7. Holland, J.: Adaptation in natural and artificial systems. No. 53, University of Michigan press (1975).Google Scholar
  8. Radcliffe, N.: Equivalence class analysis of genetic algorithms. Complex Systems 5(2), 183-205 (1991).Google Scholar
  9. Radcliffe, N.: Forma analysis and random respectful recombination. In: Proceedings of the fourth international conference on genetic algorithms. pp. 222-229. San Marco CA: Morgan Kaufmann (1991).Google Scholar
  10. Smith, R.E., Goldberg, D.E.: Diploidy and dominance in artificial genetic search. Complex Systems 6(3), 251-285 (1992).Google Scholar
  11. Vose, M.D.: Generalizing the notion of schema in genetic algorithms. Artif. Intell. 50(3), 385-396 (Aug 1991).Google Scholar
  12. Wright, A.: Genetic algorithms for real parameter optimization. Foundations of genetic algorithms 1, 205-218 (1991).Google Scholar

Copyright information

© Springer India 2013

Authors and Affiliations

  1. 1.Institute of Information and Communication Technology (DAIICT)GandhinagarIndia

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